Abstract group data - 559872.lw

Formats: - HTML - YAML - JSON - 2026-02-03T10:23:36.836543

• gps_groups •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  abelian_quotient	text
  all_subgroups_known	boolean
  almost_simple	boolean
  aut_abelian	boolean
  aut_cyclic	boolean
  aut_derived_length	smallint
  aut_exponent	numeric
  aut_gen_orders	numeric[]
  aut_gens	numeric[]
  aut_group	text
  aut_hash	bigint
  aut_nilpotency_class	smallint
  aut_nilpotent	boolean
  aut_order	numeric
  aut_permdeg	integer
  aut_perms	numeric[]
  aut_phi_ratio	double precision
  aut_solvable	boolean
  aut_stats	numeric[]
  aut_supersolvable	boolean
  aut_tex	text
  autcent_abelian	boolean
  autcent_cyclic	boolean
  autcent_exponent	numeric
  autcent_group	text
  autcent_hash	bigint
  autcent_nilpotent	boolean
  autcent_order	numeric
  autcent_solvable	boolean
  autcent_split	boolean
  autcent_supersolvable	boolean
  autcent_tex	text
  autcentquo_abelian	boolean
  autcentquo_cyclic	boolean
  autcentquo_exponent	numeric
  autcentquo_group	text
  autcentquo_hash	bigint
  autcentquo_nilpotent	boolean
  autcentquo_order	numeric
  autcentquo_solvable	boolean
  autcentquo_supersolvable	boolean
  autcentquo_tex	text
  cc_stats	numeric[]
  center_label	text
  center_order	numeric
  central_product	boolean
  central_quotient	text
  commutator_count	integer
  commutator_label	text
  complements_known	boolean
  complete	boolean
  complex_characters_known	boolean
  composition_factors	text[]
  composition_length	smallint
  conjugacy_classes_known	boolean
  counter	integer
  cyclic	boolean
  derived_length	smallint
  dihedral	boolean
  direct_factorization	jsonb
  direct_product	boolean
  div_stats	numeric[]
  element_repr_type	text
  elementary	integer
  eulerian_function	numeric
  exponent	numeric
  exponents_of_order	smallint[]
  factors_of_aut_order	integer[]
  factors_of_order	smallint[]
  faithful_reps	numeric[]
  familial	boolean
  frattini_label	text
  frattini_quotient	text
  hash	bigint
  hyperelementary	integer
  inner_abelian	boolean
  inner_cyclic	boolean
  inner_exponent	numeric
  inner_gen_orders	numeric[]
  inner_gens	numeric[]
  inner_hash	bigint
  inner_nilpotent	boolean
  inner_order	numeric
  inner_split	boolean
  inner_tex	text
  inner_used	smallint[]
  irrC_degree	integer
  irrQ_degree	integer
  irrQ_dim	integer
  irrR_degree	integer
  irrep_stats	numeric[]
  label	text
  linC_count	numeric
  linC_degree	integer
  linFp_degree	integer
  linFq_degree	integer
  linQ_degree	integer
  linQ_degree_count	numeric
  linQ_dim	integer
  linQ_dim_count	numeric
  linR_count	numeric
  linR_degree	integer
  maximal_subgroups_known	boolean
  metabelian	boolean
  metacyclic	boolean
  monomial	boolean
  name	text
  ngens	smallint
  nilpotency_class	smallint
  nilpotent	boolean
  normal_counts	integer[]
  normal_index_bound	numeric
  normal_order_bound	numeric
  normal_subgroups_known	boolean
  number_autjugacy_classes	integer
  number_characteristic_subgroups	integer
  number_conjugacy_classes	integer
  number_divisions	integer
  number_normal_subgroups	integer
  number_subgroup_autclasses	integer
  number_subgroup_classes	integer
  number_subgroups	numeric
  old_label	text
  order	numeric
  order_factorization_type	integer
  order_stats	numeric[]
  outer_abelian	boolean
  outer_cyclic	boolean
  outer_equivalence	boolean
  outer_exponent	numeric
  outer_gen_orders	numeric[]
  outer_gen_pows	numeric[]
  outer_gens	numeric[]
  outer_group	text
  outer_hash	bigint
  outer_nilpotent	boolean
  outer_order	numeric
  outer_permdeg	integer
  outer_perms	numeric[]
  outer_solvable	boolean
  outer_supersolvable	boolean
  outer_tex	text
  pc_rank	smallint
  perfect	boolean
  permutation_degree	integer
  pgroup	smallint
  primary_abelian_invariants	integer[]
  quasisimple	boolean
  rank	smallint
  rational	boolean
  rational_characters_known	boolean
  ratrep_stats	numeric[]
  representations	jsonb
  schur_multiplier	integer[]
  semidirect_product	boolean
  simple	boolean
  smith_abelian_invariants	integer[]
  solvability_type	smallint
  solvable	boolean
  subgroup_inclusions_known	boolean
  subgroup_index_bound	numeric
  supersolvable	boolean
  sylow_subgroups_known	boolean
  tex_name	text
  transitive_degree	integer
  wreath_data	text[]
  wreath_product	boolean

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [12, 4, 6, 12], 'aut_gens': [[102425954038110381731, 51212989102409650082], [55972423204982943139, 805727457719459301722], [673373283486087220564, 90268240328676669730], [57682276233957501975, 324386823455447841369], [773688830642123412979, 587505182741649985818]], 'aut_group': '2239488.hl', 'aut_hash': 7506212161471229649, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2239488, 'aut_permdeg': 756, 'aut_perms': [28416651253496803196245855580747138213112275198813237862331799439816896136530805786655294032083253335255960515882682535643784508821640753643017991037739949248850202277058772013802801586695098535771254179081918337199939113972662655440218818153274972887672016071043465602024820289517021708641853056177752379045543753319427749968551070797021619512603739753044504086807344521784431149347976680493125714213440583511681367578438856428519800482289288597080705267468396894296923530460860721897120777140787449872606798855068865818027132534750610263792089239100931982147384292737163931294484806302013586271147297627836428830876273562357353419125587775128836427630314953578778280263052468469544077108286284198736950238584232870031103961408618944376957445522335610617899856139824353253692306544799291818793009464130350626343606617041595591705059643479545972704167901600906129100694347602956349329024185152169693974329126404810313420125014455992546954013387089028999643692758024658595406584764629798501652499879876812119879519703443699234077531308980130594876278849683916703344397666673924729810736995640093360096427064841305689737315069713569718158473060328192008055845654956025437923871237912879769000447275936834022309368499856334023039285121850455308617002271096076839496959375120154506669045459384965566937656047269239192453668920846797105067684239707287346780769150747401806014140402145175693899648350139636956901288798323533939082227536786044078930303907236358467543652575563885697570539130530573693340486409944704382984309128808231277723267946051857126478496997038773246192485113149534007518400571327090011097924820057250057006676480163022323151358020356707367657964834827586038591010927052261204521926590488956161192579533920186307020014458387135872310610697134695712196624955385397895053441913218970342110896655578536415022599129143824850681477994926748, 43595515927085333516780231408848591564987643182977566419629554609795543906020284704056963690621596707834169375768432258717444440881626470445867528387123802065699752245439694224319830420581985710736335576996549987220646450935710230659754690793183957493880695744406863355165099658955419654609616411936410220399430704116550462328935875175512194971441605263507486303401362763085269883816278153518023524696799168808247601399604916327234594295814463667439946984634334759271849720055327656040953894213347791364237220909918957001990593603303164391404428583870408711314960762216937604984480638204447153685436017441795220295308784002226644049120478639738872973645776808725364706745641432935518383936487433573291714967351132145441065695065187901266019411708676724565911874424805575660553974401206921027257570106251929793412191108711796484960615957752407727888227110446878359099716761598991888167657836059107250334236643086233325846046061265301356241331983765535615689814607984537859968522144811095392105874347637357279602249444236865601221808599442996229794211522206475082195567560357336108464433509654600464136533417506930113190017822441061507877484756913645977208860360822452771042998388669558565432374289956420838108024021649109007910864664304979424073441098299717198352479960161800305420259108092101911507664623398224303950378344775782458497483426178379065074213512901712193739737247990831080147786593195469662054222964651629174263527872604537674354026437299064968266395709485319532565546745349002325884624307645576022021923038396960576202893586440826997287289461770651862213988525981700133394460167648031944922133116384816461203799005169465205976011593177464099174204295760396665640467145011272287117479345989361982254768727562243364326800512973484111709807027581982345423695526584085464013295967911345793834707885807470703649905514973515724678362427547732, 23789331795249037331701306230368758947149679379062983998917066537104875490496217391610787820557095315290283157625084203279435660132739337770456487337050024783177058539097098003723070328388379967488639108016000256225636136723688055196596012905693787900920793273757073387335992163643530259018653471689253610268628145180316024813782899700190428815305518418761045433718789478778649047127424369138657011408103399558867434782393249010594988442780914189909135679944781596985820749848206357865319390076316966020237177765431930267033605909117487172393903044344483753639621523279915143385048778963441384128569123502183766818628470653888574133371767634508315760136986814134423671771790104864695474542971114910534876284916219341401414163281435719157605610584513620571750571564939716992271701259189834554750748142579602692680710442231180943047496527982466315125131149080366238848271445183308485699264308236544057085878687892518912483909194350317199256465064386972500332649990112162772543415404333158568716665929077714560787574080940735280810752807087484547403977733600196399955640222283584639548716577491807449465713472417123063565006172657048660330289537805398873411671564693628996076678387728237606677444316663761500421456511964804224122957820797922464204762899154758987928394281566049506237445194198760000502493539841343917939105178857263133569427301720031714737670748157089511528980443576801513567352025033072009583778346695466986891781047038182090785679566041859063014977531825809550892401242602511190477286529959771087488878738135109932875897538719561710350774487352097538864746354792598864344947837138423354494152383587348109665906928466135015348062286013438095745625053142097105510437986448470636800581904325208094883969753613284618706124910782274868425328491058684215742396693811903268376343321154256618518487102895040044218996491661698150676276796332355, 17380751020904169285001251928644176420546804972545693566810030457631036029414381146911007088593468336158433321292782664150644946008537191764618093737268473157792271264550080010958739143800762264637474503791341814098327550482905891652845097576638738322534110701038313061502215582260460410362711384270259343084033766815710726845294229036481485843579595461216202534937198296443108416161409142833813803790549554792435109309452892905827700243803194598718661732348765148422415655534526941219077473710367476954933591468156383980926988977602995076685479194370291408347727426391238093874921010987538024663177644918425052067939619798861035687340792979031539480060124511426279296600186510001552903257364626069153873025996739043877069972420603908067778229516802766854913032595504102039248844131962583736885343996727677377845815622146400766953008720021499348856214450835562321509390015322828915530748123881093105073147512460970282193357180469264669005200361812710785612751283899784833951337803942172278369485918968560601317438954640931286197818990727405016859954683082371234334473033305247555917097791073944634198591638523740291906038869904305672600640553245577923568175946641638747446757758304537366644558319587758414345338312870359093417979452469186747251703913143961428103090519863884354906699025452387295745434410086952011034618444084544514842357964036495836616070874087835991609315677636186806484809042542737484171115001662409768272614071025310849662189128308839839152553674389522096598839197788216788218617195358401152789847535528356782848792475654230809829403426636556778142494474918262423686455658835814600916999249007335975885149979035591282713047124571789735791900739389880214485044206746486287970082553079221716726054761617994738352148106949471413591617085745494690243402624609977887104733994791603708330434615080494331570534215622482478694321576827303], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 54, 2, 1], [2, 108, 1, 2], [2, 243, 1, 2], [2, 324, 1, 1], [2, 486, 1, 1], [2, 486, 2, 1], [2, 648, 1, 1], [2, 972, 1, 1], [2, 1944, 1, 1], [3, 12, 1, 2], [3, 16, 1, 1], [3, 24, 1, 2], [3, 32, 1, 2], [3, 48, 1, 2], [3, 96, 1, 3], [3, 192, 1, 1], [3, 10368, 1, 1], [4, 648, 1, 1], [4, 1944, 1, 3], [4, 2916, 2, 1], [4, 3888, 2, 1], [4, 5832, 1, 3], [4, 11664, 2, 1], [6, 12, 1, 2], [6, 24, 1, 4], [6, 48, 1, 5], [6, 96, 1, 9], [6, 96, 2, 1], [6, 108, 2, 2], [6, 192, 1, 2], [6, 192, 2, 1], [6, 216, 1, 2], [6, 216, 2, 4], [6, 432, 1, 2], [6, 432, 2, 7], [6, 648, 1, 2], [6, 864, 1, 2], [6, 864, 2, 4], [6, 972, 1, 4], [6, 1296, 1, 4], [6, 1944, 1, 2], [6, 1944, 2, 3], [6, 2592, 1, 4], [6, 3888, 1, 1], [6, 5184, 1, 2], [6, 7776, 1, 2], [6, 31104, 1, 1], [9, 10368, 2, 1], [9, 20736, 1, 1], [9, 20736, 2, 1], [12, 1296, 1, 1], [12, 1944, 2, 2], [12, 2592, 1, 2], [12, 3888, 1, 2], [12, 3888, 2, 2], [12, 3888, 4, 1], [12, 5184, 1, 2], [12, 5832, 2, 1], [12, 7776, 1, 2], [12, 7776, 2, 1], [12, 7776, 4, 1], [12, 11664, 1, 3], [12, 23328, 2, 1], [18, 31104, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^6.C_2^7:S_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': 36, 'autcentquo_group': '2239488.hl', 'autcentquo_hash': 7506212161471229649, 'autcentquo_nilpotent': False, 'autcentquo_order': 2239488, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^6.C_2^7:S_4', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 54, 2], [2, 108, 2], [2, 243, 2], [2, 324, 1], [2, 486, 3], [2, 648, 1], [2, 972, 1], [2, 1944, 1], [3, 12, 2], [3, 16, 1], [3, 24, 2], [3, 32, 2], [3, 48, 2], [3, 96, 3], [3, 192, 1], [3, 10368, 1], [4, 648, 1], [4, 1944, 3], [4, 2916, 2], [4, 3888, 2], [4, 5832, 3], [4, 11664, 2], [6, 12, 2], [6, 24, 4], [6, 48, 5], [6, 96, 11], [6, 108, 4], [6, 192, 4], [6, 216, 10], [6, 432, 16], [6, 648, 2], [6, 864, 10], [6, 972, 4], [6, 1296, 4], [6, 1944, 8], [6, 2592, 4], [6, 3888, 1], [6, 5184, 2], [6, 7776, 2], [6, 31104, 1], [9, 10368, 2], [9, 20736, 3], [12, 1296, 1], [12, 1944, 4], [12, 2592, 2], [12, 3888, 10], [12, 5184, 2], [12, 5832, 2], [12, 7776, 8], [12, 11664, 3], [12, 23328, 2], [18, 31104, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '559872.lw', 'commutator_count': 1, 'commutator_label': '139968.il', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 15, 'conjugacy_classes_known': True, 'counter': 309, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 54, 1, 2], [2, 108, 1, 2], [2, 243, 1, 2], [2, 324, 1, 1], [2, 486, 1, 3], [2, 648, 1, 1], [2, 972, 1, 1], [2, 1944, 1, 1], [3, 12, 1, 2], [3, 16, 1, 1], [3, 24, 1, 2], [3, 32, 1, 2], [3, 48, 1, 2], [3, 96, 1, 3], [3, 192, 1, 1], [3, 10368, 1, 1], [4, 648, 1, 1], [4, 1944, 1, 3], [4, 2916, 1, 2], [4, 3888, 1, 2], [4, 5832, 1, 3], [4, 11664, 1, 2], [6, 12, 1, 2], [6, 24, 1, 4], [6, 48, 1, 5], [6, 96, 1, 9], [6, 96, 2, 1], [6, 108, 1, 4], [6, 192, 1, 2], [6, 192, 2, 1], [6, 216, 1, 10], [6, 432, 1, 14], [6, 432, 2, 1], [6, 648, 1, 2], [6, 864, 1, 8], [6, 864, 2, 1], [6, 972, 1, 4], [6, 1296, 1, 4], [6, 1944, 1, 8], [6, 2592, 1, 4], [6, 3888, 1, 1], [6, 5184, 1, 2], [6, 7776, 1, 2], [6, 31104, 1, 1], [9, 10368, 1, 2], [9, 20736, 1, 3], [12, 1296, 1, 1], [12, 1944, 2, 2], [12, 2592, 1, 2], [12, 3888, 1, 2], [12, 3888, 2, 4], [12, 5184, 1, 2], [12, 5832, 1, 2], [12, 7776, 1, 4], [12, 7776, 2, 2], [12, 11664, 1, 3], [12, 23328, 1, 2], [18, 31104, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [8, 7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 16], [24, 1, 24], [48, 0, 2], [48, 1, 21], [96, 0, 4], [96, 1, 18], [192, 0, 2], [192, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '559872.lw', 'hash': 5225393530267235522, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [18, 4], 'inner_gens': [[102425954038110381731, 109499800630486991761], [55969635089829741975, 51212989102409650082]], 'inner_hash': 5225393530267235522, 'inner_nilpotent': False, 'inner_order': 559872, 'inner_split': True, 'inner_tex': 'C_3^6.C_2^5:S_4', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 4], [2, 2], [3, 12], [6, 10], [12, 34], [16, 3], [24, 36], [32, 8], [48, 34], [64, 1], [96, 28], [192, 5]], 'label': '559872.lw', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^6.C2^5:S4', 'ngens': 2, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 134, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 177, 'number_divisions': 165, 'number_normal_subgroups': 20, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 559872, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 6159], [3, 11096], [4, 60912], [6, 117528], [9, 82944], [12, 219024], [18, 62208]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[752260817667307022052, 766614563158631933653], [613888536758737087451, 51283831115372971682]], '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': None, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 2], [3, 12], [6, 10], [12, 26], [16, 3], [24, 36], [32, 8], [48, 30], [64, 1], [96, 27], [192, 5], [384, 1]], 'representations': {'PC': {'code': '920005426149038267301539310497410152465106842814153960108365937931667053705713144515881921873646524386599347707876663702291889075461630706122492689169995106514837681646866211402837922311030000167204064853314087087773820078389262658303252731941909441149880268801505395676786288971785493427427927376672758501792949105180231246521955865170887030435498543540101689463323784794397868968899830863110305610427102348939947', 'gens': [1, 2, 4, 5, 7, 9, 11, 13, 15], 'pres': [15, 2, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 397260, 10050421, 76, 24246362, 2955452, 1114563, 401778, 258333, 396904, 947719, 1528459, 799, 214, 933125, 466580, 51875, 770, 52300086, 11430741, 2545236, 18951, 3216, 306, 29859847, 26127382, 63397, 34612, 2947, 44444708, 24451493, 6280778, 32453, 24368, 398, 65318409, 37324824, 154839, 7254, 21669, 3084850, 309895, 5684620, 178270, 5080, 490, 17291, 207386, 2799401, 155591, 4451, 18673212, 9448947, 18216942, 1263672, 6012, 582, 846733, 211708, 9797803, 1088713, 5203, 842414, 5429, 583244, 97334, 16364]}, 'Perm': {'d': 22, 'gens': [102425954038110381731, 51212989102409650082]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 72, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.C_2^5:S_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 164263623
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 309, 'group_order': 559872, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 164263712
    {'aut_label': '2A', 'centralizer': '3.a1', 'counter': 2, 'group_counter': 309, 'group_order': 559872, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 16, 'size': 3}
  • id: 164263723
    {'aut_label': '2B', 'centralizer': '54.N', 'counter': 3, 'group_counter': 309, 'group_order': 559872, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 186810624000, 'size': 54}
  • id: 164263734
    {'aut_label': '2B', 'centralizer': '54.N', 'counter': 4, 'group_counter': 309, 'group_order': 559872, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 186810624016, 'size': 54}
  • id: 164263745
    {'aut_label': '2D', 'centralizer': None, 'counter': 5, 'group_counter': 309, 'group_order': 559872, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 806407, 'size': 108}
  • id: 164263756
    {'aut_label': '2E', 'centralizer': None, 'counter': 6, 'group_counter': 309, 'group_order': 559872, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 572110333866828985080, 'size': 108}
  • id: 164263767
    {'aut_label': '2F', 'centralizer': None, 'counter': 7, 'group_counter': 309, 'group_order': 559872, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 34189074703781630760, 'size': 243}
  • id: 164263778
    {'aut_label': '2G', 'centralizer': None, 'counter': 8, 'group_counter': 309, 'group_order': 559872, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 1500000756780193936, 'size': 243}
  • id: 164263789
    {'aut_label': '2H', 'centralizer': None, 'counter': 9, 'group_counter': 309, 'group_order': 559872, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 572110333866828985096, 'size': 324}
  • id: 164263624
    {'aut_label': '2I', 'centralizer': None, 'counter': 10, 'group_counter': 309, 'group_order': 559872, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 900475809547733763976, 'size': 486}
  • id: 164263635
    {'aut_label': '2I', 'centralizer': None, 'counter': 11, 'group_counter': 309, 'group_order': 559872, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 1466542693805817720, 'size': 486}
  • id: 164263646
    {'aut_label': '2K', 'centralizer': None, 'counter': 12, 'group_counter': 309, 'group_order': 559872, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 854206550372062954816, 'size': 486}
  • id: 164263657
    {'aut_label': '2L', 'centralizer': None, 'counter': 13, 'group_counter': 309, 'group_order': 559872, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 109531900119338540041, 'size': 648}
  • id: 164263668
    {'aut_label': '2M', 'centralizer': None, 'counter': 14, 'group_counter': 309, 'group_order': 559872, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 905328793205574404527, 'size': 972}
  • id: 164263679
    {'aut_label': '2N', 'centralizer': None, 'counter': 15, 'group_counter': 309, 'group_order': 559872, 'label': '2N', 'order': 2, 'powers': [1, 15], 'representative': 2460694031159984054, 'size': 1944}
  • id: 164263690
    {'aut_label': '3A', 'centralizer': '12.BO', 'counter': 16, 'group_counter': 309, 'group_order': 559872, 'label': '3A', 'order': 3, 'powers': [16, 1], 'representative': 125630663558400, 'size': 12}
  • id: 164263701
    {'aut_label': '3B', 'centralizer': '12.BE', 'counter': 17, 'group_counter': 309, 'group_order': 559872, 'label': '3B', 'order': 3, 'powers': [17, 1], 'representative': 1511716211921704320, 'size': 12}
  • id: 164263710
    {'aut_label': '3C', 'centralizer': '16.A', 'counter': 18, 'group_counter': 309, 'group_order': 559872, 'label': '3C', 'order': 3, 'powers': [18, 1], 'representative': 35655700821503575680, 'size': 16}
  • id: 164263711
    {'aut_label': '3D', 'centralizer': '24.DY', 'counter': 19, 'group_counter': 309, 'group_order': 559872, 'label': '3D', 'order': 3, 'powers': [19, 1], 'representative': 1905294527136000, 'size': 24}
  • id: 164263713
    {'aut_label': '3E', 'centralizer': '24.DZ', 'counter': 20, 'group_counter': 309, 'group_order': 559872, 'label': '3E', 'order': 3, 'powers': [20, 1], 'representative': 46995288615475200, 'size': 24}
  • id: 164263714
    {'aut_label': '3F', 'centralizer': '32.A', 'counter': 21, 'group_counter': 309, 'group_order': 559872, 'label': '3F', 'order': 3, 'powers': [21, 1], 'representative': 906809998584306263040, 'size': 32}
  • id: 164263715
    {'aut_label': '3G', 'centralizer': '32.B', 'counter': 22, 'group_counter': 309, 'group_order': 559872, 'label': '3G', 'order': 3, 'powers': [22, 1], 'representative': 850718446880115392040, 'size': 32}
  • id: 164263716
    {'aut_label': '3H', 'centralizer': '48.EW', 'counter': 23, 'group_counter': 309, 'group_order': 559872, 'label': '3H', 'order': 3, 'powers': [23, 1], 'representative': 47078980293945600, 'size': 48}
  • id: 164263717
    {'aut_label': '3I', 'centralizer': '48.FF', 'counter': 24, 'group_counter': 309, 'group_order': 559872, 'label': '3I', 'order': 3, 'powers': [24, 1], 'representative': 35702570479455492480, 'size': 48}
  • id: 164263718
    {'aut_label': '3J', 'centralizer': None, 'counter': 25, 'group_counter': 309, 'group_order': 559872, 'label': '3J', 'order': 3, 'powers': [25, 1], 'representative': 1511820913568353920, 'size': 96}
  • id: 164263719
    {'aut_label': '3K', 'centralizer': None, 'counter': 26, 'group_counter': 309, 'group_order': 559872, 'label': '3K', 'order': 3, 'powers': [26, 1], 'representative': 35657480485367153280, 'size': 96}
  • id: 164263720
    {'aut_label': '3L', 'centralizer': None, 'counter': 27, 'group_counter': 309, 'group_order': 559872, 'label': '3L', 'order': 3, 'powers': [27, 1], 'representative': 1513600570725909120, 'size': 96}
  • id: 164263721
    {'aut_label': '3M', 'centralizer': '192.A', 'counter': 28, 'group_counter': 309, 'group_order': 559872, 'label': '3M', 'order': 3, 'powers': [28, 1], 'representative': 35702654171133962880, 'size': 192}
  • id: 164263722
    {'aut_label': '3N', 'centralizer': None, 'counter': 29, 'group_counter': 309, 'group_order': 559872, 'label': '3N', 'order': 3, 'powers': [29, 1], 'representative': 535384138549365036123, 'size': 10368}
  • id: 164263724
    {'aut_label': '4A', 'centralizer': None, 'counter': 30, 'group_counter': 309, 'group_order': 559872, 'label': '4A', 'order': 4, 'powers': [2, 30], 'representative': 273416585459251540458, 'size': 648}
  • id: 164263725
    {'aut_label': '4B', 'centralizer': None, 'counter': 31, 'group_counter': 309, 'group_order': 559872, 'label': '4B', 'order': 4, 'powers': [2, 31], 'representative': 156071738783933856017, 'size': 1944}
  • id: 164263726
    {'aut_label': '4C', 'centralizer': None, 'counter': 32, 'group_counter': 309, 'group_order': 559872, 'label': '4C', 'order': 4, 'powers': [7, 32], 'representative': 514035058002856277886, 'size': 1944}
  • id: 164263727
    {'aut_label': '4D', 'centralizer': None, 'counter': 33, 'group_counter': 309, 'group_order': 559872, 'label': '4D', 'order': 4, 'powers': [8, 33], 'representative': 28364716520671104009, 'size': 1944}
  • id: 164263728
    {'aut_label': '4E', 'centralizer': None, 'counter': 34, 'group_counter': 309, 'group_order': 559872, 'label': '4E', 'order': 4, 'powers': [7, 34], 'representative': 580187032212391027207, 'size': 2916}
  • id: 164263729
    {'aut_label': '4E', 'centralizer': None, 'counter': 35, 'group_counter': 309, 'group_order': 559872, 'label': '4F', 'order': 4, 'powers': [7, 35], 'representative': 317068931846190636840, 'size': 2916}
  • id: 164263730
    {'aut_label': '4G', 'centralizer': None, 'counter': 36, 'group_counter': 309, 'group_order': 559872, 'label': '4G', 'order': 4, 'powers': [4, 36], 'representative': 2473495109898099969, 'size': 3888}
  • id: 164263731
    {'aut_label': '4G', 'centralizer': None, 'counter': 37, 'group_counter': 309, 'group_order': 559872, 'label': '4H', 'order': 4, 'powers': [3, 37], 'representative': 33248310314003326085, 'size': 3888}
  • id: 164263732
    {'aut_label': '4I', 'centralizer': None, 'counter': 38, 'group_counter': 309, 'group_order': 559872, 'label': '4I', 'order': 4, 'powers': [7, 38], 'representative': 703489734452482675941, 'size': 5832}
  • id: 164263733
    {'aut_label': '4J', 'centralizer': None, 'counter': 39, 'group_counter': 309, 'group_order': 559872, 'label': '4J', 'order': 4, 'powers': [7, 39], 'representative': 321947519030216311703, 'size': 5832}
  • id: 164263735
    {'aut_label': '4K', 'centralizer': None, 'counter': 40, 'group_counter': 309, 'group_order': 559872, 'label': '4K', 'order': 4, 'powers': [8, 40], 'representative': 766614560530872741853, 'size': 5832}
  • id: 164263736
    {'aut_label': '4L', 'centralizer': None, 'counter': 41, 'group_counter': 309, 'group_order': 559872, 'label': '4L', 'order': 4, 'powers': [10, 41], 'representative': 329424194912169738369, 'size': 11664}
  • id: 164263737
    {'aut_label': '4L', 'centralizer': None, 'counter': 42, 'group_counter': 309, 'group_order': 559872, 'label': '4M', 'order': 4, 'powers': [11, 42], 'representative': 582395370742276091414, 'size': 11664}
  • id: 164263738
    {'aut_label': '6A', 'centralizer': '12.BO', 'counter': 43, 'group_counter': 309, 'group_order': 559872, 'label': '6A', 'order': 6, 'powers': [16, 2], 'representative': 27555085958416, 'size': 12}
  • id: 164263739
    {'aut_label': '6B', 'centralizer': '12.BE', 'counter': 44, 'group_counter': 309, 'group_order': 559872, 'label': '6B', 'order': 6, 'powers': [17, 2], 'representative': 1511716211921704343, 'size': 12}
  • id: 164263740
    {'aut_label': '6C', 'centralizer': '24.EC', 'counter': 45, 'group_counter': 309, 'group_order': 559872, 'label': '6C', 'order': 6, 'powers': [16, 2], 'representative': 27555085958407, 'size': 24}
  • id: 164263741
    {'aut_label': '6D', 'centralizer': '24.DR', 'counter': 46, 'group_counter': 309, 'group_order': 559872, 'label': '6D', 'order': 6, 'powers': [17, 2], 'representative': 1255621276147351687, 'size': 24}
  • id: 164263742
    {'aut_label': '6E', 'centralizer': '24.DZ', 'counter': 47, 'group_counter': 309, 'group_order': 559872, 'label': '6E', 'order': 6, 'powers': [20, 2], 'representative': 820048792127995186687, 'size': 24}
  • id: 164263743
    {'aut_label': '6F', 'centralizer': '24.DY', 'counter': 48, 'group_counter': 309, 'group_order': 559872, 'label': '6F', 'order': 6, 'powers': [19, 2], 'representative': 872330575802787325447, 'size': 24}
  • id: 164263744
    {'aut_label': '6G', 'centralizer': '48.EY', 'counter': 49, 'group_counter': 309, 'group_order': 559872, 'label': '6G', 'order': 6, 'powers': [19, 2], 'representative': 1115720264736007, 'size': 48}
  • id: 164263746
    {'aut_label': '6H', 'centralizer': '48.EZ', 'counter': 50, 'group_counter': 309, 'group_order': 559872, 'label': '6H', 'order': 6, 'powers': [20, 2], 'representative': 33479266459161607, 'size': 48}
  • id: 164263747
    {'aut_label': '6I', 'centralizer': '48.EW', 'counter': 51, 'group_counter': 309, 'group_order': 559872, 'label': '6I', 'order': 6, 'powers': [23, 2], 'representative': 33504205677465616, 'size': 48}
  • id: 164263748
    {'aut_label': '6J', 'centralizer': '48.EZ', 'counter': 52, 'group_counter': 309, 'group_order': 559872, 'label': '6J', 'order': 6, 'powers': [18, 2], 'representative': 30546508528755480247, 'size': 48}
  • id: 164263749
    {'aut_label': '6K', 'centralizer': '48.FF', 'counter': 53, 'group_counter': 309, 'group_order': 559872, 'label': '6K', 'order': 6, 'powers': [24, 2], 'representative': 35458569078138944656, 'size': 48}
  • id: 164263750
    {'aut_label': '6L', 'centralizer': None, 'counter': 54, 'group_counter': 309, 'group_order': 559872, 'label': '6L', 'order': 6, 'powers': [23, 2], 'representative': 33504205677465607, 'size': 96}
  • id: 164263751
    {'aut_label': '6M', 'centralizer': None, 'counter': 55, 'group_counter': 309, 'group_order': 559872, 'label': '6M', 'order': 6, 'powers': [25, 2], 'representative': 1255647523519025287, 'size': 96}
  • id: 164263752
    {'aut_label': '6N', 'centralizer': None, 'counter': 56, 'group_counter': 309, 'group_order': 559872, 'label': '6N', 'order': 6, 'powers': [25, 2], 'representative': 1255647523519025296, 'size': 96}
  • id: 164263753
    {'aut_label': '6O', 'centralizer': None, 'counter': 57, 'group_counter': 309, 'group_order': 559872, 'label': '6O', 'order': 6, 'powers': [25, 2], 'representative': 1255647523519025303, 'size': 96}
  • id: 164263754
    {'aut_label': '6P', 'centralizer': None, 'counter': 58, 'group_counter': 309, 'group_order': 559872, 'label': '6P', 'order': 6, 'powers': [26, 2], 'representative': 30547596693934257847, 'size': 96}
  • id: 164263755
    {'aut_label': '6Q', 'centralizer': None, 'counter': 59, 'group_counter': 309, 'group_order': 559872, 'label': '6Q', 'order': 6, 'powers': [24, 2], 'representative': 30579960240128683447, 'size': 96}
  • id: 164263757
    {'aut_label': '6R', 'centralizer': None, 'counter': 60, 'group_counter': 309, 'group_order': 559872, 'label': '6R', 'order': 6, 'powers': [21, 2], 'representative': 850596387420809847727, 'size': 96}
  • id: 164263758
    {'aut_label': '6S', 'centralizer': None, 'counter': 61, 'group_counter': 309, 'group_order': 559872, 'label': '6S', 'order': 6, 'powers': [22, 2], 'representative': 906565938424342444816, 'size': 96}
  • id: 164263759
    {'aut_label': '6T', 'centralizer': None, 'counter': 62, 'group_counter': 309, 'group_order': 559872, 'label': '6T', 'order': 6, 'powers': [27, 2], 'representative': 905341618876254709696, 'size': 96}
  • id: 164263760
    {'aut_label': '6U1', 'centralizer': None, 'counter': 63, 'group_counter': 309, 'group_order': 559872, 'label': '6U1', 'order': 6, 'powers': [26, 2], 'representative': 30547596693934257856, 'size': 96}
  • id: 164263761
    {'aut_label': '6U1', 'centralizer': None, 'counter': 64, 'group_counter': 309, 'group_order': 559872, 'label': '6U-1', 'order': 6, 'powers': [26, 2], 'representative': 30547596693934257863, 'size': 96}
  • id: 164263762
    {'aut_label': '6V', 'centralizer': None, 'counter': 65, 'group_counter': 309, 'group_order': 559872, 'label': '6V', 'order': 6, 'powers': [16, 3], 'representative': 27741896582400, 'size': 108}
  • id: 164263763
    {'aut_label': '6V', 'centralizer': None, 'counter': 66, 'group_counter': 309, 'group_order': 559872, 'label': '6W', 'order': 6, 'powers': [16, 4], 'representative': 27741896582416, 'size': 108}
  • id: 164263764
    {'aut_label': '6X', 'centralizer': None, 'counter': 67, 'group_counter': 309, 'group_order': 559872, 'label': '6X', 'order': 6, 'powers': [16, 3], 'representative': 820049881407810687480, 'size': 108}
  • id: 164263765
    {'aut_label': '6X', 'centralizer': None, 'counter': 68, 'group_counter': 309, 'group_order': 559872, 'label': '6Y', 'order': 6, 'powers': [16, 4], 'representative': 33834953887257743, 'size': 108}
  • id: 164263766
    {'aut_label': '6Z', 'centralizer': '192.A', 'counter': 69, 'group_counter': 309, 'group_order': 559872, 'label': '6Z', 'order': 6, 'powers': [27, 2], 'representative': 1256735595292490887, 'size': 192}
  • id: 164263768
    {'aut_label': '6AA', 'centralizer': '192.A', 'counter': 70, 'group_counter': 309, 'group_order': 559872, 'label': '6AA', 'order': 6, 'powers': [28, 2], 'representative': 30579985179346987456, 'size': 192}
  • id: 164263769
    {'aut_label': '6AB1', 'centralizer': '192.A', 'counter': 71, 'group_counter': 309, 'group_order': 559872, 'label': '6AB1', 'order': 6, 'powers': [28, 2], 'representative': 30579985179346987447, 'size': 192}
  • id: 164263770
    {'aut_label': '6AB1', 'centralizer': '192.A', 'counter': 72, 'group_counter': 309, 'group_order': 559872, 'label': '6AB-1', 'order': 6, 'powers': [28, 2], 'representative': 30579985179346987463, 'size': 192}
  • id: 164263771
    {'aut_label': '6AC', 'centralizer': None, 'counter': 73, 'group_counter': 309, 'group_order': 559872, 'label': '6AC', 'order': 6, 'powers': [16, 5], 'representative': 27555086764807, 'size': 216}
  • id: 164263772
    {'aut_label': '6AD', 'centralizer': None, 'counter': 74, 'group_counter': 309, 'group_order': 559872, 'label': '6AD', 'order': 6, 'powers': [16, 3], 'representative': 27568019001720, 'size': 216}
  • id: 164263773
    {'aut_label': '6AD', 'centralizer': None, 'counter': 75, 'group_counter': 309, 'group_order': 559872, 'label': '6AE', 'order': 6, 'powers': [16, 4], 'representative': 27568019001727, 'size': 216}
  • id: 164263774
    {'aut_label': '6AF', 'centralizer': None, 'counter': 76, 'group_counter': 309, 'group_order': 559872, 'label': '6AF', 'order': 6, 'powers': [16, 5], 'representative': 27568019001736, 'size': 216}
  • id: 164263775
    {'aut_label': '6AF', 'centralizer': None, 'counter': 77, 'group_counter': 309, 'group_order': 559872, 'label': '6AG', 'order': 6, 'powers': [16, 5], 'representative': 27568019001743, 'size': 216}
  • id: 164263776
    {'aut_label': '6AH', 'centralizer': None, 'counter': 78, 'group_counter': 309, 'group_order': 559872, 'label': '6AH', 'order': 6, 'powers': [16, 5], 'representative': 27741896582407, 'size': 216}
  • id: 164263777
    {'aut_label': '6AI', 'centralizer': None, 'counter': 79, 'group_counter': 309, 'group_order': 559872, 'label': '6AI', 'order': 6, 'powers': [17, 3], 'representative': 1255621363325643000, 'size': 216}
  • id: 164263779
    {'aut_label': '6AI', 'centralizer': None, 'counter': 80, 'group_counter': 309, 'group_order': 559872, 'label': '6AJ', 'order': 6, 'powers': [17, 4], 'representative': 1255621363325643023, 'size': 216}
  • id: 164263780
    {'aut_label': '6AK', 'centralizer': None, 'counter': 81, 'group_counter': 309, 'group_order': 559872, 'label': '6AK', 'order': 6, 'powers': [20, 4], 'representative': 30593476262284548496, 'size': 216}
  • id: 164263781
    {'aut_label': '6AK', 'centralizer': None, 'counter': 82, 'group_counter': 309, 'group_order': 559872, 'label': '6AL', 'order': 6, 'powers': [20, 3], 'representative': 871152559957452695040, 'size': 216}
  • id: 164263782
    {'aut_label': '6AM', 'centralizer': None, 'counter': 83, 'group_counter': 309, 'group_order': 559872, 'label': '6AM', 'order': 6, 'powers': [19, 3], 'representative': 1115720265542400, 'size': 432}
  • id: 164263783
    {'aut_label': '6AN', 'centralizer': None, 'counter': 84, 'group_counter': 309, 'group_order': 559872, 'label': '6AN', 'order': 6, 'powers': [19, 5], 'representative': 1115720265542407, 'size': 432}
  • id: 164263784
    {'aut_label': '6AM', 'centralizer': None, 'counter': 85, 'group_counter': 309, 'group_order': 559872, 'label': '6AO', 'order': 6, 'powers': [19, 4], 'representative': 1115720265542416, 'size': 432}
  • id: 164263785
    {'aut_label': '6AN', 'centralizer': None, 'counter': 86, 'group_counter': 309, 'group_order': 559872, 'label': '6AP', 'order': 6, 'powers': [19, 5], 'representative': 1115720265542423, 'size': 432}
  • id: 164263786
    {'aut_label': '6AQ', 'centralizer': None, 'counter': 87, 'group_counter': 309, 'group_order': 559872, 'label': '6AQ', 'order': 6, 'powers': [20, 5], 'representative': 33479266459968007, 'size': 432}
  • id: 164263787
    {'aut_label': '6AR', 'centralizer': None, 'counter': 88, 'group_counter': 309, 'group_order': 559872, 'label': '6AR', 'order': 6, 'powers': [20, 3], 'representative': 33483282887663280, 'size': 432}
  • id: 164263788
    {'aut_label': '6AS', 'centralizer': None, 'counter': 89, 'group_counter': 309, 'group_order': 559872, 'label': '6AS', 'order': 6, 'powers': [20, 5], 'representative': 33483282887663287, 'size': 432}
  • id: 164263790
    {'aut_label': '6AS', 'centralizer': None, 'counter': 90, 'group_counter': 309, 'group_order': 559872, 'label': '6AT', 'order': 6, 'powers': [20, 5], 'representative': 33483282887663296, 'size': 432}
  • id: 164263791
    {'aut_label': '6AR', 'centralizer': None, 'counter': 91, 'group_counter': 309, 'group_order': 559872, 'label': '6AU', 'order': 6, 'powers': [20, 4], 'representative': 33483282887663303, 'size': 432}
  • id: 164263792
    {'aut_label': '6AV', 'centralizer': None, 'counter': 92, 'group_counter': 309, 'group_order': 559872, 'label': '6AV', 'order': 6, 'powers': [17, 5], 'representative': 1255621363325643007, 'size': 432}
  • id: 164263793
    {'aut_label': '6AW', 'centralizer': None, 'counter': 93, 'group_counter': 309, 'group_order': 559872, 'label': '6AW', 'order': 6, 'powers': [18, 3], 'representative': 30546508541688523560, 'size': 432}
  • id: 164263794
    {'aut_label': '6AW', 'centralizer': None, 'counter': 94, 'group_counter': 309, 'group_order': 559872, 'label': '6AX', 'order': 6, 'powers': [18, 4], 'representative': 30546508541688523567, 'size': 432}
  • id: 164263795
    {'aut_label': '6AY', 'centralizer': None, 'counter': 95, 'group_counter': 309, 'group_order': 559872, 'label': '6AY', 'order': 6, 'powers': [23, 4], 'representative': 46309021147872016, 'size': 432}
  • id: 164263796
    {'aut_label': '6AY', 'centralizer': None, 'counter': 96, 'group_counter': 309, 'group_order': 559872, 'label': '6AZ', 'order': 6, 'powers': [23, 3], 'representative': 35689079396517931440, 'size': 432}
  • id: 164263797
    {'aut_label': '6BA1', 'centralizer': None, 'counter': 97, 'group_counter': 309, 'group_order': 559872, 'label': '6BA1', 'order': 6, 'powers': [18, 5], 'representative': 30546508541688523576, 'size': 432}
  • id: 164263798
    {'aut_label': '6BA1', 'centralizer': None, 'counter': 98, 'group_counter': 309, 'group_order': 559872, 'label': '6BA-1', 'order': 6, 'powers': [18, 5], 'representative': 30546508541688523583, 'size': 432}
  • id: 164263799
    {'aut_label': '6BB', 'centralizer': None, 'counter': 99, 'group_counter': 309, 'group_order': 559872, 'label': '6BB', 'order': 6, 'powers': [17, 6], 'representative': 265564645435461542520, 'size': 648}
  • id: 164263625
    {'aut_label': '6BC', 'centralizer': None, 'counter': 100, 'group_counter': 309, 'group_order': 559872, 'label': '6BC', 'order': 6, 'powers': [17, 9], 'representative': 265564645435461542536, 'size': 648}
  • id: 164263626
    {'aut_label': '6BD', 'centralizer': None, 'counter': 101, 'group_counter': 309, 'group_order': 559872, 'label': '6BD', 'order': 6, 'powers': [21, 6], 'representative': 321943962940538410920, 'size': 864}
  • id: 164263627
    {'aut_label': '6BE', 'centralizer': None, 'counter': 102, 'group_counter': 309, 'group_order': 559872, 'label': '6BE', 'order': 6, 'powers': [25, 5], 'representative': 849373214683544057647, 'size': 864}
  • id: 164263628
    {'aut_label': '6BF', 'centralizer': None, 'counter': 103, 'group_counter': 309, 'group_order': 559872, 'label': '6BF', 'order': 6, 'powers': [23, 5], 'representative': 872607370190161582223, 'size': 864}
  • id: 164263629
    {'aut_label': '6BG', 'centralizer': None, 'counter': 104, 'group_counter': 309, 'group_order': 559872, 'label': '6BG', 'order': 6, 'powers': [25, 4], 'representative': 872331769983513461056, 'size': 864}
  • id: 164263630
    {'aut_label': '6BH', 'centralizer': None, 'counter': 105, 'group_counter': 309, 'group_order': 559872, 'label': '6BH', 'order': 6, 'powers': [26, 4], 'representative': 901821775498156407607, 'size': 864}
  • id: 164263631
    {'aut_label': '6BH', 'centralizer': None, 'counter': 106, 'group_counter': 309, 'group_order': 559872, 'label': '6BI', 'order': 6, 'powers': [26, 3], 'representative': 906795335825094608760, 'size': 864}
  • id: 164263632
    {'aut_label': '6BG', 'centralizer': None, 'counter': 107, 'group_counter': 309, 'group_order': 559872, 'label': '6BJ', 'order': 6, 'powers': [25, 3], 'representative': 871139760547077106560, 'size': 864}
  • id: 164263633
    {'aut_label': '6BE', 'centralizer': None, 'counter': 108, 'group_counter': 309, 'group_order': 559872, 'label': '6BK', 'order': 6, 'powers': [25, 5], 'representative': 906764009083571485576, 'size': 864}
  • id: 164263634
    {'aut_label': '6BL1', 'centralizer': None, 'counter': 109, 'group_counter': 309, 'group_order': 559872, 'label': '6BL1', 'order': 6, 'powers': [26, 5], 'representative': 854251823708365391407, 'size': 864}
  • id: 164263636
    {'aut_label': '6BL1', 'centralizer': None, 'counter': 110, 'group_counter': 309, 'group_order': 559872, 'label': '6BL-1', 'order': 6, 'powers': [26, 5], 'representative': 905330257732809186487, 'size': 864}
  • id: 164263637
    {'aut_label': '6BM', 'centralizer': None, 'counter': 111, 'group_counter': 309, 'group_order': 559872, 'label': '6BM', 'order': 6, 'powers': [17, 7], 'representative': 35457500708180374440, 'size': 972}
  • id: 164263638
    {'aut_label': '6BN', 'centralizer': None, 'counter': 112, 'group_counter': 309, 'group_order': 559872, 'label': '6BN', 'order': 6, 'powers': [16, 8], 'representative': 821516402998243054216, 'size': 972}
  • id: 164263639
    {'aut_label': '6BO', 'centralizer': None, 'counter': 113, 'group_counter': 309, 'group_order': 559872, 'label': '6BO', 'order': 6, 'powers': [17, 8], 'representative': 35689495043969141887, 'size': 972}
  • id: 164263640
    {'aut_label': '6BP', 'centralizer': None, 'counter': 114, 'group_counter': 309, 'group_order': 559872, 'label': '6BP', 'order': 6, 'powers': [16, 7], 'representative': 871153649437011863160, 'size': 972}
  • id: 164263641
    {'aut_label': '6BQ', 'centralizer': None, 'counter': 115, 'group_counter': 309, 'group_order': 559872, 'label': '6BQ', 'order': 6, 'powers': [24, 9], 'representative': 326921933111145534023, 'size': 1296}
  • id: 164263642
    {'aut_label': '6BR', 'centralizer': None, 'counter': 116, 'group_counter': 309, 'group_order': 559872, 'label': '6BR', 'order': 6, 'powers': [17, 13], 'representative': 738936875734015312086, 'size': 1296}
  • id: 164263643
    {'aut_label': '6BS', 'centralizer': None, 'counter': 117, 'group_counter': 309, 'group_order': 559872, 'label': '6BS', 'order': 6, 'powers': [17, 9], 'representative': 579411849373197418943, 'size': 1296}
  • id: 164263644
    {'aut_label': '6BT', 'centralizer': None, 'counter': 118, 'group_counter': 309, 'group_order': 559872, 'label': '6BT', 'order': 6, 'powers': [24, 6], 'representative': 270434006409920301480, 'size': 1296}
  • id: 164263645
    {'aut_label': '6BU', 'centralizer': None, 'counter': 119, 'group_counter': 309, 'group_order': 559872, 'label': '6BU', 'order': 6, 'powers': [19, 10], 'representative': 901700130410680533256, 'size': 1944}
  • id: 164263647
    {'aut_label': '6BU', 'centralizer': None, 'counter': 120, 'group_counter': 309, 'group_order': 559872, 'label': '6BV', 'order': 6, 'powers': [19, 11], 'representative': 35700790908997589880, 'size': 1944}
  • id: 164263648
    {'aut_label': '6BW', 'centralizer': None, 'counter': 121, 'group_counter': 309, 'group_order': 559872, 'label': '6BW', 'order': 6, 'powers': [16, 11], 'representative': 872364410656562568360, 'size': 1944}
  • id: 164263649
    {'aut_label': '6BX', 'centralizer': None, 'counter': 122, 'group_counter': 309, 'group_order': 559872, 'label': '6BX', 'order': 6, 'powers': [16, 14], 'representative': 905329881277347870127, 'size': 1944}
  • id: 164263650
    {'aut_label': '6BW', 'centralizer': None, 'counter': 123, 'group_counter': 309, 'group_order': 559872, 'label': '6BY', 'order': 6, 'powers': [16, 10], 'representative': 30670032850157438776, 'size': 1944}
  • id: 164263651
    {'aut_label': '6BZ', 'centralizer': None, 'counter': 124, 'group_counter': 309, 'group_order': 559872, 'label': '6BZ', 'order': 6, 'powers': [17, 12], 'representative': 855705460541312959936, 'size': 1944}
  • id: 164263652
    {'aut_label': '6CA', 'centralizer': None, 'counter': 125, 'group_counter': 309, 'group_order': 559872, 'label': '6CA', 'order': 6, 'powers': [16, 12], 'representative': 820050258118140091447, 'size': 1944}
  • id: 164263653
    {'aut_label': '6BX', 'centralizer': None, 'counter': 126, 'group_counter': 309, 'group_order': 559872, 'label': '6CB', 'order': 6, 'powers': [16, 14], 'representative': 35459365470988399936, 'size': 1944}
  • id: 164263654
    {'aut_label': '6CC', 'centralizer': None, 'counter': 127, 'group_counter': 309, 'group_order': 559872, 'label': '6CC', 'order': 6, 'powers': [19, 13], 'representative': 109499800655275647241, 'size': 2592}
  • id: 164263655
    {'aut_label': '6CD', 'centralizer': None, 'counter': 128, 'group_counter': 309, 'group_order': 559872, 'label': '6CD', 'order': 6, 'powers': [24, 13], 'representative': 726861892903797828966, 'size': 2592}
  • id: 164263656
    {'aut_label': '6CE', 'centralizer': None, 'counter': 129, 'group_counter': 309, 'group_order': 559872, 'label': '6CE', 'order': 6, 'powers': [21, 9], 'representative': 270491663224198413496, 'size': 2592}
  • id: 164263658
    {'aut_label': '6CF', 'centralizer': None, 'counter': 130, 'group_counter': 309, 'group_order': 559872, 'label': '6CF', 'order': 6, 'powers': [24, 9], 'representative': 326448409412261576176, 'size': 2592}
  • id: 164263659
    {'aut_label': '6CG', 'centralizer': None, 'counter': 131, 'group_counter': 309, 'group_order': 559872, 'label': '6CG', 'order': 6, 'powers': [19, 14], 'representative': 855429782035187893687, 'size': 3888}
  • id: 164263660
    {'aut_label': '6CH', 'centralizer': None, 'counter': 132, 'group_counter': 309, 'group_order': 559872, 'label': '6CH', 'order': 6, 'powers': [22, 13], 'representative': 701906607546367557741, 'size': 5184}
  • id: 164263661
    {'aut_label': '6CI', 'centralizer': None, 'counter': 133, 'group_counter': 309, 'group_order': 559872, 'label': '6CI', 'order': 6, 'powers': [27, 13], 'representative': 91177697837863209002, 'size': 5184}
  • id: 164263662
    {'aut_label': '6CJ', 'centralizer': None, 'counter': 134, 'group_counter': 309, 'group_order': 559872, 'label': '6CJ', 'order': 6, 'powers': [24, 15], 'representative': 33108881028041191094, 'size': 7776}
  • id: 164263663
    {'aut_label': '6CK', 'centralizer': None, 'counter': 135, 'group_counter': 309, 'group_order': 559872, 'label': '6CK', 'order': 6, 'powers': [20, 15], 'representative': 545701909639349040601, 'size': 7776}
  • id: 164263664
    {'aut_label': '6CL', 'centralizer': None, 'counter': 136, 'group_counter': 309, 'group_order': 559872, 'label': '6CL', 'order': 6, 'powers': [29, 6], 'representative': 685384511885526394084, 'size': 31104}
  • id: 164263665
    {'aut_label': '9A', 'centralizer': None, 'counter': 137, 'group_counter': 309, 'group_order': 559872, 'label': '9A', 'order': 9, 'powers': [137, 21], 'representative': 465871600104279351248, 'size': 10368}
  • id: 164263666
    {'aut_label': '9A', 'centralizer': None, 'counter': 138, 'group_counter': 309, 'group_order': 559872, 'label': '9B', 'order': 9, 'powers': [138, 21], 'representative': 236569019154933670564, 'size': 10368}
  • id: 164263667
    {'aut_label': '9C', 'centralizer': None, 'counter': 139, 'group_counter': 309, 'group_order': 559872, 'label': '9C', 'order': 9, 'powers': [139, 18], 'representative': 363081134192697135375, 'size': 20736}
  • id: 164263669
    {'aut_label': '9D', 'centralizer': None, 'counter': 140, 'group_counter': 309, 'group_order': 559872, 'label': '9D', 'order': 9, 'powers': [140, 22], 'representative': 524441960130368811731, 'size': 20736}
  • id: 164263670
    {'aut_label': '9C', 'centralizer': None, 'counter': 141, 'group_counter': 309, 'group_order': 559872, 'label': '9E', 'order': 9, 'powers': [141, 18], 'representative': 536869323620296627683, 'size': 20736}
  • id: 164263671
    {'aut_label': '12A', 'centralizer': None, 'counter': 142, 'group_counter': 309, 'group_order': 559872, 'label': '12A', 'order': 12, 'powers': [44, 30], 'representative': 701908370371887362653, 'size': 1296}
  • id: 164263672
    {'aut_label': '12B1', 'centralizer': None, 'counter': 143, 'group_counter': 309, 'group_order': 559872, 'label': '12B1', 'order': 12, 'powers': [111, 32], 'representative': 383482990415904478581, 'size': 1944}
  • id: 164263673
    {'aut_label': '12B1', 'centralizer': None, 'counter': 144, 'group_counter': 309, 'group_order': 559872, 'label': '12B5', 'order': 12, 'powers': [111, 32], 'representative': 383226895498688922981, 'size': 1944}
  • id: 164263674
    {'aut_label': '12C1', 'centralizer': None, 'counter': 145, 'group_counter': 309, 'group_order': 559872, 'label': '12C1', 'order': 12, 'powers': [113, 33], 'representative': 188026744785953312177, 'size': 1944}
  • id: 164263675
    {'aut_label': '12C1', 'centralizer': None, 'counter': 146, 'group_counter': 309, 'group_order': 559872, 'label': '12C5', 'order': 12, 'powers': [113, 33], 'representative': 183161650575726149057, 'size': 1944}
  • id: 164263676
    {'aut_label': '12D', 'centralizer': None, 'counter': 147, 'group_counter': 309, 'group_order': 559872, 'label': '12D', 'order': 12, 'powers': [53, 30], 'representative': 278087472543710431569, 'size': 2592}
  • id: 164263677
    {'aut_label': '12E', 'centralizer': None, 'counter': 148, 'group_counter': 309, 'group_order': 559872, 'label': '12E', 'order': 12, 'powers': [48, 30], 'representative': 118665997310418445577, 'size': 2592}
  • id: 164263678
    {'aut_label': '12F', 'centralizer': None, 'counter': 149, 'group_counter': 309, 'group_order': 559872, 'label': '12F', 'order': 12, 'powers': [111, 32], 'representative': 545792590405300338006, 'size': 3888}
  • id: 164263680
    {'aut_label': '12G', 'centralizer': None, 'counter': 150, 'group_counter': 309, 'group_order': 559872, 'label': '12G', 'order': 12, 'powers': [113, 33], 'representative': 540804460338886962977, 'size': 3888}
  • id: 164263681
    {'aut_label': '12H1', 'centralizer': None, 'counter': 151, 'group_counter': 309, 'group_order': 559872, 'label': '12H1', 'order': 12, 'powers': [67, 37], 'representative': 904337870187641264645, 'size': 3888}
  • id: 164263682
    {'aut_label': '12H1', 'centralizer': None, 'counter': 152, 'group_counter': 309, 'group_order': 559872, 'label': '12H5', 'order': 12, 'powers': [67, 37], 'representative': 853246928015931824765, 'size': 3888}
  • id: 164263683
    {'aut_label': '12I1', 'centralizer': None, 'counter': 153, 'group_counter': 309, 'group_order': 559872, 'label': '12I1', 'order': 12, 'powers': [112, 33], 'representative': 899246555191608876738, 'size': 3888}
  • id: 164263684
    {'aut_label': '12I1', 'centralizer': None, 'counter': 154, 'group_counter': 309, 'group_order': 559872, 'label': '12I5', 'order': 12, 'powers': [112, 33], 'representative': 848155613019899436858, 'size': 3888}
  • id: 164263685
    {'aut_label': '12J1', 'centralizer': None, 'counter': 155, 'group_counter': 309, 'group_order': 559872, 'label': '12J1', 'order': 12, 'powers': [114, 32], 'representative': 156892877392471034401, 'size': 3888}
  • id: 164263686
    {'aut_label': '12J1', 'centralizer': None, 'counter': 156, 'group_counter': 309, 'group_order': 559872, 'label': '12J5', 'order': 12, 'powers': [114, 32], 'representative': 156892166365370004001, 'size': 3888}
  • id: 164263687
    {'aut_label': '12H1', 'centralizer': None, 'counter': 157, 'group_counter': 309, 'group_order': 559872, 'label': '12K1', 'order': 12, 'powers': [68, 36], 'representative': 370093869999637797610, 'size': 3888}
  • id: 164263688
    {'aut_label': '12H1', 'centralizer': None, 'counter': 158, 'group_counter': 309, 'group_order': 559872, 'label': '12K5', 'order': 12, 'powers': [68, 36], 'representative': 370081065277054591210, 'size': 3888}
  • id: 164263689
    {'aut_label': '12L', 'centralizer': None, 'counter': 159, 'group_counter': 309, 'group_order': 559872, 'label': '12L', 'order': 12, 'powers': [61, 30], 'representative': 314530139414437189218, 'size': 5184}
  • id: 164263691
    {'aut_label': '12M', 'centralizer': None, 'counter': 160, 'group_counter': 309, 'group_order': 559872, 'label': '12M', 'order': 12, 'powers': [62, 30], 'representative': 278090924381101682778, 'size': 5184}
  • id: 164263692
    {'aut_label': '12N', 'centralizer': None, 'counter': 161, 'group_counter': 309, 'group_order': 559872, 'label': '12N', 'order': 12, 'powers': [111, 34], 'representative': 275962114898821623727, 'size': 5832}
  • id: 164263693
    {'aut_label': '12N', 'centralizer': None, 'counter': 162, 'group_counter': 309, 'group_order': 559872, 'label': '12O', 'order': 12, 'powers': [111, 35], 'representative': 584332450879682065800, 'size': 5832}
  • id: 164263694
    {'aut_label': '12P', 'centralizer': None, 'counter': 163, 'group_counter': 309, 'group_order': 559872, 'label': '12P', 'order': 12, 'powers': [47, 31], 'representative': 513920346048529188502, 'size': 7776}
  • id: 164263695
    {'aut_label': '12Q', 'centralizer': None, 'counter': 164, 'group_counter': 309, 'group_order': 559872, 'label': '12Q', 'order': 12, 'powers': [81, 36], 'representative': 823832617387196804409, 'size': 7776}
  • id: 164263696
    {'aut_label': '12R', 'centralizer': None, 'counter': 165, 'group_counter': 309, 'group_order': 559872, 'label': '12R', 'order': 12, 'powers': [53, 31], 'representative': 540919681825981093342, 'size': 7776}
  • id: 164263697
    {'aut_label': '12Q', 'centralizer': None, 'counter': 166, 'group_counter': 309, 'group_order': 559872, 'label': '12S', 'order': 12, 'powers': [82, 37], 'representative': 156892877596805133601, 'size': 7776}
  • id: 164263698
    {'aut_label': '12T1', 'centralizer': None, 'counter': 167, 'group_counter': 309, 'group_order': 559872, 'label': '12T1', 'order': 12, 'powers': [95, 36], 'representative': 2458638696645739578, 'size': 7776}
  • id: 164263699
    {'aut_label': '12T1', 'centralizer': None, 'counter': 168, 'group_counter': 309, 'group_order': 559872, 'label': '12T5', 'order': 12, 'powers': [95, 36], 'representative': 2440775528998737978, 'size': 7776}
  • id: 164263700
    {'aut_label': '12T1', 'centralizer': None, 'counter': 169, 'group_counter': 309, 'group_order': 559872, 'label': '12U1', 'order': 12, 'powers': [96, 37], 'representative': 4029021028057092614, 'size': 7776}
  • id: 164263702
    {'aut_label': '12T1', 'centralizer': None, 'counter': 170, 'group_counter': 309, 'group_order': 559872, 'label': '12U5', 'order': 12, 'powers': [96, 37], 'representative': 4059531587736939014, 'size': 7776}
  • id: 164263703
    {'aut_label': '12V', 'centralizer': None, 'counter': 171, 'group_counter': 309, 'group_order': 559872, 'label': '12V', 'order': 12, 'powers': [111, 38], 'representative': 701729501534899413981, 'size': 11664}
  • id: 164263704
    {'aut_label': '12W', 'centralizer': None, 'counter': 172, 'group_counter': 309, 'group_order': 559872, 'label': '12W', 'order': 12, 'powers': [111, 39], 'representative': 572900991752017113143, 'size': 11664}
  • id: 164263705
    {'aut_label': '12X', 'centralizer': None, 'counter': 173, 'group_counter': 309, 'group_order': 559872, 'label': '12X', 'order': 12, 'powers': [113, 40], 'representative': 88501504098299125810, 'size': 11664}
  • id: 164263706
    {'aut_label': '12Y', 'centralizer': None, 'counter': 174, 'group_counter': 309, 'group_order': 559872, 'label': '12Y', 'order': 12, 'powers': [119, 41], 'representative': 263426629233953607258, 'size': 23328}
  • id: 164263707
    {'aut_label': '12Y', 'centralizer': None, 'counter': 175, 'group_counter': 309, 'group_order': 559872, 'label': '12Z', 'order': 12, 'powers': [120, 42], 'representative': 587433703339677168014, 'size': 23328}
  • id: 164263708
    {'aut_label': '18A', 'centralizer': None, 'counter': 176, 'group_counter': 309, 'group_order': 559872, 'label': '18A', 'order': 18, 'powers': [137, 101], 'representative': 650508728401302674412, 'size': 31104}
  • id: 164263709
    {'aut_label': '18A', 'centralizer': None, 'counter': 177, 'group_counter': 309, 'group_order': 559872, 'label': '18B', 'order': 18, 'powers': [138, 101], 'representative': 139124694984423242523, 'size': 31104}
• group 559872.lw does not appear in gps_qchar
• group 559872.lw does not appear in gps_char
• gps_subgroup_search •

  Column	Type
  Agroup	boolean
  Zgroup	boolean
  abelian	boolean
  ambient	text
  ambient_counter	integer
  ambient_order	numeric
  ambient_tex	text
  central	boolean
  central_factor	boolean
  centralizer_order	numeric
  characteristic	boolean
  core_order	numeric
  counter	integer
  cyclic	boolean
  direct	boolean
  hall	numeric
  label	text
  maximal	boolean
  maximal_normal	boolean
  metabelian	boolean
  metacyclic	boolean
  minimal	boolean
  minimal_normal	boolean
  nilpotent	boolean
  normal	boolean
  old_label	text
  outer_equivalence	boolean
  perfect	boolean
  proper	boolean
  quotient	text
  quotient_Agroup	boolean
  quotient_abelian	boolean
  quotient_cyclic	boolean
  quotient_hash	bigint
  quotient_metabelian	boolean
  quotient_nilpotent	boolean
  quotient_order	numeric
  quotient_simple	boolean
  quotient_solvable	boolean
  quotient_supersolvable	boolean
  quotient_tex	text
  simple	boolean
  solvable	boolean
  special_labels	text[]
  split	boolean
  standard_generators	boolean
  stem	boolean
  subgroup	text
  subgroup_hash	bigint
  subgroup_order	numeric
  subgroup_tex	text
  supersolvable	boolean
  sylow	smallint

  
  
  • id: 227126130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 559872, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '559872.lw.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, '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': '559872.lw', 'subgroup_hash': 5225393530267235522, 'subgroup_order': 559872, 'subgroup_tex': 'C_3^6.C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 279936, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.2.A', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '279936.kq', 'subgroup_hash': 5797817892626894546, 'subgroup_order': 279936, 'subgroup_tex': 'C_3^6.C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126352
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 279936, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '279936.li', 'subgroup_hash': 2300175376283795754, 'subgroup_order': 279936, 'subgroup_tex': 'C_3^6.C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126463
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 279936, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.2.C', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '279936.ld', 'subgroup_hash': 5191151052135726066, 'subgroup_order': 279936, 'subgroup_tex': 'C_3^6.C_2^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 93312, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, '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': 4180934677241163436, 'subgroup_order': 186624, 'subgroup_tex': 'C_3^6.C_2^5.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 139968, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.4.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '139968.il', 'subgroup_hash': 5577375599796130639, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^6.C_2^4:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.4.B', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, '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': '139968.ii', 'subgroup_hash': 2633360467956557097, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^3.C_6^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126907
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.4.C', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, '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': '139968.j', 'subgroup_hash': 8118045935722796121, 'subgroup_order': 139968, 'subgroup_tex': 'C_3^6:C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 93312, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 608380945256032537, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^4.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, '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': 3302519774128523141, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^4.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, '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': 1867486635275120501, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, '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': 3327907458606863683, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126164
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, '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': 5492332200277717697, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126175
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, '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': 4220432609860327564, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^4.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126186
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, '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': 1516418852869429020, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^4.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126197
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, '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': 752535141108439284, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^4.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, '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': 2624415265106007181, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^4.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 46656, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, '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': 2166833741647587046, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 46656, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.6.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, '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': 4910984264044612315, 'subgroup_order': 93312, 'subgroup_tex': 'C_3^6.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, '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': '69984.fh', 'subgroup_hash': 4661714835825224956, 'subgroup_order': 69984, 'subgroup_tex': 'C_6^2.C_3^4:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, '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': '69984.et', 'subgroup_hash': 8600534953555024501, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, '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': '69984.fi', 'subgroup_hash': 7749381191568221425, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7089219303109197366, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.C_2^4.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, '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': '69984.fi', 'subgroup_hash': 7749381191568221425, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, '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': '69984.h', 'subgroup_hash': 4814747757799365679, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6:C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126308
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, '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': '69984.p', 'subgroup_hash': 6223392654250980061, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126319
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, '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': '69984.m', 'subgroup_hash': 1356545172062492268, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.C_2^4.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126330
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, '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': '69984.m', 'subgroup_hash': 1356545172062492268, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6.C_2^4.S_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126341
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, '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': '69984.h', 'subgroup_hash': 4814747757799365679, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^6:C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.8.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, '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': '69984.p', 'subgroup_hash': 6223392654250980061, 'subgroup_order': 69984, 'subgroup_tex': 'C_3^5:D_6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126364
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 46656, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7068667559697133147, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 227126375
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, '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': 9173151587739159445, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, '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': 6411595700492242868, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^5.C_3:D_4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, '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': 8608401082536474743, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^4.D_6\\wr C_2.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126408
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, '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': 7692979779675684191, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2.C_2^5', 'supersolvable': False, 'sylow': 0}
  • id: 227126419
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, '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': 2342274060607504255, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126430
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, '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': 510945036613689339, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, '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': 8608401082536474743, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, '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': 734831721182354695, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, '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': 8608401082536474743, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^4.D_6\\wr C_2.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, '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': 683230365161169590, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, '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': 3197775277545717125, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, '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': 510945036613689339, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, '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': 510945036613689339, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, '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': 5413116922237540958, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, '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': 3530772200379742751, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126541
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, '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': 7901209864065605864, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126552
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, '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': 8608401082536474743, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, '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': 8374148963253002059, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1', 'outer_equivalence': True, 'perfect': False, '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': 6458815477890902507, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1', 'outer_equivalence': True, 'perfect': False, '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': 8608401082536474743, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1', 'outer_equivalence': True, 'perfect': False, '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': 8608401082536474743, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^4.D_6\\wr C_2.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1', 'outer_equivalence': True, 'perfect': False, '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': 8374148963253002059, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1', 'outer_equivalence': True, 'perfect': False, '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': 734831721182354695, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^5.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1', 'outer_equivalence': True, 'perfect': False, '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': 6458815477890902507, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^5.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1', 'outer_equivalence': True, 'perfect': False, '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': 3970256358966135366, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126652
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1', 'outer_equivalence': True, 'perfect': False, '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': 8164043480209888828, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^5.C_3:D_4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1', 'outer_equivalence': True, 'perfect': False, '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': 4617910592972433171, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1', 'outer_equivalence': True, 'perfect': False, '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': 3075455748178474907, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1', 'outer_equivalence': True, 'perfect': False, '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': 813521448219481239, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1', 'outer_equivalence': True, 'perfect': False, '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': 3003980035624344064, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^4.C_6^2.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1', 'outer_equivalence': True, 'perfect': False, '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': 40823479920551986, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2.C_2^5', 'supersolvable': False, 'sylow': 0}
  • id: 227126719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1', 'outer_equivalence': True, 'perfect': False, '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': 9057541740317096319, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1', 'outer_equivalence': True, 'perfect': False, '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': 3151339149299703980, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1', 'outer_equivalence': True, 'perfect': False, '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': 9057541740317096319, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1', 'outer_equivalence': True, 'perfect': False, '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': 2156679736962415692, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1', 'outer_equivalence': True, 'perfect': False, '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': 6759257206892262065, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1', 'outer_equivalence': True, 'perfect': False, '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': 2612067439787378347, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1', 'outer_equivalence': True, 'perfect': False, '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': 3151339149299703980, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bn1', 'outer_equivalence': True, 'perfect': False, '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': 1398499281287278490, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1', 'outer_equivalence': True, 'perfect': False, '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': 8398015361063468680, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^4.C_6^2.C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1', 'outer_equivalence': True, 'perfect': False, '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': 361765369323614749, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1', 'outer_equivalence': True, 'perfect': False, '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': 3165490960556907383, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1', 'outer_equivalence': True, 'perfect': False, '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': 2437636929952142122, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1', 'outer_equivalence': True, 'perfect': False, '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': 4239048060621557984, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1', 'outer_equivalence': True, 'perfect': False, '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': '46656.y', 'subgroup_hash': 3987093188507500600, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126874
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1', 'outer_equivalence': True, 'perfect': False, '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': '46656.y', 'subgroup_hash': 3987093188507500600, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bv1', 'outer_equivalence': True, 'perfect': False, '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': '46656.y', 'subgroup_hash': 3987093188507500600, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.12.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bw1', 'outer_equivalence': True, 'perfect': False, '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': '46656.y', 'subgroup_hash': 3987093188507500600, 'subgroup_order': 46656, 'subgroup_tex': 'C_3^6:C_2\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126908
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, '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': '34992.dp', 'subgroup_hash': 102809146006925307, 'subgroup_order': 34992, 'subgroup_tex': 'C_6^2.C_3\\wr A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, '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': '34992.ea', 'subgroup_hash': 2629802307446330472, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^5.(S_3\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, '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': '34992.ec', 'subgroup_hash': 5259153456382818826, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^5:D_6.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, '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': '34992.ec', 'subgroup_hash': 5259153456382818826, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^5:D_6.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, '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': '34992.ba', 'subgroup_hash': 2689379680719931661, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6:(C_2^2:A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, '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': '34992.ba', 'subgroup_hash': 2689379680719931661, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6:(C_2^2:A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, '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': '34992.ba', 'subgroup_hash': 2689379680719931661, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6:(C_2^2:A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, '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': '34992.z', 'subgroup_hash': 6894873872155127119, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, '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': '34992.z', 'subgroup_hash': 6894873872155127119, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, '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': '34992.ba', 'subgroup_hash': 2689379680719931661, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6:(C_2^2:A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.16.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, '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': '34992.ba', 'subgroup_hash': 2689379680719931661, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6:(C_2^2:A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126942
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.18.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, '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': 5700014980097704673, 'subgroup_order': 31104, 'subgroup_tex': 'C_3^5.C_2^4.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.18.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, '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': 266300703118843139, 'subgroup_order': 31104, 'subgroup_tex': 'C_3^5.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 23328, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6244292881112398141, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 23328, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, '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': 8223243507191048194, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, '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': 9009948751024660394, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, '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': 9009948751024660394, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.D_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, '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': 9009948751024660394, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, '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': 9009948751024660394, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126136
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, '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': 8318134687151164002, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, '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': 3444601254431247117, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_6.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, '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': 4333611414200424064, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, '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': 8396394846720189864, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.(C_{12}\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, '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': 6715994133103664320, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_2^4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, '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': 2456017717584838798, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126146
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, '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': 2456017717584838798, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, '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': 41086210421305338, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, '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': 7230148969063641557, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1', 'outer_equivalence': True, 'perfect': False, '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': 8318134687151164002, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1', 'outer_equivalence': True, 'perfect': False, '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': 1497495241319377599, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1', 'outer_equivalence': True, 'perfect': False, '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': 8318134687151164002, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126152
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1', 'outer_equivalence': True, 'perfect': False, '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': 2182036038573997430, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126154
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1', 'outer_equivalence': True, 'perfect': False, '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': 1416383836467067887, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1', 'outer_equivalence': True, 'perfect': False, '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': 575434036859630044, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.D_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126158
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1', 'outer_equivalence': True, 'perfect': False, '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': 2182036038573997430, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1', 'outer_equivalence': True, 'perfect': False, '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': 8223243507191048194, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bh1', 'outer_equivalence': True, 'perfect': False, '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': 1416383836467067887, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bi1', 'outer_equivalence': True, 'perfect': False, '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': 9009948751024660394, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126162
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bj1', 'outer_equivalence': True, 'perfect': False, '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': 575434036859630044, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126163
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bk1', 'outer_equivalence': True, 'perfect': False, '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': 9009948751024660394, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126165
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bl1', 'outer_equivalence': True, 'perfect': False, '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': 4534891277406410398, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126166
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bm1', 'outer_equivalence': True, 'perfect': False, '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': 6058618402848689811, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bn1', 'outer_equivalence': True, 'perfect': False, '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': 7508166748631020771, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_6.C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bo1', 'outer_equivalence': True, 'perfect': False, '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': 7508166748631020771, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126169
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bp1', 'outer_equivalence': True, 'perfect': False, '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': 2456017717584838798, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126170
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bq1', 'outer_equivalence': True, 'perfect': False, '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': 2456017717584838798, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.br1', 'outer_equivalence': True, 'perfect': False, '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': 2456017717584838798, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126172
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1', 'outer_equivalence': True, 'perfect': False, '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': 2343664491708682057, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126173
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bt1', 'outer_equivalence': True, 'perfect': False, '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': 7801314158921746420, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126174
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1', 'outer_equivalence': True, 'perfect': False, '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': 2914553298719008825, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126176
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1', 'outer_equivalence': True, 'perfect': False, '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': 6136043706076375489, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126177
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1', 'outer_equivalence': True, 'perfect': False, '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': 7951807917472232930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126179
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.by1', 'outer_equivalence': True, 'perfect': False, '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': 7490627827309170252, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126180
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bz1', 'outer_equivalence': True, 'perfect': False, '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': 1659447752879100757, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126181
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ca1', 'outer_equivalence': True, 'perfect': False, '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': 1965719201125136580, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126182
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cb1', 'outer_equivalence': True, 'perfect': False, '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': 6312839968643102496, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126183
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1', 'outer_equivalence': True, 'perfect': False, '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': 6946732157061139528, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126184
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1', 'outer_equivalence': True, 'perfect': False, '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': 5261378304153122779, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126185
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1', 'outer_equivalence': True, 'perfect': False, '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': 5629183917111081423, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126187
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1', 'outer_equivalence': True, 'perfect': False, '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': 7951807917472232930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126188
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1', 'outer_equivalence': True, 'perfect': False, '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': 1897718261945143606, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1', 'outer_equivalence': True, 'perfect': False, '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': 6312839968643102496, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126190
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1', 'outer_equivalence': True, 'perfect': False, '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': 208237543768760401, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126191
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.D_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126192
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1', 'outer_equivalence': True, 'perfect': False, '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': 7951807917472232930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126193
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cl1', 'outer_equivalence': True, 'perfect': False, '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': 208237543768760401, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126194
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cm1', 'outer_equivalence': True, 'perfect': False, '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': 1265597237479450990, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cn1', 'outer_equivalence': True, 'perfect': False, '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': 7801314158921746420, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.co1', 'outer_equivalence': True, 'perfect': False, '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': 3155521867654420275, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126198
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cp1', 'outer_equivalence': True, 'perfect': False, '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': 2716969616535862999, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126199
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cq1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cr1', 'outer_equivalence': True, 'perfect': False, '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': 5669090363516194699, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126201
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cs1', 'outer_equivalence': True, 'perfect': False, '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': 8223243507191048194, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126202
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ct1', 'outer_equivalence': True, 'perfect': False, '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': 9009948751024660394, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126203
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1', 'outer_equivalence': True, 'perfect': False, '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': 5202490323145008602, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.D_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126204
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cv1', 'outer_equivalence': True, 'perfect': False, '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': 8318134687151164002, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126205
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cw1', 'outer_equivalence': True, 'perfect': False, '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': 5669090363516194699, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126206
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx1', 'outer_equivalence': True, 'perfect': False, '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': 9009948751024660394, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cy1', 'outer_equivalence': True, 'perfect': False, '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': 1897718261945143606, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126209
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cz1', 'outer_equivalence': True, 'perfect': False, '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': 1795557925131121907, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.da1', 'outer_equivalence': True, 'perfect': False, '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': 6876389003451251353, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.db1', 'outer_equivalence': True, 'perfect': False, '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': 5171473298835405346, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.D_6:C_4:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dc1', 'outer_equivalence': True, 'perfect': False, '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': 4619965942527604980, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dd1', 'outer_equivalence': True, 'perfect': False, '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': 8905862969014779526, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.D_6:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1', 'outer_equivalence': True, 'perfect': False, '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': 6876389003451251353, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.df1', 'outer_equivalence': True, 'perfect': False, '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': 1728806998721349743, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.(C_4.D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dg1', 'outer_equivalence': True, 'perfect': False, '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': 6876389003451251353, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dh1', 'outer_equivalence': True, 'perfect': False, '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': 1965719201125136580, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.di1', 'outer_equivalence': True, 'perfect': False, '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': 5875484477590780701, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dj1', 'outer_equivalence': True, 'perfect': False, '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': 4355430546143901145, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 227126221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dk1', 'outer_equivalence': True, 'perfect': False, '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': 1897718261945143606, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dl1', 'outer_equivalence': True, 'perfect': False, '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': 6312839968643102496, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dm1', 'outer_equivalence': True, 'perfect': False, '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': 7490627827309170252, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dn1', 'outer_equivalence': True, 'perfect': False, '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': 5171473298835405346, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.D_6:C_4:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.do1', 'outer_equivalence': True, 'perfect': False, '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': 5726515916367426717, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.(D_6.D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dp1', 'outer_equivalence': True, 'perfect': False, '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': 1602395466420191206, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_4^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dq1', 'outer_equivalence': True, 'perfect': False, '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': 895491281241004127, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126228
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dr1', 'outer_equivalence': True, 'perfect': False, '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': 176889538652350037, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_6.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ds1', 'outer_equivalence': True, 'perfect': False, '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': 1529340190382242392, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dt1', 'outer_equivalence': True, 'perfect': False, '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': 7186816222633167291, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.du1', 'outer_equivalence': True, 'perfect': False, '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': 3709307816778312944, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dv1', 'outer_equivalence': True, 'perfect': False, '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': 7034609365494058808, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126234
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dw1', 'outer_equivalence': True, 'perfect': False, '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': 3169183837605719365, 'subgroup_order': 23328, 'subgroup_tex': '(C_3^5\\times C_6).C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dx1', 'outer_equivalence': True, 'perfect': False, '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': 1529340190382242392, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dy1', 'outer_equivalence': True, 'perfect': False, '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': 7186816222633167291, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dz1', 'outer_equivalence': True, 'perfect': False, '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': 7985794199177055633, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^3.C_6^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ea1', 'outer_equivalence': True, 'perfect': False, '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': '23328.gl', 'subgroup_hash': 8071431671743114400, 'subgroup_order': 23328, 'subgroup_tex': '(C_3^3\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eb1', 'outer_equivalence': True, 'perfect': False, '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': '23328.gj', 'subgroup_hash': 2044693089275019873, 'subgroup_order': 23328, 'subgroup_tex': '(C_3^3\\times C_6^2).S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ec1', 'outer_equivalence': True, 'perfect': False, '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': 5765228179707392335, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ed1', 'outer_equivalence': True, 'perfect': False, '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': 6993090365765039457, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ee1', 'outer_equivalence': True, 'perfect': False, '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': 2791406443359560728, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ef1', 'outer_equivalence': True, 'perfect': False, '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': 892628184716961126, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126246
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eg1', 'outer_equivalence': True, 'perfect': False, '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': 4598964012758753681, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eh1', 'outer_equivalence': True, 'perfect': False, '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': 2234881432173561073, 'subgroup_order': 23328, 'subgroup_tex': '(C_3^5\\times C_6).C_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126248
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ei1', 'outer_equivalence': True, 'perfect': False, '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': 7687244559361622590, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126249
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ej1', 'outer_equivalence': True, 'perfect': False, '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': 81319308721045951, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ek1', 'outer_equivalence': True, 'perfect': False, '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': 7253632072093408531, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.el1', 'outer_equivalence': True, 'perfect': False, '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': 7253632072093408531, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.em1', 'outer_equivalence': True, 'perfect': False, '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': 31596375027809905, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.en1', 'outer_equivalence': True, 'perfect': False, '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': 8252009931052584088, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.(C_{12}\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eo1', 'outer_equivalence': True, 'perfect': False, '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': 6829559345201375691, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ep1', 'outer_equivalence': True, 'perfect': False, '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': 2528172751119169657, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eq1', 'outer_equivalence': True, 'perfect': False, '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': 2164706162023654834, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.ER', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.er1', 'outer_equivalence': True, 'perfect': False, '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': 81319308721045951, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.ES', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.es1', 'outer_equivalence': True, 'perfect': False, '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': 6136490364733810191, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2.C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.ET', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.et1', 'outer_equivalence': True, 'perfect': False, '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': 2164706162023654834, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eu1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bq', 'subgroup_hash': 3321270330191417480, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_{12}:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ev1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ew1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bq', 'subgroup_hash': 3321270330191417480, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_{12}:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126265
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ex1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bg', 'subgroup_hash': 384851452488720713, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6:C_2^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ey1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.EZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ez1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126268
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fa1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fb1', 'outer_equivalence': True, 'perfect': False, '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': 5902720563681028683, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126270
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fc1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126271
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fd1', 'outer_equivalence': True, 'perfect': False, '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': 5902720563681028683, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126272
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fe1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bg', 'subgroup_hash': 384851452488720713, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6:C_2^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126273
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ff1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bq', 'subgroup_hash': 3321270330191417480, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_{12}:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126274
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fg1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bg', 'subgroup_hash': 384851452488720713, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6:C_2^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126276
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fh1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bg', 'subgroup_hash': 384851452488720713, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6:C_2^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126277
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fi1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bg', 'subgroup_hash': 384851452488720713, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6:C_2^3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fj1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bk', 'subgroup_hash': 4714706730556463421, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5:D_6.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126279
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fk1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bk', 'subgroup_hash': 4714706730556463421, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^5:D_6.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fl1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126281
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fm1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126282
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fn1', 'outer_equivalence': True, 'perfect': False, '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': 5902720563681028683, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126283
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fo1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126284
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fp1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126285
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fq1', 'outer_equivalence': True, 'perfect': False, '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': 5902720563681028683, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fr1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fs1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ft1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fu1', 'outer_equivalence': True, 'perfect': False, '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': 5902720563681028683, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fv1', 'outer_equivalence': True, 'perfect': False, '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': 5902720563681028683, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^6.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fw1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fx1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.24.FY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.fy1', 'outer_equivalence': True, 'perfect': False, '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': '23328.bc', 'subgroup_hash': 8776325882520248930, 'subgroup_order': 23328, 'subgroup_tex': 'C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, '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': '20736.cm', 'subgroup_hash': 5868933892363537971, 'subgroup_order': 20736, 'subgroup_tex': 'S_3^4:(C_2\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.ei', 'subgroup_hash': 5270193385651284609, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^5.(C_6\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.ep', 'subgroup_hash': 2747873475092840641, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': 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': 2571402229033553937, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^4.C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.ck', 'subgroup_hash': 4567682212904675162, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.cd', 'subgroup_hash': 1796585124855714195, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.cd', 'subgroup_hash': 1796585124855714195, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.cd', 'subgroup_hash': 1796585124855714195, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.cl', 'subgroup_hash': 2621064800206398668, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126305
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.eh', 'subgroup_hash': 6198948203698366938, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126306
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.cl', 'subgroup_hash': 2621064800206398668, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126307
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.eh', 'subgroup_hash': 6198948203698366938, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.32.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17496.cl', 'subgroup_hash': 2621064800206398668, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126310
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, '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': 7281097177657747957, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, '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': 3697836707831949249, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126312
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, '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': 7506229295869530425, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126313
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, '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': 8968701508403963499, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^4.C_3:D_4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126314
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, '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': 1192427147664465002, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126315
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, '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': 8684774609072445800, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126316
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, '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': 9099829573743547736, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126317
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, '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': 561765051292877887, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126318
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, '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': 6516492480479895852, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, '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': 3977957658910212822, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126321
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, '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': 6516492480479895852, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, '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': 3977957658910212822, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126323
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, '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': 7506229295869530425, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126324
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, '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': 8968701508403963499, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^4.C_3:D_4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126325
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, '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': 7506229295869530425, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126326
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, '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': 1572365930176063374, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126327
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, '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': 9099829573743547736, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126328
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, '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': 561765051292877887, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126329
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', 'outer_equivalence': True, 'perfect': False, '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': 782217360048882738, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', 'outer_equivalence': True, 'perfect': False, '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': 9002921183342087216, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126332
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', 'outer_equivalence': True, 'perfect': False, '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': 1495583755944215009, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^4.(C_2\\times C_6).C_2^4', 'supersolvable': False, 'sylow': 0}
  • id: 227126333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1', 'outer_equivalence': True, 'perfect': False, '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': 7256269227783423031, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126334
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1', 'outer_equivalence': True, 'perfect': False, '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': 8064943040474794916, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126335
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1', 'outer_equivalence': True, 'perfect': False, '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': 8427508876649716005, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126336
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1', 'outer_equivalence': True, 'perfect': False, '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': 4747584011650819014, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126337
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1', 'outer_equivalence': True, 'perfect': False, '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': 5920850949822816530, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126338
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ba1', 'outer_equivalence': True, 'perfect': False, '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': 5920850949822816530, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126339
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1', 'outer_equivalence': True, 'perfect': False, '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': 6380250503809823134, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126340
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1', 'outer_equivalence': True, 'perfect': False, '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': 6380250503809823134, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bd1', 'outer_equivalence': True, 'perfect': False, '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': 2530802079273513679, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126343
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1', 'outer_equivalence': True, 'perfect': False, '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': 9183686102294595921, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bf1', 'outer_equivalence': True, 'perfect': False, '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': 312976494944158344, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^4.(C_3\\times C_2^5.C_2)', 'supersolvable': False, 'sylow': 0}
  • id: 227126345
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bg1', 'outer_equivalence': True, 'perfect': False, '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': 563586210640782586, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126346
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bh1', 'outer_equivalence': True, 'perfect': False, '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': 6441243791077728546, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126347
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bi1', 'outer_equivalence': True, 'perfect': False, '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': 5522585748114891967, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1', 'outer_equivalence': True, 'perfect': False, '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': 6523079305320400555, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 227126349
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1', 'outer_equivalence': True, 'perfect': False, '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': 8064943040474794916, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126350
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1', 'outer_equivalence': True, 'perfect': False, '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': 8427508876649716005, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126351
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1', 'outer_equivalence': True, 'perfect': False, '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': 1547021237320512976, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.D_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126354
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1', 'outer_equivalence': True, 'perfect': False, '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': 1052032070791515372, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^4.D_{12}:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1', 'outer_equivalence': True, 'perfect': False, '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': 5920850949822816530, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126356
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1', 'outer_equivalence': True, 'perfect': False, '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': 6380250503809823134, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126357
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1', 'outer_equivalence': True, 'perfect': False, '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': 6439086800539652225, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126358
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.36.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1', 'outer_equivalence': True, 'perfect': False, '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': 4246665208082657837, 'subgroup_order': 15552, 'subgroup_tex': 'C_3^5.C_2^3.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 11664, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5636321934058844511, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 11664, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126361
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126363
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2735486710913243641, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fB', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fC', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fD', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126370
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126371
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2735486710913243641, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126373
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.lB', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.lC', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126376
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 4194970215943679881, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5030504032202617747, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2735486710913243641, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126379
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7826985657616248990, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126380
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 1425665953610939483, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126381
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.r1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7779361525104033554, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126382
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7272190538923289900, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126383
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.t1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126384
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.u1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126385
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.v1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 1425665953610939483, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126387
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.w1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 1425665953610939483, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.x1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2735486710913243641, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.y1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 4704807466899321907, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.z1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5925708763017807932, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126391
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.baB', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 1425665953610939483, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126392
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.baC', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 1425665953610939483, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bb1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2735486710913243641, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bc1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2735486710913243641, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126395
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126396
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.be1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7826985657616248990, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bf1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 464220220992917933, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bg1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5377570539422286596, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126400
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bh1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5377570539422286596, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bi1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2986940936352665975, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bj1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126404
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bl1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 1425665953610939483, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bm1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 1425665953610939483, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 1425665953610939483, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126407
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 6944280701234929003, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bp1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2735486710913243641, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bq1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126411
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2045816226714732281, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7425560839207602543, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bt1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bu1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126415
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 539086016557348176, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126416
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bw1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 766788833787936508, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126417
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bx1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7674602939066518002, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.by1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8772687073164860700, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bz1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8772687073164860700, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ca1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2045816226714732281, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126422
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cb1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2045816226714732281, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cc1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cd1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2045816226714732281, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126425
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ce1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2735486710913243641, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126426
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cf1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2735486710913243641, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126427
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cg1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3870750937451594960, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126428
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ch1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7826985657616248990, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126429
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ci1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 9037673993322972821, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cj1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126432
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ck1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3875876828674349339, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cl1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cm1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5887722784045948334, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cn1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7425560839207602543, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.co1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cp1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3566543984831311417, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cq1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cr1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 766788833787936508, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cs1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7674602939066518002, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ct1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 4377005509791510282, 'subgroup_order': 11664, 'subgroup_tex': '(C_3^5\\times C_6).C_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cu1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 4377005509791510282, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cv1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8180389887416064328, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126445
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cw1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2045816226714732281, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cx1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 930162984200414709, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cy1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 6474872158494573293, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cz1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7265936174040276683, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.da1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8180389887416064328, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126450
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.db1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8180389887416064328, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dc1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8180389887416064328, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dd1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3566543984831311417, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.de1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.df1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7674602939066518002, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126456
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dg1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8772687073164860700, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126457
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dh1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 4377005509791510282, 'subgroup_order': 11664, 'subgroup_tex': '(C_3^5\\times C_6).C_2^2.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126458
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.di1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 930162984200414709, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126459
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dj1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7265936174040276683, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126460
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dk1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5068182763000196557, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126461
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dl1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 9093747410323043009, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126462
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dm1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8180389887416064328, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dn1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5068182763000196557, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.do1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 9047155306437262820, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126467
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dp1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3904309008466486233, 'subgroup_order': 11664, 'subgroup_tex': '(C_3^5\\times C_6).C_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126468
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dq1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3964478006540351279, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126469
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dr1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2459504829922643093, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_4^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126470
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ds1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8355694595231365624, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126471
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dt1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8070340678023490183, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.du1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8185570280061032116, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dv1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8185570280061032116, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126474
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dw1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 1271021566916869590, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126476
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dx1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dy1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 930162984200414709, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126478
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dz1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 9093747410323043009, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126479
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ea1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7265936174040276683, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126480
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eb1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8180389887416064328, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ec1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126482
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ed1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2045816226714732281, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ee1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126484
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ef1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 930162984200414709, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eg1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 9093747410323043009, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eh1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7265936174040276683, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126488
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ei1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8180389887416064328, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126489
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ej1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8180389887416064328, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ek1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 8180389887416064328, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126491
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.el1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3566543984831311417, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227126492
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.em1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5068182763000196557, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126493
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.ER', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.en1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 472107549014112311, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126494
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.ES', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eo1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 9093747410323043009, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126495
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.ET', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ep1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 4743047561509310881, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126496
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eq1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 4743047561509310881, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.er1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 9083522900097463848, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.(C_6\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 227126499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.es1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 280631567219266045, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126500
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EX', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.et1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3090050723974798692, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126501
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eu1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3090050723974798692, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126502
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.EZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ev1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5230618756363534578, 'subgroup_order': 11664, 'subgroup_tex': 'C_3\\times C_3^5.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ew1', 'outer_equivalence': True, 'perfect': False, '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': '11664.fu', 'subgroup_hash': 3261503099577954566, 'subgroup_order': 11664, 'subgroup_tex': '(C_3^3\\times C_6^2):A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ex1', 'outer_equivalence': True, 'perfect': False, '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': '11664.fs', 'subgroup_hash': 1128315374088684399, 'subgroup_order': 11664, 'subgroup_tex': '(C_3^3\\times C_6^2).A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ey1', 'outer_equivalence': True, 'perfect': False, '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': '11664.fz', 'subgroup_hash': 2315907378402822896, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126506
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ez1', 'outer_equivalence': True, 'perfect': False, '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': '11664.fn', 'subgroup_hash': 683248466890019260, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126507
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fa1', 'outer_equivalence': True, 'perfect': False, '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': '11664.fg', 'subgroup_hash': 4073617038561463600, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.(C_6\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fb1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3363746085705724552, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.(C_6\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 227126510
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fc1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5001799824249695713, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126511
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fd1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5636321934058844511, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fe1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7936068927506954207, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.(C_6\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 227126513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ff1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 3802240717299006500, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fg1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5364691784462105810, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126515
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fh1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 6319227933702980649, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fi1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 9174334353335488939, 'subgroup_order': 11664, 'subgroup_tex': '(C_3^5\\times C_6).C_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fj1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 7936068927506954207, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.(C_6\\times D_4)', 'supersolvable': True, 'sylow': 0}
  • id: 227126518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fk1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 9174334353335488939, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4.C_6^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fl1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5636321934058844511, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fm1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fn1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fo1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fp1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fq1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cm', 'subgroup_hash': 4430434000555957391, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:D_{12}:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fr1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fs1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 965574430148079371, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ft1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2259942204192075790, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fu1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 965574430148079371, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.FZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fv1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2259942204192075790, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^2.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fwB', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126533
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fwC', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126534
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fx1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fyB', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fyC', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.fz1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ga1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gb1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126540
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gc1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cm', 'subgroup_hash': 4430434000555957391, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:D_{12}:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126542
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gd1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ge1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gf1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 6851367555991339112, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126545
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gg1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cg', 'subgroup_hash': 5348409027808355560, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gh1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126547
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gi1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gj1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gk1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gl1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126551
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gm1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126553
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gn1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 6851367555991339112, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126554
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.go1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gp1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gq1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cg', 'subgroup_hash': 5348409027808355560, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gr1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126558
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gs1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.GZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gt1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 6851367555991339112, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gu1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cg', 'subgroup_hash': 5348409027808355560, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gv1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gw1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gx1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 6851367555991339112, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gy1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cg', 'subgroup_hash': 5348409027808355560, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:D_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.gz1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126567
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ha1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126568
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hbB', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hbC', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hcB', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hcC', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HL', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hd1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126573
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.heB', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.heC', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hf1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hg1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 965574430148079371, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^3.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hh1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2259942204192075790, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^2.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hi1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 965574430148079371, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.D_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hj1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 2259942204192075790, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5.C_6.C_2^2.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hk1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hl1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126584
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hm1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cb', 'subgroup_hash': 4246210895308136341, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 227126585
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hn1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cb', 'subgroup_hash': 4246210895308136341, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 227126587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ho1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hp1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.HZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hqB', 'outer_equivalence': True, 'perfect': False, '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': '11664.cb', 'subgroup_hash': 4246210895308136341, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 227126590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hqC', 'outer_equivalence': True, 'perfect': False, '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': '11664.cb', 'subgroup_hash': 4246210895308136341, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 227126591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hr1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cb', 'subgroup_hash': 4246210895308136341, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 227126592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hs1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cj', 'subgroup_hash': 6211947034589030353, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:D_{12}:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.ID', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ht1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hu1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cb', 'subgroup_hash': 4246210895308136341, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 227126595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hv1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hw1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hx1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.II', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hy1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.hz1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ia1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ib1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ic1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.id1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ie1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.if1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ig1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ih1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ii1', 'outer_equivalence': True, 'perfect': False, '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': '11664.bu', 'subgroup_hash': 8101063118467249249, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ij1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cc', 'subgroup_hash': 7520893705400725096, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IU', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ik1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.il1', 'outer_equivalence': True, 'perfect': False, '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': None, 'subgroup_hash': 5383307682686422122, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 227126614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.im1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cb', 'subgroup_hash': 4246210895308136341, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 227126615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.in1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cj', 'subgroup_hash': 6211947034589030353, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:D_{12}:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.io1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cj', 'subgroup_hash': 6211947034589030353, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:D_{12}:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.IZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ip1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cb', 'subgroup_hash': 4246210895308136341, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(S_3\\times D_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 227126618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.48.JA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.iq1', 'outer_equivalence': True, 'perfect': False, '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': '11664.cj', 'subgroup_hash': 6211947034589030353, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^5:D_{12}:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, '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': '10368.en', 'subgroup_hash': 6583907325997176286, 'subgroup_order': 10368, 'subgroup_tex': 'S_3^4:C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, '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': '10368.eo', 'subgroup_hash': 6995490179611000573, 'subgroup_order': 10368, 'subgroup_tex': 'S_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, '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': '10368.em', 'subgroup_hash': 2975315908451175031, 'subgroup_order': 10368, 'subgroup_tex': 'S_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, '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': '10368.em', 'subgroup_hash': 2975315908451175031, 'subgroup_order': 10368, 'subgroup_tex': 'S_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, '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': '10368.dk', 'subgroup_hash': 1324931324736411877, 'subgroup_order': 10368, 'subgroup_tex': 'C_6:S_3^3:C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, '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': '10368.dt', 'subgroup_hash': 1292327758745591869, 'subgroup_order': 10368, 'subgroup_tex': 'C_6:S_3^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, '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': '10368.dy', 'subgroup_hash': 1132388829163838985, 'subgroup_order': 10368, 'subgroup_tex': 'C_6:S_3^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126627
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, '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': '10368.dy', 'subgroup_hash': 1132388829163838985, 'subgroup_order': 10368, 'subgroup_tex': 'C_6:S_3^3.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, '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': 7936768958288056923, 'subgroup_order': 10368, 'subgroup_tex': 'C_3^4.C_2^4.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, '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': '10368.ke', 'subgroup_hash': 7883340048705160529, 'subgroup_order': 10368, 'subgroup_tex': '(C_2\\times C_6^3):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, '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': '10368.ea', 'subgroup_hash': 100370156498004401, 'subgroup_order': 10368, 'subgroup_tex': 'S_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, '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': '10368.ea', 'subgroup_hash': 100370156498004401, 'subgroup_order': 10368, 'subgroup_tex': 'S_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1', 'outer_equivalence': True, 'perfect': False, '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': '10368.ea', 'subgroup_hash': 100370156498004401, 'subgroup_order': 10368, 'subgroup_tex': 'S_3^4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.54.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1', 'outer_equivalence': True, 'perfect': False, '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': 4007638591266692352, 'subgroup_order': 10368, 'subgroup_tex': 'C_3^4.C_2^5.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.64.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': 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': 4028377453847893583, 'subgroup_order': 8748, 'subgroup_tex': '(C_3^4\\times C_6^2).C_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.64.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8748.eo', 'subgroup_hash': 4974128333272795695, 'subgroup_order': 8748, 'subgroup_tex': 'C_3\\wr A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.64.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8748.ev', 'subgroup_hash': 1612280316408804683, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227126638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.64.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8748.eo', 'subgroup_hash': 4974128333272795695, 'subgroup_order': 8748, 'subgroup_tex': 'C_3\\wr A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.64.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8748.ew', 'subgroup_hash': 4236140793975228850, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.64.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8748.ew', 'subgroup_hash': 4236140793975228850, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.64.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8748.ew', 'subgroup_hash': 4236140793975228850, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.64.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8748.ew', 'subgroup_hash': 4236140793975228850, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126644
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.64.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8748.ew', 'subgroup_hash': 4236140793975228850, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126646
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, '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': 1707161943332188540, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126651
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, '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': 1294964887966964064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, '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': 6266107691031418446, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, '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': 6718106479182777641, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126656
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126657
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126658
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1', 'outer_equivalence': True, 'perfect': False, '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': 7048878855151006912, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_6\\times D_4:C_2)', 'supersolvable': False, 'sylow': 0}
  • id: 227126660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1', 'outer_equivalence': True, 'perfect': False, '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': 5769699342332692219, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_{12}\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1', 'outer_equivalence': True, 'perfect': False, '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': 6160654942337789657, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1', 'outer_equivalence': True, 'perfect': False, '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': 1398439473578044064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4:C_2.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1', 'outer_equivalence': True, 'perfect': False, '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': 6878048746794315800, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126668
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1', 'outer_equivalence': True, 'perfect': False, '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': 1719159748243730139, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.w1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1', 'outer_equivalence': True, 'perfect': False, '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': 2954438143557713092, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.z1', 'outer_equivalence': True, 'perfect': False, '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': 2726058422358207720, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ba1', 'outer_equivalence': True, 'perfect': False, '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': 5950953608038405430, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126675
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bb1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126676
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bc1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1', 'outer_equivalence': True, 'perfect': False, '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': 8999595210760011646, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_6\\times D_4).C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1', 'outer_equivalence': True, 'perfect': False, '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': 8998589501287802796, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bf1', 'outer_equivalence': True, 'perfect': False, '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': 1294964887966964064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bg1', 'outer_equivalence': True, 'perfect': False, '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': 5647083529745991790, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_2\\times C_6).C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bh1', 'outer_equivalence': True, 'perfect': False, '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': 8998589501287802796, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bi1', 'outer_equivalence': True, 'perfect': False, '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': 3688189279088881677, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bj1', 'outer_equivalence': True, 'perfect': False, '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': 6266107691031418446, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1', 'outer_equivalence': True, 'perfect': False, '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': 2651476832904464391, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1', 'outer_equivalence': True, 'perfect': False, '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': 1294964887966964064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bm1', 'outer_equivalence': True, 'perfect': False, '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': 6266107691031418446, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bn1', 'outer_equivalence': True, 'perfect': False, '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': 2844789448540286657, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bo1', 'outer_equivalence': True, 'perfect': False, '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': 2844789448540286657, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126691
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bp1', 'outer_equivalence': True, 'perfect': False, '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': 4416952245775169121, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126692
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1', 'outer_equivalence': True, 'perfect': False, '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': 4355383333738797014, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126693
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.br1', 'outer_equivalence': True, 'perfect': False, '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': 4416952245775169121, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bt1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1', 'outer_equivalence': True, 'perfect': False, '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': 2844789448540286657, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126698
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1', 'outer_equivalence': True, 'perfect': False, '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': 2844789448540286657, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw1', 'outer_equivalence': True, 'perfect': False, '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': 4416952245775169121, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1', 'outer_equivalence': True, 'perfect': False, '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': 4355383333738797014, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6:C_4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.by1', 'outer_equivalence': True, 'perfect': False, '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': 1707161943332188540, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.BZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bz1', 'outer_equivalence': True, 'perfect': False, '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': 4416952245775169121, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126703
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ca1', 'outer_equivalence': True, 'perfect': False, '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': 8661760179562915779, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126704
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cb1', 'outer_equivalence': True, 'perfect': False, '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': 2510397304885548996, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1', 'outer_equivalence': True, 'perfect': False, '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': 4644893349620621505, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_2\\times C_6).C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1', 'outer_equivalence': True, 'perfect': False, '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': 4644893349620621505, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_2\\times C_6).C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1', 'outer_equivalence': True, 'perfect': False, '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': 7867936062834371013, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1', 'outer_equivalence': True, 'perfect': False, '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': 140933940059007479, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126710
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126711
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126712
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126713
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126714
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1', 'outer_equivalence': True, 'perfect': False, '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': 8305924806804315323, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cl1', 'outer_equivalence': True, 'perfect': False, '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': 1960399982546797199, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cm1', 'outer_equivalence': True, 'perfect': False, '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': 5280084987548361466, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cn1', 'outer_equivalence': True, 'perfect': False, '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': 5280084987548361466, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126718
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.co1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126720
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cp1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126721
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cq1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cr1', 'outer_equivalence': True, 'perfect': False, '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': 6135572585864323189, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cs1', 'outer_equivalence': True, 'perfect': False, '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': 8999595210760011646, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_6\\times D_4).C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ct1', 'outer_equivalence': True, 'perfect': False, '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': 1294964887966964064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cu1', 'outer_equivalence': True, 'perfect': False, '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': 8998589501287802796, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cv1', 'outer_equivalence': True, 'perfect': False, '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': 5647083529745991790, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_2\\times C_6).C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cw1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cx1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cy1', 'outer_equivalence': True, 'perfect': False, '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': 1398439473578044064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126731
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.CZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cz1', 'outer_equivalence': True, 'perfect': False, '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': 6878048746794315800, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.da1', 'outer_equivalence': True, 'perfect': False, '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': 1719159748243730139, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.db1', 'outer_equivalence': True, 'perfect': False, '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': 8998589501287802796, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dc1', 'outer_equivalence': True, 'perfect': False, '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': 6266107691031418446, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dd1', 'outer_equivalence': True, 'perfect': False, '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': 3688189279088881677, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.de1', 'outer_equivalence': True, 'perfect': False, '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': 2651476832904464391, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.df1', 'outer_equivalence': True, 'perfect': False, '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': 1294964887966964064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dg1', 'outer_equivalence': True, 'perfect': False, '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': 2844789448540286657, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dh1', 'outer_equivalence': True, 'perfect': False, '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': 6266107691031418446, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.di1', 'outer_equivalence': True, 'perfect': False, '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': 4416952245775169121, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dj1', 'outer_equivalence': True, 'perfect': False, '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': 1294964887966964064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dk1', 'outer_equivalence': True, 'perfect': False, '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': 1388514764116415010, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dl1', 'outer_equivalence': True, 'perfect': False, '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': 9151776972543767772, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dm1', 'outer_equivalence': True, 'perfect': False, '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': 2821771571300290632, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6:C_4:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dn1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.do1', 'outer_equivalence': True, 'perfect': False, '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': 2844789448540286657, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dp1', 'outer_equivalence': True, 'perfect': False, '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': 4915296062467486412, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dq1', 'outer_equivalence': True, 'perfect': False, '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': 2464001624744977224, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dr1', 'outer_equivalence': True, 'perfect': False, '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': 5901339047917690491, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ds1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dt1', 'outer_equivalence': True, 'perfect': False, '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': 8625508799213115664, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.du1', 'outer_equivalence': True, 'perfect': False, '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': 4234806743712921454, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dv1', 'outer_equivalence': True, 'perfect': False, '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': 3612033627028589181, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(D_6.D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126756
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dw1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dx1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dy1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126759
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.DZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dz1', 'outer_equivalence': True, 'perfect': False, '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': 1707161943332188540, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ea1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eb1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ec1', 'outer_equivalence': True, 'perfect': False, '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': 2844789448540286657, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.ED', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ed1', 'outer_equivalence': True, 'perfect': False, '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': 1707161943332188540, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ee1', 'outer_equivalence': True, 'perfect': False, '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': 4416952245775169121, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ef1', 'outer_equivalence': True, 'perfect': False, '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': 8999595210760011646, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_2\\times C_6).C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eg1', 'outer_equivalence': True, 'perfect': False, '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': 8949170025008187196, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eh1', 'outer_equivalence': True, 'perfect': False, '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': 7164993940398537913, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ei1', 'outer_equivalence': True, 'perfect': False, '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': 3425860065844722576, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_6\\times Q_8).C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ej1', 'outer_equivalence': True, 'perfect': False, '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': 8949170025008187196, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ek1', 'outer_equivalence': True, 'perfect': False, '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': 1388514764116415010, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.el1', 'outer_equivalence': True, 'perfect': False, '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': 8972878797145235093, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.em1', 'outer_equivalence': True, 'perfect': False, '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': 2386831472364992478, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4.D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eo1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ep1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eq1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.ER', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.er1', 'outer_equivalence': True, 'perfect': False, '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': 1707161943332188540, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.ES', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.es1', 'outer_equivalence': True, 'perfect': False, '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': 2473238347541257631, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.ET', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.et1', 'outer_equivalence': True, 'perfect': False, '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': 1294964887966964064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eu1', 'outer_equivalence': True, 'perfect': False, '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': 6266107691031418446, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ev1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ew1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ex1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ey1', 'outer_equivalence': True, 'perfect': False, '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': 1294964887966964064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.EZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ez1', 'outer_equivalence': True, 'perfect': False, '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': 9151776972543767772, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fa1', 'outer_equivalence': True, 'perfect': False, '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': 1388514764116415010, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fb1', 'outer_equivalence': True, 'perfect': False, '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': 2821771571300290632, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6:C_4:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fc1', 'outer_equivalence': True, 'perfect': False, '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': 8949170025008187196, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fd1', 'outer_equivalence': True, 'perfect': False, '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': 8972878797145235093, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fe1', 'outer_equivalence': True, 'perfect': False, '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': 1388514764116415010, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ff1', 'outer_equivalence': True, 'perfect': False, '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': 2386831472364992478, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4.D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fg1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fh1', 'outer_equivalence': True, 'perfect': False, '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': 8625508799213115664, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fi1', 'outer_equivalence': True, 'perfect': False, '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': 4234806743712921454, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fj1', 'outer_equivalence': True, 'perfect': False, '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': 3612033627028589181, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(D_6.D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126801
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fk1', 'outer_equivalence': True, 'perfect': False, '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': 3400988634635037216, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fl1', 'outer_equivalence': True, 'perfect': False, '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': 7990253850771325440, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_4:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fm1', 'outer_equivalence': True, 'perfect': False, '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': 4234806743712921454, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126804
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fn1', 'outer_equivalence': True, 'perfect': False, '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': 5701115237072501677, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4.D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fo1', 'outer_equivalence': True, 'perfect': False, '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': 1388514764116415010, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fp1', 'outer_equivalence': True, 'perfect': False, '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': 1719159748243730139, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fq1', 'outer_equivalence': True, 'perfect': False, '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': 4234806743712921454, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_4:D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fr1', 'outer_equivalence': True, 'perfect': False, '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': 5901339047917690491, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fs1', 'outer_equivalence': True, 'perfect': False, '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': 3905757440611663456, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ft1', 'outer_equivalence': True, 'perfect': False, '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': 5901339047917690491, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fu1', 'outer_equivalence': True, 'perfect': False, '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': 6924127455306298297, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 227126813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fv1', 'outer_equivalence': True, 'perfect': False, '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': 7214824093916150900, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 227126814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fw1', 'outer_equivalence': True, 'perfect': False, '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': 1294964887966964064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fx1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fy1', 'outer_equivalence': True, 'perfect': False, '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': 6266107691031418446, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.FZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fz1', 'outer_equivalence': True, 'perfect': False, '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': 1908305770382960135, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ga1', 'outer_equivalence': True, 'perfect': False, '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': 1398439473578044064, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gb1', 'outer_equivalence': True, 'perfect': False, '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': 2821771571300290632, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6:C_4:C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gc1', 'outer_equivalence': True, 'perfect': False, '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': 4915296062467486412, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gd1', 'outer_equivalence': True, 'perfect': False, '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': 3612033627028589181, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(D_6.D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126823
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ge1', 'outer_equivalence': True, 'perfect': False, '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': 3753794644867823515, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(D_6.D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gf1', 'outer_equivalence': True, 'perfect': False, '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': 3612033627028589181, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(D_6.D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gg1', 'outer_equivalence': True, 'perfect': False, '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': 8072175820368712747, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_4^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gh1', 'outer_equivalence': True, 'perfect': False, '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': 3711620301349366533, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gi1', 'outer_equivalence': True, 'perfect': False, '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': 4031479185665355972, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gj1', 'outer_equivalence': True, 'perfect': False, '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': 4031479185665355972, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gk1', 'outer_equivalence': True, 'perfect': False, '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': 4031479185665355972, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gl1', 'outer_equivalence': True, 'perfect': False, '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': 9034307526760386456, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gm1', 'outer_equivalence': True, 'perfect': False, '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': 2238128005150459124, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GN', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gn1', 'outer_equivalence': True, 'perfect': False, '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': 2860019313257035485, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126834
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.go1', 'outer_equivalence': True, 'perfect': False, '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': 2568290864577579560, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gp1', 'outer_equivalence': True, 'perfect': False, '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': 2658858121305366788, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^3.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gq1', 'outer_equivalence': True, 'perfect': False, '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': 2860019313257035485, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126837
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gr1', 'outer_equivalence': True, 'perfect': False, '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': 2860019313257035485, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GS', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gs1', 'outer_equivalence': True, 'perfect': False, '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': 5442635732034531883, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^2.C_6^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gt1', 'outer_equivalence': True, 'perfect': False, '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': 8662341793152810623, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_6\\times D_4).C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gu1', 'outer_equivalence': True, 'perfect': False, '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': 2623669814133710654, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gv1', 'outer_equivalence': True, 'perfect': False, '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': 1334659533467612424, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126843
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gw1', 'outer_equivalence': True, 'perfect': False, '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': 1334659533467612424, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gx1', 'outer_equivalence': True, 'perfect': False, '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': 657822997330637045, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_6\\times D_4).C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gy1', 'outer_equivalence': True, 'perfect': False, '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': 4814966372628946507, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.GZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gz1', 'outer_equivalence': True, 'perfect': False, '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': 3356596114106820924, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ha1', 'outer_equivalence': True, 'perfect': False, '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': 3356596114106820924, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hb1', 'outer_equivalence': True, 'perfect': False, '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': 4378108058603099600, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^4\\times C_6).C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HC', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hc1', 'outer_equivalence': True, 'perfect': False, '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': 269388299765126781, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^4\\times C_6).C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HD', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hd1', 'outer_equivalence': True, 'perfect': False, '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': 5971669344876647731, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.he1', 'outer_equivalence': True, 'perfect': False, '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': 4378108058603099600, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^4\\times C_6).C_2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126853
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hf1', 'outer_equivalence': True, 'perfect': False, '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': 1334659533467612424, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126854
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hg1', 'outer_equivalence': True, 'perfect': False, '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': 1334659533467612424, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hh1', 'outer_equivalence': True, 'perfect': False, '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': 657822997330637045, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_6\\times D_4).C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hi1', 'outer_equivalence': True, 'perfect': False, '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': 4814966372628946507, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126857
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hj1', 'outer_equivalence': True, 'perfect': False, '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': 91197257142414677, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126858
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HK', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hk1', 'outer_equivalence': True, 'perfect': False, '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': 91197257142414677, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hl1', 'outer_equivalence': True, 'perfect': False, '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': 3501222145529552557, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^3.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hm1', 'outer_equivalence': True, 'perfect': False, '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': 3501222145529552557, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^3.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hn1', 'outer_equivalence': True, 'perfect': False, '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': 3501222145529552557, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^3.C_6^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ho1', 'outer_equivalence': True, 'perfect': False, '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': 9095383112064665735, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hp1', 'outer_equivalence': True, 'perfect': False, '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': '7776.hl', 'subgroup_hash': 5967056670001601497, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HQ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hq1', 'outer_equivalence': True, 'perfect': False, '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': '7776.hi', 'subgroup_hash': 8819936940392691699, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times C_6^2).S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hr1', 'outer_equivalence': True, 'perfect': False, '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': 4027265402072828524, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hs1', 'outer_equivalence': True, 'perfect': False, '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': 4027265402072828524, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HT', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ht1', 'outer_equivalence': True, 'perfect': False, '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': 4753023724528392461, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hu1', 'outer_equivalence': True, 'perfect': False, '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': 2623669814133710654, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hv1', 'outer_equivalence': True, 'perfect': False, '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': 657822997330637045, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_6\\times D_4).C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hw1', 'outer_equivalence': True, 'perfect': False, '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': 3356596114106820924, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126872
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hx1', 'outer_equivalence': True, 'perfect': False, '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': 4814966372628946507, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^4:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 227126873
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HY', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hy1', 'outer_equivalence': True, 'perfect': False, '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': 4378108058603099600, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^4\\times C_6).C_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126875
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.HZ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.hz1', 'outer_equivalence': True, 'perfect': False, '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': 3432191523706517424, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ia1', 'outer_equivalence': True, 'perfect': False, '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': 3115455142614757550, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126877
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ib1', 'outer_equivalence': True, 'perfect': False, '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': 1659944167560433402, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ic1', 'outer_equivalence': True, 'perfect': False, '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': 8673713304961923658, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.ID', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.id1', 'outer_equivalence': True, 'perfect': False, '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': 8673713304961923658, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IE', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ie1', 'outer_equivalence': True, 'perfect': False, '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': 3979058812225639096, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126881
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IF', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.if1', 'outer_equivalence': True, 'perfect': False, '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': 1334659533467612424, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 227126882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IG', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ig1', 'outer_equivalence': True, 'perfect': False, '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': 1659944167560433402, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126883
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ih1', 'outer_equivalence': True, 'perfect': False, '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': 3979058812225639096, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.II', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ii1', 'outer_equivalence': True, 'perfect': False, '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': 1659944167560433402, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^4.C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227126886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ij1', 'outer_equivalence': True, 'perfect': False, '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': 8673713304961923658, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ik1', 'outer_equivalence': True, 'perfect': False, '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': 8673713304961923658, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.il1', 'outer_equivalence': True, 'perfect': False, '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': 8673713304961923658, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IM', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.im1', 'outer_equivalence': True, 'perfect': False, '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': 3979058812225639096, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^3.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 227126890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.in1', 'outer_equivalence': True, 'perfect': False, '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': 573909937441527994, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IO', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.io1', 'outer_equivalence': True, 'perfect': False, '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': 7694724724096945537, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_{12}\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IP', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ip1', 'outer_equivalence': True, 'perfect': False, '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': 5436754338545421017, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IQ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iq1', 'outer_equivalence': True, 'perfect': False, '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': 6998442788040507822, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IR', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ir1', 'outer_equivalence': True, 'perfect': False, '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': 6677428518899400387, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IS', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.is1', 'outer_equivalence': True, 'perfect': False, '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': 6998442788040507822, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
  • id: 227126897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IT', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.it1', 'outer_equivalence': True, 'perfect': False, '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': 271766078695063454, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.(C_6\\times Q_8).C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IU', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iu1', 'outer_equivalence': True, 'perfect': False, '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': 8146466388469970007, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 227126899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IV', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iv1', 'outer_equivalence': True, 'perfect': False, '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': 6432203779445787939, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IW', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iw1', 'outer_equivalence': True, 'perfect': False, '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': 8673713304961923658, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IX', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ix1', 'outer_equivalence': True, 'perfect': False, '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': 8673713304961923658, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IY', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iy1', 'outer_equivalence': True, 'perfect': False, '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': 8673713304961923658, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126903
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.IZ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.iz1', 'outer_equivalence': True, 'perfect': False, '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': 8673713304961923658, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JA', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ja1', 'outer_equivalence': True, 'perfect': False, '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': 3070884861930519010, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.D_6.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 227126905
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jb1', 'outer_equivalence': True, 'perfect': False, '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': 6432203779445787939, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4.C_2^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126906
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jc1', 'outer_equivalence': True, 'perfect': False, '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': 8673713304961923658, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^5.C_2^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 227126909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jd1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cl', 'subgroup_hash': 8516351652658594549, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:D_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.je1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cl', 'subgroup_hash': 8516351652658594549, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:D_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jf1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cl', 'subgroup_hash': 8516351652658594549, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:D_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126912
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jg1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cd', 'subgroup_hash': 154017820873362602, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times S_3^2):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126913
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jh1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cd', 'subgroup_hash': 154017820873362602, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times S_3^2):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126914
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ji1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cl', 'subgroup_hash': 8516351652658594549, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:D_4:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 227126915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jj1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cd', 'subgroup_hash': 154017820873362602, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times S_3^2):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126916
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jk1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cd', 'subgroup_hash': 154017820873362602, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times S_3^2):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jl1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cd', 'subgroup_hash': 154017820873362602, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times S_3^2):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jm1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cd', 'subgroup_hash': 154017820873362602, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times S_3^2):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jn1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cd', 'subgroup_hash': 154017820873362602, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times S_3^2):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.72.JO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.jo1', 'outer_equivalence': True, 'perfect': False, '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': '7776.cd', 'subgroup_hash': 154017820873362602, 'subgroup_order': 7776, 'subgroup_tex': '(C_3^2\\times S_3^2):D_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 227126922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 5832, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.96.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.227', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 227, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5832.de', 'subgroup_hash': 5576727447320419126, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^6:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 227126923
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2916, 'characteristic': True, 'core_order': 2916, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.192.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.955', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 955, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7820949075331676098, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 227126924
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 2916, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.192.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1538', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1538, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.ld', 'subgroup_hash': 2310896937790502961, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227126925
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 2916, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.192.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.955', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 955, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2916.ld', 'subgroup_hash': 2310896937790502961, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227126926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '559872.lw.256.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.2052', 'subgroup_hash': 6501777776849519009, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^2\\wr C_3', 'supersolvable': True, 'sylow': 3}
  • id: 227126927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.729.A', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '729.a1.M', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 729, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090070', 'subgroup_hash': 1090070, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 227126928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2916, 'characteristic': True, 'core_order': 729, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.768.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '768.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '768.1090070', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1090070, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^5:S_4', 'simple': False, 'solvable': True, 'special_labels': ['D3', 'C6'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
  • id: 227126929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '559872.lw.2187.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2187.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2187, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.16888', 'subgroup_hash': 16888, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 227126931
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 93312, 'characteristic': True, 'core_order': 4, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.lw.139968.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '139968.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '139968.j', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8118045935722796121, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 139968, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^6:C_2^3:S_4', '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: 227126932
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '559872.lw', 'ambient_counter': 309, 'ambient_order': 559872, 'ambient_tex': 'C_3^6.C_2^5:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 559872, 'characteristic': True, 'core_order': 1, 'counter': 821, 'cyclic': True, 'direct': None, 'hall': 1, 'label': '559872.lw.559872.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '559872.a1.N', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '559872.lw', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5225393530267235522, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 559872, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^6.C_2^5:S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D4', 'C7'], '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 •

  Column	Type
  ambient	text
  aut_centralizer_order	numeric
  aut_label	text
  aut_quo_index	numeric
  aut_stab_index	numeric
  aut_weyl_group	text
  aut_weyl_index	numeric
  centralizer	text
  complements	text[]
  conjugacy_class_count	numeric
  contained_in	text[]
  contains	text[]
  core	text
  coset_action_label	text
  count	numeric
  diagramx	smallint[]
  generators	numeric[]
  label	text
  mobius_quo	bigint
  mobius_sub	bigint
  normal_closure	text
  normal_contained_in	text[]
  normal_contains	text[]
  normalizer	text
  old_label	text
  projective_image	text
  quotient_action_image	text
  quotient_action_kernel	text
  quotient_action_kernel_order	numeric
  quotient_fusion	jsonb
  short_label	text
  subgroup_fusion	integer[]
  weyl_group	text

  
  
  • id: 227126568
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [820016402241462860280, 1089305682393623, 46287837780393007, 35700769812329758080, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 1255647523519025280], 'label': '559872.lw.48.HH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.A', 'old_label': '48.hbB', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HH', 'subgroup_fusion': None, 'weyl_group': '34992.ba'}
  • id: 227126569
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [820016402241462860280, 1089305682393623, 46287837780393007, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 1255647523519025280], 'label': '559872.lw.48.HI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.hbC', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126570
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.HJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '48.hcB', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HJ', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126571
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288098357943687, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.HK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '48.hcC', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126130
    {'ambient': '559872.lw', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [32, 2715, 6, 296], 'generators': [6645229879800, 1466521590431963520, 35700769812329758080, 32389886532326400, 871108433886504447360, 186811430400, 51212989102409650082, 12933849720, 1089479559168143, 163151836496911558923, 1255647523519025280, 545784629489036427721, 32389973710617736, 806400, 820016402241462860280], 'label': '559872.lw.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '559872.lw'}
  • id: 227126131
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.B', 'coset_action_label': None, 'count': 6, 'diagramx': [156, -1, 146, -1], 'generators': [820016402241462860280, 806400, 46283920465305607, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 631982000885991493081, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.6.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.B', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126132
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1946, -1, 1819, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 51212989102409650082, 6812879759400, 12933849720, 1255647523519025280], 'label': '559872.lw.24.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '24.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.H', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126133
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [3343, -1, 2272, -1], 'generators': [1089479559168143, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 45194808301171216, 6645229879800, 820016402241462860280, 1255647523519025280, 327056278482747566040], 'label': '559872.lw.24.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.I', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126134
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1870, -1, 1795, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 45194808301171216, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 327043829428991226840, 1255647523519025280], 'label': '559872.lw.24.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.j1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.J', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126135
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1908, -1, 1807, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 45194808301171216, 1089479559168143, 32389886532326400, 871108433886504447360, 326922163405792506840, 6645229879800, 1255647523519025280], 'label': '559872.lw.24.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.k1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.K', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126136
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5992, -1, 3130, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 51212988854246581922, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 45200132882916496, 1255647523519025280], 'label': '559872.lw.24.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '24.l1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.L', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126137
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3533, -1, 2333, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 46995301548518527, 871108433886504447360, 6645229879800, 12933043320, 734042992041763141081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.m1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.M', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126138
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2319, -1, 1940, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 46995301548518527, 871108433886504447360, 6645229879800, 545791031688864574921, 12933043320, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.24.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.n1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.N', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126139
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4933, -1, 2787, -1], 'generators': [820016402241462860280, 183166629153579833777, 35700769812329758080, 1466521590431963520, 32389886532326400, 46995301548518527, 871108433886504447360, 6645229879800, 12933043320, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.24.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.o1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.O', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126140
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1712, -1, 1743, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 46995301548518527, 871108433886504447360, 6645229879800, 12933043320, 188032435611404269097, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.24.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.p1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.P', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126141
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [3419, -1, 2297, -1], 'generators': [820016402241462860280, 806400, 1094803701954623, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 326922163405792506840, 1255647523519025280], 'label': '559872.lw.24.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.q1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Q', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126142
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.B', 'coset_action_label': None, 'count': 6, 'diagramx': [33, -1, 106, -1], 'generators': [820016402241462860280, 806400, 46283920465305607, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 188032435611404269097, 12933849720, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.6.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.C', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126143
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [3192, -1, 2223, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 326922163405792506840, 6645229879800, 1255647523519025280], 'label': '559872.lw.24.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.r1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.R', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126144
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2248, -1, 1917, -1], 'generators': [820016402241462860280, 32395211114197696, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229199400, 12933849720, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.24.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '24.s1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.S', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126145
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [2118, -1, 1875, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229199400, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '24.t1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.T', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126146
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [2149, -1, 1885, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 186811430400, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.u1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.U', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126147
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2640, -1, 2044, -1], 'generators': [820016402241462860280, 183166629153579833777, 35700769812329758080, 1466521590431963520, 32389886532326400, 46995301548518527, 871108433886504447360, 6645229879800, 12933043320, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.24.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.v1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.V', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126148
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1261, -1, 1597, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 46995301548518527, 871108433886504447360, 6645229879800, 12933043320, 188032435611404269097, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.24.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.w1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.W', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126149
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5954, -1, 3118, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 46995301548518527, 871108433886504447360, 6645229879800, 12933043320, 636726196416785585897, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.x1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.X', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126150
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2561, -1, 2019, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 46995301548518527, 871108433886504447360, 6645229879800, 545791031688864574921, 12933043320, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.24.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.y1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Y', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126151
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [5879, -1, 3093, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6812879759400, 6632296156080, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.24.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.z1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Z', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126152
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 3, 'diagramx': [5722, -1, 3043, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 438743340800442968521, 1800761010854543, 1255647523519025280], 'label': '559872.lw.24.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ba1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126153
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [323, -1, 200, -1], 'generators': [820016402241462860280, 806400, 46283920465305607, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 188032435611404269097, 12933849720, 631982000885991493081, 1255647523519025280], 'label': '559872.lw.6.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.D', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126154
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 3, 'diagramx': [3078, -1, 2186, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 45194808301171216, 32389886532326400, 871108433886504447360, 6645229879800, 545791031688864574921, 12933043320, 1800761010854543, 1255647523519025280], 'label': '559872.lw.24.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126155
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [892, -1, 1478, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1800761010854543, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.24.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '24.bc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126156
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [3229, -1, 2235, -1], 'generators': [820016402241462860280, 806400, 317081359326433454783, 35700769812329758080, 186811430400, 1466521590431963520, 45194808301171216, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.24.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126157
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [3267, -1, 2247, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.24.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.be1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126158
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [5760, -1, 3055, -1], 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 540918822857334411721, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.24.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126159
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [31, -1, 1199, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 51821612150358114853, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.24.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126160
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [3040, -1, 2174, -1], 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 188032435611404269097, 1255647523519025280], 'label': '559872.lw.24.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126161
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1757, -1, 1758, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 186811430400, 1466521590431963520, 45194808301171216, 32389886532326400, 871108433886504447360, 6645229879800, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.24.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BI', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126162
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [855, -1, 1466, -1], 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 183166628979702253097, 12933043320, 1255647523519025280], 'label': '559872.lw.24.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126163
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1794, -1, 1770, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 51212989102409650082, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.24.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126164
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [114, -1, 133, -1], 'generators': [820016402241462860280, 806400, 46283920465305607, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 636726196416785585897, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.6.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.E', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126165
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5579, -1, 2996, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 33834866709772807, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.24.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '24.bl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126166
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4795, -1, 2742, -1], 'generators': [820016402241462860280, 806400, 183166629153579833777, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 33834866709772807, 1255647523519025280], 'label': '559872.lw.24.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '24.bm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126167
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [655, -1, 1401, -1], 'generators': [820016402241462860280, 806400, 438736938339558949321, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 33834866709772807, 1255647523519025280], 'label': '559872.lw.24.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '24.bn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126168
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [700, -1, 1415, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 188032435611404269097, 33834866709772807, 1255647523519025280], 'label': '559872.lw.24.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '24.bo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126169
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2180, -1, 1895, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 45200132882916496, 1255647523519025280], 'label': '559872.lw.24.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '24.bp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126170
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [2087, -1, 1865, -1], 'generators': [820016402241462860280, 806400, 1094797475614103, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '24.bq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126171
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [2056, -1, 1855, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 186811430400, 1466521590431963520, 45194808301171216, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.24.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.br1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BR', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126172
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2602, -1, 2032, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 45194627716761736, 734042992041763141081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BS', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126173
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1621, -1, 1714, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 545791031688864574921, 45194627716761736, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.24.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bt1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126174
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4891, -1, 2773, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 636726180724725829081, 45194627716761736, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BU', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126175
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': [447, -1, 240, -1], 'generators': [1089479559168143, 32389886532326400, 6645229879800, 35700769812329758080, 540918822857334411721, 1255647523519025280, 12933043320, 820016402241462860280, 32389973711424136, 1466521590431963520, 871108433886504447360, 186811430400, 734164596604266565081], 'label': '559872.lw.6.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.f1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.F', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126176
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1132, -1, 1556, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 545791031688864574921, 636726180724725829081, 45194627716761736, 1255647523519025280], 'label': '559872.lw.24.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126177
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [3457, -1, 2309, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 45194808301171216, 1089473332953623, 32389886532326400, 871108433886504447360, 326922163405792506840, 6645229199400, 1255647523519025280], 'label': '559872.lw.24.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BW', 'subgroup_fusion': None, 'weyl_group': '23328.bq'}
  • id: 227126178
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [741, -1, 1429, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 33479179281676927, 6645229879800, 180584409720, 734042992041763141081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126179
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2678, -1, 2056, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 33479179281676927, 871108433886504447360, 6645229879800, 734164596604266565081, 180584409720, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.by1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126180
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2998, -1, 2160, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 33479179281676927, 6645229879800, 188032435611404269097, 636847820594404529897, 180584409720, 1255647523519025280], 'label': '559872.lw.24.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.bz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126181
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2397, -1, 1966, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 33479179281676927, 6645229879800, 188032435611404269097, 180584409720, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.24.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ca1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126182
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4584, -1, 2674, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734042992041763141081, 438743340800442968521, 1800761010854543, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126183
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6188, -1, 3193, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 545791031688864574921, 734042992041763141081, 1800761010854543, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126184
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1455, -1, 1660, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 636726180724725829081, 438743340800442968521, 1800761010854543, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126185
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5651, -1, 3020, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 545791031688864574921, 636726180724725829081, 1800761010854543, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ce1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126186
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': [366, -1, 214, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280, 545784629489036427721, 32389973711424136], 'label': '559872.lw.6.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.G', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126187
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [817, -1, 1453, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734042992041763141081, 438743340800442968521, 1800767237875223, 1255647523519025280], 'label': '559872.lw.24.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126188
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [1091, -1, 1542, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 45194808301171216, 32389886532326400, 871108433886504447360, 6645229879800, 545791031688864574921, 734042992041763141081, 1800767237875223, 1255647523519025280], 'label': '559872.lw.24.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126189
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [4636, -1, 2691, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 45194808301171216, 32389886532326400, 871108433886504447360, 6645229879800, 636726180724725829081, 438743340800442968521, 1800767237875223, 1255647523519025280], 'label': '559872.lw.24.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ch1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126363
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7043, -1, 6202, -1], 'generators': [820016402241462860280, 1089305682393623, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 1255647523519025280], 'label': '559872.lw.48.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.E', 'subgroup_fusion': None, 'weyl_group': '8000.eg'}
  • id: 227126190
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [2795, -1, 2095, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 45194808301171216, 32389886532326400, 871108433886504447360, 6645229879800, 545791031688864574921, 636726180724725829081, 1800767237875223, 1255647523519025280], 'label': '559872.lw.24.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ci1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126191
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [3154, -1, 2211, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CJ', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126192
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [779, -1, 1441, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734042992041763141081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ck1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126193
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2755, -1, 2081, -1], 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 188032435611404269097, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.24.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126194
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5614, -1, 3008, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 636847846747924549081, 871108433886504447360, 6645229879800, 45194627716761736, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126195
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1664, -1, 1728, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 636847846747924549081, 871108433886504447360, 6645229879800, 545791031688864574921, 45194627716761736, 1255647523519025280], 'label': '559872.lw.24.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126196
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1530, -1, 1685, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 45194627716761736, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.co1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126197
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [199, -1, 160, -1], 'generators': [1089479559168143, 32389886532326400, 6645229879800, 35700769812329758080, 545784629489036427721, 1255647523519025280, 12933043320, 820016402241462860280, 32389973711424136, 1466521590431963520, 871108433886504447360, 186811430400, 734164596604266565081], 'label': '559872.lw.6.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.H', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126198
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2487, -1, 1995, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 545791031688864574921, 734164596604266565081, 45194627716761736, 1255647523519025280], 'label': '559872.lw.24.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126199
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 3, 'diagramx': [3305, -1, 2260, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 51212988841832457242, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126200
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [5463, -1, 2959, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 45194808301171216, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 180584409720, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126201
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 3, 'diagramx': [68, -1, 1211, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 1255647523519025280, 51212989114823775002, 32389973710617736], 'label': '559872.lw.24.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CS', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126202
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [2021, -1, 1844, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 51212989102409650082, 6812879759400, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '24.ct1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126203
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [3116, -1, 2198, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 327056278482747566040, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.cu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CU', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126204
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [5916, -1, 3106, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280, 51212989114823775002, 32389973710617736], 'label': '559872.lw.24.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126205
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [5501, -1, 2971, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 438743340800442968521, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126206
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1832, -1, 1782, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 327043829428991226840, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.cx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CX', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126207
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1012, -1, 1517, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 33479179281676927, 6645229879800, 188032435611404269097, 180584409720, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.24.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126208
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [281, -1, 186, -1], 'generators': [820016402241462860280, 540918822857334411721, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280, 32389973711424136], 'label': '559872.lw.6.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.I', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126209
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.CZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1494, -1, 1673, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 33479179281676927, 871108433886504447360, 6645229879800, 636847820594404529897, 180584409720, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.cz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126210
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [496, -1, 1350, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 33479179281676927, 6645229879800, 180584409720, 636726196416785585897, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.da1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126211
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5799, -1, 3068, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 33479179281676927, 6645229879800, 734164596604266565081, 188032435611404269097, 180584409720, 1255647523519025280], 'label': '559872.lw.24.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.db1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126212
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2212, -1, 1906, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 636847846747924549081, 871108433886504447360, 6645229879800, 438743340800442968521, 1800761010854543, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126213
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5540, -1, 2984, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 636847846747924549081, 871108433886504447360, 6645229879800, 545791031688864574921, 1800761010854543, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126214
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [534, -1, 1362, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 438743340800442968521, 1800761010854543, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.de1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126215
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2958, -1, 2147, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 545791031688864574921, 734164596604266565081, 1800761010854543, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.df1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126216
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [572, -1, 1374, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 45194808301171216, 32389886532326400, 636847846747924549081, 871108433886504447360, 6645229879800, 438743340800442968521, 1800767237875223, 1255647523519025280], 'label': '559872.lw.24.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126217
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [2443, -1, 1980, -1], 'generators': [636847846747924549081, 35700769812329758080, 1466521590431963520, 32389886532326400, 1800767237875223, 871108433886504447360, 45194808301171216, 6645229879800, 820016402241462860280, 1255647523519025280, 545791031688864574921], 'label': '559872.lw.24.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126218
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [1367, -1, 1632, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 438743340800442968521, 1800767237875223, 1255647523519025280], 'label': '559872.lw.24.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.di1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126219
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 3, 'diagramx': [73, -1, 119, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 51212989102409650082, 6645229879800, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.6.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.j1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.J', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126220
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [2283, -1, 1929, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 45194808301171216, 32389886532326400, 871108433886504447360, 6645229879800, 545791031688864574921, 734164596604266565081, 1800767237875223, 1255647523519025280], 'label': '559872.lw.24.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126221
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1051, -1, 1530, -1], 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 188032435611404269097, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.24.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126222
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [4531, -1, 2657, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 636726196416785585897, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126223
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [2716, -1, 2069, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126224
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [5839, -1, 3081, -1], 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 188032435611404269097, 1255647523519025280], 'label': '559872.lw.24.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126225
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [2356, -1, 1952, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 636847820594404529897, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.do1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126226
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [3610, -1, 2358, -1], 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 188032435611404269097, 636847820594404529897, 1255647523519025280], 'label': '559872.lw.24.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126227
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5264, -1, 2894, -1], 'generators': [820016402241462860280, 1094797475614103, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 12933849720, 45194627717568136, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.24.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '24.dq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126228
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4486, -1, 2642, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332953623, 32389886532326400, 871108433886504447360, 326922163405792506840, 1255647523519025280], 'label': '559872.lw.24.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DR', 'subgroup_fusion': None, 'weyl_group': '8000.eh'}
  • id: 227126229
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1329, -1, 1619, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6645229199400, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '24.ds1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DS', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126230
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 3, 'diagramx': [240, -1, 173, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280, 545784629489036427721, 32389973710617736], 'label': '559872.lw.6.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.k1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.K', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126231
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [147, -1, 1237, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6812879759400, 6632296156080, 1255647523519025280, 51212989114823775002, 32389973710617736], 'label': '559872.lw.24.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dt1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126232
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5188, -1, 2870, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 12933043320, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.du1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DU', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126233
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [2879, -1, 2122, -1], 'generators': [1089479559168143, 35700769812329758080, 12933043320, 1466521590431963520, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 820016402241462860280, 1255647523519025280, 545791031688864574921], 'label': '559872.lw.24.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DV', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126234
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [612, -1, 1387, -1], 'generators': [820016402241462860280, 35700769812329758080, 438736938339558949321, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.24.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '24.dw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126235
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1298, -1, 1609, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 45194808301171216, 1089473332953623, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.24.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.dx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DX', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126236
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [189, -1, 1250, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 51212988854246581922, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 45194627717568136, 1255647523519025280], 'label': '559872.lw.24.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '24.dy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126237
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.DZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [971, -1, 1503, -1], 'generators': [820016402241462860280, 35700769812329758080, 186810624000, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 180583603320, 438743340800442968521, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '24.dz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126238
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6236, -1, 3209, -1], 'generators': [820016402241462860280, 422268757434669560403, 186810624000, 1089479559168143, 32389886532326400, 871108433886504447360, 180583603320, 438743340800442968521, 35457479611512819840, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EA', 'old_label': '24.ea1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EA', 'subgroup_fusion': None, 'weyl_group': '23328.gl'}
  • id: 227126239
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 48, 'diagramx': [1177, -1, 1570, -1], 'generators': [820016402241462860280, 186810624000, 1089479559168143, 32389886532326400, 524693765904234127323, 871108433886504447360, 180583603320, 438743340800442968521, 35457479611512819840, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EB', 'old_label': '24.eb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EB', 'subgroup_fusion': None, 'weyl_group': '23328.gj'}
  • id: 227126240
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5688, -1, 3031, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '24.ec1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EC', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126241
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '2.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2.A', 'coset_action_label': None, 'count': 1, 'diagramx': [107, 8670, 42, 2280], 'generators': [32389886532326400, 163151836496911558923, 6645229879800, 35700769812329758080, 806400, 1255647523519025280, 12933043320, 820016402241462860280, 1094530192041023, 46288117478091007, 1466521590431963520, 755373106332052917963, 871108433886504447360, 186811430400], 'label': '559872.lw.2.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.A', 'subgroup_fusion': None, 'weyl_group': '559872.lw'}
  • id: 227126242
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': [34, -1, 255, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 186810624000, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 180583603320, 438743340800442968521, 1255647523519025280, 32389973710617736], 'label': '559872.lw.8.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.A', 'old_label': '8.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.A', 'subgroup_fusion': None, 'weyl_group': '69984.fh'}
  • id: 227126243
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.ED', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2920, -1, 2135, -1], 'generators': [32389886532326400, 35700769812329758080, 1255647523519025280, 326922163405792506840, 820016402241462860280, 1466521590431963520, 871108433886504447360, 1089473332147223, 6645229199400, 45194808301171216, 186811430400], 'label': '559872.lw.24.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ed1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ED', 'subgroup_fusion': None, 'weyl_group': '23328.bq'}
  • id: 227126244
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [458, -1, 1337, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 734042992041763141081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ee1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126245
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2837, -1, 2108, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 545791031688864574921, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.24.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ef1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126246
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1220, -1, 1584, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 636726180724725829081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.eg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126247
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4843, -1, 2758, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 545791031688864574921, 636726180724725829081, 1255647523519025280], 'label': '559872.lw.24.EH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.eh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126248
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4681, -1, 2705, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 51212988841832457242, 45200132882916496, 1255647523519025280], 'label': '559872.lw.24.EI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ei1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126249
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4756, -1, 2730, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 180584409720, 438743340800442968521, 1255647523519025280, 32389973711424136], 'label': '559872.lw.24.EJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ej1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126250
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4411, -1, 2618, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 45200132882916496, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.24.EK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ek1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126251
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4449, -1, 2630, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 51212988854246581922, 1089479559974543, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 45200132882916496, 1255647523519025280], 'label': '559872.lw.24.EL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '24.el1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126252
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [930, -1, 1490, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 636847846747924549081, 871108433886504447360, 32389886532326416, 6645229879800, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.EM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.em1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126253
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 4, 'diagramx': [189, -1, 305, -1], 'generators': [32389886532326400, 6645229879800, 35700769812329758080, 1255647523519025280, 820016402241462860280, 1466521590431963520, 755373106332052917963, 871108433886504447360, 163151878342488069003, 1089473332147223, 45194808301171216, 186811430400], 'label': '559872.lw.8.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '8.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.B', 'subgroup_fusion': None, 'weyl_group': '139968.ii'}
  • id: 227126254
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1573, -1, 1699, -1], 'generators': [636847846747924549081, 35700769812329758080, 1089473332147223, 1466521590431963520, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 820016402241462860280, 1255647523519025280, 545791031688864574921], 'label': '559872.lw.24.EN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.en1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126255
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1413, -1, 1647, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 734164596604266565081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.EO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.eo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126256
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6147, -1, 3180, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 545791031688864574921, 734164596604266565081, 1255647523519025280], 'label': '559872.lw.24.EP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.ep1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126257
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5388, -1, 2934, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.24.EQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.eq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126258
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.ER', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4718, -1, 2718, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.ER', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.er1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ER', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126259
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.ES', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5226, -1, 2882, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 45194808301171216, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.24.ES', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.es1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ES', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126260
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.ET', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5426, -1, 2947, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 51212988854246581922, 1089479559974543, 32389886532326400, 871108433886504447360, 12933849720, 6812880439800, 45200132882236096, 1255647523519025280], 'label': '559872.lw.24.ET', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '24.et1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ET', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126261
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6106, -1, 3167, -1], 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 180584409720, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.EU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '24.eu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EU', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126262
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3844, -1, 2434, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 45194808300364816, 1466521590431963520, 326934612459548846040, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.24.EV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ev1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EV', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126263
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6030, -1, 3143, -1], 'generators': [820016402241462860280, 186811430400, 540918822857334411721, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 734164596604266565081, 1255647523519025280], 'label': '559872.lw.24.EW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ew1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EW', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126264
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': [379, -1, 366, -1], 'generators': [32389886532326400, 163151878255309777683, 6645229879800, 35700769812329758080, 1255647523519025280, 820016402241462860280, 1466521590431963520, 871108433886504447360, 51212989114823775002, 1089473332147223, 45194808301171216, 186811430400], 'label': '559872.lw.8.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '8.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.C', 'subgroup_fusion': None, 'weyl_group': '139968.ii'}
  • id: 227126265
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4977, -1, 2801, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.24.EX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ex1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EX', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126266
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [3940, -1, 2465, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 45194808300364816, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.24.EY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.ey1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EY', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126267
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.EZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [3796, -1, 2419, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 45194808300364816, 1089479559168143, 32389886532326400, 871108433886504447360, 326922163405792506840, 6645229879800, 1255647523519025280], 'label': '559872.lw.24.EZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.ez1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.EZ', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126268
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [4177, -1, 2542, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 51212989102409650082, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.24.FA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fa1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FA', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126269
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [268, -1, 1276, -1], 'generators': [820016402241462860280, 186811430400, 46283920465305607, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.24.FB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FB', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126270
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4321, -1, 2589, -1], 'generators': [820016402241462860280, 32395211114197696, 806400, 35700769812329758080, 1466521590431963520, 51212988854246581922, 32389886532326400, 871108433886504447360, 1806091379855303, 12933849720, 1255647523519025280], 'label': '559872.lw.24.FC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '24.fc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FC', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126271
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 12, 'diagramx': [306, -1, 1288, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 12933849720, 1800761010854543, 1255647523519025280, 32389973710617736, 545784629489036427721], 'label': '559872.lw.24.FD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '24.fd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126272
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5147, -1, 2857, -1], 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 180584409720, 631982000885991493081, 1255647523519025280, 183160226605996524977], 'label': '559872.lw.24.FE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.M', 'old_label': '24.fe1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126273
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [6068, -1, 3155, -1], 'generators': [820016402241462860280, 186811430400, 540918822857334411721, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 624676887256985797086, 12933043320, 1255647523519025280], 'label': '559872.lw.24.FF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ff1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FF', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126274
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5105, -1, 2843, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 726859482975260869086, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.24.FG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FG', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126275
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': [151, -1, 292, -1], 'generators': [820016402241462860280, 163151836496911558923, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.8.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '8.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.D', 'subgroup_fusion': None, 'weyl_group': '139968.ii'}
  • id: 227126276
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5020, -1, 2815, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 734164596604266565081, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.24.FH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FH', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126277
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5062, -1, 2829, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 624676887256985797086, 12933043320, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.24.FI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FI', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126278
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5305, -1, 2907, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280], 'label': '559872.lw.24.FJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FJ', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126279
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5347, -1, 2921, -1], 'generators': [820016402241462860280, 186811430400, 540918822857334411721, 35700769812329758080, 726859482975260869086, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.24.FK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FK', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126280
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3987, -1, 2481, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 327056278482747566040, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.FL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.fl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FL', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126281
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4225, -1, 2558, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6812879759400, 6632296156080, 1255647523519025280, 51212989114823775002, 32389973711424136], 'label': '559872.lw.24.FM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.V', 'old_label': '24.fm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FM', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126282
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [382, -1, 1313, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6645229879800, 180584409720, 438743340800442968521, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.FN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '24.fn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126283
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [4035, -1, 2496, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 327043829428991226840, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.FO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.fo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126284
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [4082, -1, 2511, -1], 'generators': [820016402241462860280, 317081359326433454783, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.FP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.fp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126285
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [344, -1, 1300, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 1806091379855303, 12933849720, 45200132882916496, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.24.FQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '24.fq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126286
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': [417, -1, 378, -1], 'generators': [163151878255309295283, 820016402241462860280, 35700769812329758080, 1466521590431963520, 51212988854246581922, 1089479559974543, 32389886532326400, 871108433886504447360, 6812880439800, 12933849720, 45200132882236096, 1255647523519025280], 'label': '559872.lw.8.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.E', 'old_label': '8.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.E', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126287
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 12, 'diagramx': [4272, -1, 2573, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 51212988854246581922, 32389886532326400, 871108433886504447360, 1806091379855303, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.FR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '24.fr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FR', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126288
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [3749, -1, 2403, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 321582228041560963816, 1255647523519025280], 'label': '559872.lw.24.FS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.fs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FS', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126289
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 12, 'diagramx': [4130, -1, 2527, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 51212989102409650082, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.24.FT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ft1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FT', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126290
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 12, 'diagramx': [231, -1, 1263, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 45194808300364816, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6645229879800, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.FU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.fu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FU', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126291
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 12, 'diagramx': [420, -1, 1325, -1], 'generators': [820016402241462860280, 1094803701954623, 35700769812329758080, 186810624000, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 180583603320, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.24.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '24.fv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126292
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 2, 'diagramx': [3701, -1, 2388, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 326934612459548846040, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.FW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '24.fw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FW', 'subgroup_fusion': None, 'weyl_group': '69984.h'}
  • id: 227126293
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [3892, -1, 2450, -1], 'generators': [1089479559168143, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 32389973710617736, 6645229879800, 820016402241462860280, 1255647523519025280, 327056278482747566040], 'label': '559872.lw.24.FX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.fx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126294
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.FY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 12, 'diagramx': [4368, -1, 2604, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 51212988854246581922, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 6812880439800, 1255647523519025280, 32389973710617736], 'label': '559872.lw.24.FY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '24.fy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.FY', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126295
    {'ambient': '559872.lw', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 27, 'diagramx': [33, -1, 3225, -1], 'generators': [820016402241462860280, 156276420197455355161, 820016402254395903383, 35700769812330206640, 1466521590431963520, 35700769999140830640, 32389886532326400, 6645229879800, 35700769818557227560, 631982000885991493081, 1255647523519025280, 32389973710617736], 'label': '559872.lw.27.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126296
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [218, -1, 3299, -1], 'generators': [35700769812329758080, 1089473332147223, 1466521590431963520, 32389886532326400, 871108433886504447360, 32389886532326416, 755373106332052917963, 163151878342488069003, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.32.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.B', 'old_label': '32.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.A', 'subgroup_fusion': None, 'weyl_group': '11664.gc'}
  • id: 227126297
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.B', 'coset_action_label': None, 'count': 8, 'diagramx': [228, -1, 317, -1], 'generators': [820016402241462860280, 163151836496911558923, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 755373106332052917963, 12933849720, 1255647523519025280], 'label': '559872.lw.8.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '8.f1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.F', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126298
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [386, -1, 3354, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 163151878255309777683, 1089473332147223, 32389886532326400, 871108433886504447360, 32389886532326416, 51212988841832457242, 1255647523519025280], 'label': '559872.lw.32.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.B', 'old_label': '32.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.B', 'subgroup_fusion': None, 'weyl_group': '11664.fz'}
  • id: 227126299
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [261, -1, 3313, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 32389886532326416, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.32.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.B', 'old_label': '32.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.C', 'subgroup_fusion': None, 'weyl_group': '34992.ea'}
  • id: 227126300
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': [127, -1, 3270, -1], 'generators': [820016402241462860280, 1094797474933703, 163151836496911558923, 35700769812329758080, 1466521590431963520, 32389886532326400, 32389886533132816, 871108433886504447360, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.32.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.D', 'old_label': '32.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.D', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126301
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 16, 'diagramx': [61, -1, 3248, -1], 'generators': [1806085152834623, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 755373106332052917963, 45194808301171216, 163151878342488069003, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.32.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.H', 'old_label': '32.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.E', 'subgroup_fusion': None, 'weyl_group': '36000.o'}
  • id: 227126302
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [94, -1, 3259, -1], 'generators': [820016402241462860280, 1094803702635023, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 163151878342488069003, 755373106332052917963, 32395298292489016, 1255647523519025280], 'label': '559872.lw.32.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.F', 'old_label': '32.f1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.F', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126303
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 16, 'diagramx': [28, -1, 3238, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 163151878342488069003, 6645229879800, 755373106332052917963, 1255647523519025280], 'label': '559872.lw.32.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.I', 'old_label': '32.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.G', 'subgroup_fusion': None, 'weyl_group': '36000.o'}
  • id: 227126304
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 16, 'diagramx': [293, -1, 3323, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 163151878255309777683, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.32.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.I', 'old_label': '32.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.H', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126305
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 16, 'diagramx': [157, -1, 3279, -1], 'generators': [820016402241462860280, 163151836496911558923, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.32.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.I', 'old_label': '32.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.I', 'subgroup_fusion': None, 'weyl_group': '34992.z'}
  • id: 227126306
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 16, 'diagramx': [318, -1, 3332, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 45194808301171216, 163151878255309777683, 32389886532326400, 871108433886504447360, 1806085152834623, 51212988841832457242, 1255647523519025280], 'label': '559872.lw.32.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.H', 'old_label': '32.j1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.J', 'subgroup_fusion': None, 'weyl_group': '36000.o'}
  • id: 227126307
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 16, 'diagramx': [182, -1, 3288, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 1466521590431963520, 45194808301171216, 32389886532326400, 871108433886504447360, 1806085152834623, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.32.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.H', 'old_label': '32.k1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.K', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126308
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 8, 'diagramx': [303, -1, 342, -1], 'generators': [820016402241462860280, 163151836496911558923, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 51212989102409650082, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.8.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '8.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.G', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126309
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '32.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': [344, -1, 3340, -1], 'generators': [820016402241462860280, 163151878255309295283, 35700769812329758080, 1466521590431963520, 51212988854246581922, 32389886532326400, 871108433886504447360, 12933849720, 6812880439800, 1255647523519025280], 'label': '559872.lw.32.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.L', 'old_label': '32.l1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.L', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126310
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T30999', 'count': 18, 'diagramx': [1682, -1, 3904, -1], 'generators': [820016402241462860280, 45194808301171216, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871107344593756709903, 12933043320, 734042992041763141081, 545785340919656389321, 1255647523519025280], 'label': '559872.lw.36.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126311
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31012', 'count': 18, 'diagramx': [424, -1, 3496, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 820063397630190476296, 6645229879800, 12933043320, 737198985574543056601, 438743340800442968521, 1800761010854543, 1255647523519025280], 'label': '559872.lw.36.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.B', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126312
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T30995', 'count': 18, 'diagramx': [1336, -1, 3792, -1], 'generators': [820016402241462860280, 820017491534212210583, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 737198985574543056601, 871153628333638412176, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.36.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.C', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126313
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31016', 'count': 18, 'diagramx': [1141, -1, 3729, -1], 'generators': [820016402241462860280, 901687304653300983600, 45194808301171216, 1466521590431963520, 32389886532326400, 6645229879800, 871107344593756709903, 12933043320, 737198985574543056601, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.36.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.D', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126314
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T30990', 'count': 18, 'diagramx': [349, -1, 3472, -1], 'generators': [820016402241462860280, 46283920466112007, 540918822857334411721, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 871108433718854693760, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.36.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.E', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126315
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31021', 'count': 18, 'diagramx': [64, -1, 3380, -1], 'generators': [820016402241462860280, 46283920466112007, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 871108433718854693760, 188026744842196083497, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.36.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.f1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.F', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126316
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31002', 'count': 18, 'diagramx': [837, -1, 3630, -1], 'generators': [820016402241462860280, 186811430400, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 734164596604266565081, 188026744842196083497, 820061597049764031487, 1255647523519025280], 'label': '559872.lw.36.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.G', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126317
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31009', 'count': 18, 'diagramx': [264, -1, 3445, -1], 'generators': [820016402241462860280, 46283920466112007, 540918822857334411721, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 871108433718854693760, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.36.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.H', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126318
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31204', 'count': 36, 'diagramx': [223, -1, 3431, -1], 'generators': [820016402241462860280, 806400, 156276420197455355161, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1800761010854543, 1255647523519025280, 32389973710617736], 'label': '559872.lw.36.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.I', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126319
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 8, 'diagramx': [75, -1, 268, -1], 'generators': [820016402241462860280, 163151836496911558923, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.8.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '8.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.H', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126320
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31203', 'count': 36, 'diagramx': [690, -1, 3583, -1], 'generators': [820016402241462860280, 30578870847268356600, 30578870860201399680, 30580315927556331023, 438736938339558949321, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280, 32389973710617736], 'label': '559872.lw.36.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.j1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.J', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126321
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31202', 'count': 36, 'diagramx': [185, -1, 3419, -1], 'generators': [820016402241462860280, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 30579960227195191823, 6645229879800, 12933043320, 30578870934446647680, 1255647523519025280, 32389973710617736], 'label': '559872.lw.36.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.k1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.K', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126322
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31205', 'count': 36, 'diagramx': [651, -1, 3570, -1], 'generators': [820016402241462860280, 156276420197455355161, 186811430400, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 32389973710617736], 'label': '559872.lw.36.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.l1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.L', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126323
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31007', 'count': 18, 'diagramx': [1398, -1, 3812, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 820063397630190476296, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280, 820018203002473714560], 'label': '559872.lw.36.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.m1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.M', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126324
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31004', 'count': 18, 'diagramx': [1181, -1, 3742, -1], 'generators': [820016402241462860280, 871108433705921650680, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871153628333638412176, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.36.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.n1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.N', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126325
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31019', 'count': 18, 'diagramx': [1367, -1, 3802, -1], 'generators': [820016402241462860280, 871108433705921650680, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 737198985574543056601, 871153628333638412176, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.36.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.o1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.O', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126326
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T30992', 'count': 18, 'diagramx': [1597, -1, 3876, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 820063397630190476296, 6645229879800, 438743340800442968521, 738908776443002781001, 1255647523519025280, 820018203002473714560], 'label': '559872.lw.36.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.p1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.P', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126327
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31014', 'count': 18, 'diagramx': [880, -1, 3644, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 871140823592453977096, 906809203692128183040, 6645229879800, 871108433718854693760, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.36.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.q1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.Q', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126328
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T30997', 'count': 18, 'diagramx': [307, -1, 3458, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 820050237195350924176, 1466521590431963520, 32389886532326400, 820018203008700735480, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.36.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.r1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.R', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126329
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31010', 'count': 18, 'diagramx': [1098, -1, 3715, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 820050237195350924176, 1466521590431963520, 32389886532326400, 820018203008700735480, 6645229879800, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.36.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.s1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.S', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126330
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 8, 'diagramx': [113, -1, 280, -1], 'generators': [820016402241462860280, 163151836496911558923, 1094803701954623, 35700769812329758080, 45194808301171216, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 180583603320, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.8.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.I', 'old_label': '8.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.I', 'subgroup_fusion': None, 'weyl_group': '69984.m'}
  • id: 227126331
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': '36T31001', 'count': 18, 'diagramx': [549, -1, 3537, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 871140823592453977096, 906809203692128183040, 6645229879800, 871108433718854693760, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.36.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.t1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.T', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126332
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1048, -1, 3699, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 32389886532326416, 6645229879800, 12933043320, 734042992041763141081, 545785340919656389321, 1255647523519025280], 'label': '559872.lw.36.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.u1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.U', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126333
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [27, -1, 3368, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 12933043320, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.36.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.v1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.V', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126334
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [586, -1, 3549, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 32389886532326416, 6645229879800, 12933043320, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.36.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.w1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.W', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126335
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1472, -1, 3836, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 12933043320, 737198985574543056601, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.36.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '36.x1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.X', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126336
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [797, -1, 3617, -1], 'generators': [806400, 872620233870097889280, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332953623, 32389886532326400, 326922163405792506840, 6645229879800, 821272049764981885560], 'label': '559872.lw.36.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.y1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.Y', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126337
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1301, -1, 3781, -1], 'generators': [820016402241462860280, 806400, 820016402254395903383, 872364080008464791040, 35700769812329758080, 871153632263367498256, 1466521590431963520, 51212988854246581922, 32389886532326400, 12933849720, 871108438943364341160], 'label': '559872.lw.36.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '36.z1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.Z', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126338
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1221, -1, 3755, -1], 'generators': [820016402241462860280, 34189081155494057520, 186811430400, 1268452426166916616, 1089479559974543, 1268452252289335680, 871108433886504447360, 6645229879800, 12933849720, 51212989114823775002, 1268530712751415680], 'label': '559872.lw.36.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.ba1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126339
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [920, -1, 3657, -1], 'generators': [820016402241462860280, 30591675769036395016, 540918822857334411721, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 30578870934446647680, 1255647523519025280], 'label': '559872.lw.36.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.bb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126340
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [958, -1, 3669, -1], 'generators': [820016402241462860280, 820016402254395903383, 540918822857334411721, 1466521590431963520, 32389886532326400, 871140823592453977096, 906809203692128183040, 6645229879800, 12933043320, 871108433718854693760, 1255647523519025280], 'label': '559872.lw.36.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.bc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126341
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 8, 'diagramx': [265, -1, 329, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 163151878342488069003, 871108433886504447360, 6645229879800, 755373106332052917963, 1255647523519025280, 32389973710617736], 'label': '559872.lw.8.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.J', 'old_label': '8.j1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.J', 'subgroup_fusion': None, 'weyl_group': '69984.h'}
  • id: 227126342
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1432, -1, 3823, -1], 'generators': [820016402241462860280, 156276420197455355161, 186811430400, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 32389973711424136], 'label': '559872.lw.36.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.bd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126343
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [390, -1, 3485, -1], 'generators': [820016402241462860280, 806400, 156276420197455355161, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 45194627717568136, 1255647523519025280], 'label': '559872.lw.36.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.be1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126344
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [499, -1, 3521, -1], 'generators': [820016402241462860280, 30578870847268356600, 30578870860201399680, 438736938339558949321, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 30546480986602116616, 6645229879800, 1255647523519025280], 'label': '559872.lw.36.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.bf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BF', 'subgroup_fusion': None, 'weyl_group': '25000.de'}
  • id: 227126345
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [147, -1, 3407, -1], 'generators': [806400, 872620233870097889280, 820016402254395903383, 34189081155494057520, 1466521590431963520, 1466647221095521920, 820018208158965815040, 45194627717568136, 820018202921522444160, 545792454581040018121, 821272049764981885560], 'label': '559872.lw.36.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '36.bg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126346
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1555, -1, 3863, -1], 'generators': [820016402241462860280, 806400, 820016402254395903383, 35700769812329758080, 1466521590431963520, 32389886532326400, 6645229879800, 12933849720, 45194627717568136, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.36.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.bh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126347
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [759, -1, 3605, -1], 'generators': [820016402241462860280, 806400, 820016402254395903383, 438736938339558949321, 35700769812329758080, 1466521590431963520, 32389886532326400, 6645229879800, 12933849720, 45194627717568136, 1255647523519025280], 'label': '559872.lw.36.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '36.bi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126348
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [455, -1, 3507, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 32389973710617736], 'label': '559872.lw.36.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.bj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BJ', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126349
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [617, -1, 3559, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 820050237195350924176, 1466521590431963520, 32389886532326400, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280, 820018203002473714560], 'label': '559872.lw.36.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.bk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126350
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1515, -1, 3850, -1], 'generators': [820016402241462860303, 1466521590431963520, 32389886532326400, 738908776443002781001, 871140823592453977096, 6645229879800, 438743340800442968521, 820016402241462860280, 1255647523519025280, 871108433705921650680, 906809203692128183040], 'label': '559872.lw.36.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.bl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126351
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [725, -1, 3594, -1], 'generators': [820016402241462860280, 820016402241462860303, 871108433705921650680, 1466521590431963520, 32389886532326400, 871140823592453977096, 906809203692128183040, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.36.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.bm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126352
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '2.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2.B', 'coset_action_label': None, 'count': 1, 'diagramx': [70, 5684, 30, 1620], 'generators': [32389886532326400, 163151836496911558923, 6645229879800, 35700769812329758080, 806400, 1255647523519025280, 12933043320, 820016402241462860280, 1094530192041023, 46288117478091007, 1466521590431963520, 871108433886504447360, 51212989102409650082, 186811430400], 'label': '559872.lw.2.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.B', 'subgroup_fusion': None, 'weyl_group': '559872.lw'}
  • id: 227126353
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '8.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 8, 'diagramx': [341, -1, 354, -1], 'generators': [163151878255309295283, 820016402241462860280, 35700769812329758080, 1466521590431963520, 51212988854246581922, 1089479559168143, 32389886532326400, 871108433886504447360, 6812880439800, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.8.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '8.k1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.K', 'subgroup_fusion': None, 'weyl_group': '69984.p'}
  • id: 227126354
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1723, -1, 3917, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 820050237195350924176, 1466521590431963520, 32389886532326400, 6645229879800, 438743340800442968521, 738908776443002781001, 1255647523519025280, 820018203002473714560], 'label': '559872.lw.36.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.bn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126355
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1261, -1, 3768, -1], 'generators': [820016402241462860280, 820016402241462860303, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871108433718854693760, 737198985574543056601, 871153628333638412176, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.36.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.bo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126356
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [998, -1, 3683, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 820018203008700735480, 820063397630190476296, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.36.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.bp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126357
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [107, -1, 3394, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 820018203008700735480, 820063397630190476296, 6645229879800, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.36.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.bq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126358
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '36.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1639, -1, 3890, -1], 'generators': [820016402241462860280, 820016402241462860303, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871108433718854693760, 871153628333638412176, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.36.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '36.br1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126359
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 1, 'diagramx': [4049, 2332, 5232, 6108], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.A', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126360
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 2, 'diagramx': [5677, 4773, 5759, 6647], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.48.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.B', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126361
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5646, -1, 5749, -1], 'generators': [820016402241462860280, 1094803702635023, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288117477410607, 6645229879800, 180584409720, 1255647523519025280], 'label': '559872.lw.48.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.C', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126362
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5522, -1, 5709, -1], 'generators': [820016402241462860280, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 6812880439800, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.D', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126364
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 1, 'diagramx': [1071, 2332, 728, 4200], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.12.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.A', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126365
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46284088115865607, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.fB', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.F', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126366
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 806400, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.fC', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.G', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126367
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 806400, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995388727616016, 6645229879800, 1255647523519025280], 'label': '559872.lw.48.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.fD', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.H', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126368
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5553, -1, 5719, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 6812879759400, 46284088116672007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.I', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126369
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5461, -1, 5689, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 6812879759400, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '48.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.J', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126370
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 12, 'diagramx': [5584, -1, 5729, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6812879759400, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.K', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126371
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7082, -1, 6214, -1], 'generators': [820016402241462860280, 1089305682393623, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 572644575773341708447, 32389886532326400, 871108433886504447360, 1255647523519025280], 'label': '559872.lw.48.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.j1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.L', 'subgroup_fusion': None, 'weyl_group': '5000.dl'}
  • id: 227126372
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [5430, -1, 5679, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.k1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.M', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126373
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 1089305682393623, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 46995288615475216, 12933043320, 1255647523519025280], 'label': '559872.lw.48.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '48.lB', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.N', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126374
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 1089305682393623, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995288615475216, 12933043320, 6812880439800, 1255647523519025280], 'label': '559872.lw.48.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.lC', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.O', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126375
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [198, -1, 445, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 438743340800442968521, 734042992041763141081, 1800761010854543, 1255647523519025280], 'label': '559872.lw.12.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.B', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126376
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4606, -1, 5412, -1], 'generators': [820016402241462860280, 1094803702635023, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '48.m1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.P', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126377
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2632, -1, 4773, -1], 'generators': [35700769812329758080, 1466521590431963520, 1094803702635023, 32389886532326400, 871108433886504447360, 6632296836480, 545784629489036427721, 820016402241462860280, 1255647523519025280, 46284088115865607], 'label': '559872.lw.48.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '48.n1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.Q', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126378
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7119, -1, 6226, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 12933043320, 51213026689624962741, 1255647523519025280], 'label': '559872.lw.48.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '48.o1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.R', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126379
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5007, -1, 5542, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 52064920397561058730, 12933043320, 1255647523519025280], 'label': '559872.lw.48.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '48.p1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.S', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126380
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4234, -1, 5292, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288117477410607, 12933043320, 6812879759400, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.q1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.T', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126381
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7784, -1, 6442, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6632296836480, 1094803701954623, 444096792106841549662, 820016402241462860280, 1255647523519025280, 46284088115865607], 'label': '559872.lw.48.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '48.r1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.U', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126382
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [715, -1, 4151, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6632296836480, 1094803701954623, 545784629489036427721, 820016402241462860280, 1255647523519025280, 46284088115865607], 'label': '559872.lw.48.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '48.s1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.V', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126383
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5615, -1, 5739, -1], 'generators': [820016402241462860280, 806400, 1094803702635023, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 180584409720, 1255647523519025280], 'label': '559872.lw.48.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.t1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.W', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126384
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5492, -1, 5699, -1], 'generators': [820016402241462860280, 806400, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.u1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.X', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126385
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4296, -1, 5312, -1], 'generators': [820016402241462860280, 1094803702635023, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288117477410607, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.48.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.v1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.Y', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126386
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [293, -1, 476, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 545791031688864574921, 6645229879800, 12933043320, 734042992041763141081, 1800761010854543, 1255647523519025280], 'label': '559872.lw.12.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.C', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126387
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4172, -1, 5272, -1], 'generators': [820016402241462860280, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 12933043320, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.w1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.Z', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126388
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6816, -1, 6128, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 46995388727616016, 1255647523519025280], 'label': '559872.lw.48.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.x1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BA', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126389
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4568, -1, 5400, -1], 'generators': [820016402241462860280, 438736938339558949321, 35700769812329758080, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '48.y1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126390
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7900, -1, 6479, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 541412874089333050462, 186810624000, 32389886532326400, 871108433886504447360, 12933043320, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '48.z1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126391
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 1089305682393623, 35700769812329758080, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995288615475216, 12933043320, 1255647523519025280], 'label': '559872.lw.48.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '48.baB', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BD', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126392
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 1089305682393623, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995288615475216, 12933043320, 1255647523519025280], 'label': '559872.lw.48.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.baC', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BE', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126393
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6854, -1, 6140, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 572644575773341708447, 32389886532326400, 871108433886504447360, 46995388727616016, 1255647523519025280], 'label': '559872.lw.48.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BF', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126394
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6967, -1, 6177, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6812879759400, 1094530192041023, 6632296156080, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.48.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126395
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [5399, -1, 5669, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126396
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4922, -1, 5514, -1], 'generators': [820016402241462860280, 52064920385146934050, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6812879759400, 1094530192041023, 6632296156080, 1255647523519025280], 'label': '559872.lw.48.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.be1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126397
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [522, -1, 550, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 326922163405792506840, 6645229879800, 1255647523519025280, 32389973710617736], 'label': '559872.lw.12.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '12.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.D', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126398
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7821, -1, 6454, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 439230989398159008862, 6645229879800, 12933043320, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126399
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [790, -1, 4176, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 46288117478091007, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BK', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126400
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [828, -1, 4188, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 546278676798015591262, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BL', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126401
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7746, -1, 6429, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 46288117478091007, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.48.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '48.bi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126402
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 3, 'diagramx': [5337, -1, 5649, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BN', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126403
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [5275, -1, 5629, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995388727616016, 6645229879800, 1255647523519025280], 'label': '559872.lw.48.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.bk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BO', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126404
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4265, -1, 5302, -1], 'generators': [820016402241462860280, 806400, 1094803702635023, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.48.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.bl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BP', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126405
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4203, -1, 5282, -1], 'generators': [820016402241462860280, 46287837780393007, 35700769812329758080, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.bm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BQ', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126406
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4142, -1, 5262, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 12933043320, 6812879759400, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '48.bn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BR', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126407
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5045, -1, 5555, -1], 'generators': [636847846747924549081, 35700769812329758080, 1466521590431963520, 1094803702635023, 32389886532326400, 871108433886504447360, 540918822857334411721, 820016402241462860280, 1255647523519025280, 46284088115865607], 'label': '559872.lw.48.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EE', 'old_label': '48.bo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BS', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126408
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1037, -1, 717, -1], 'generators': [820016402241462860280, 46283920466112007, 540918822857334411721, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 12933043320, 1255647523519025280], 'label': '559872.lw.12.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.E', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126409
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6892, -1, 6153, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 46995388727616016, 46284088116672007, 1255647523519025280], 'label': '559872.lw.48.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BT', 'subgroup_fusion': None, 'weyl_group': '8000.eh'}
  • id: 227126410
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1121, -1, 4283, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 6645229199400, 46995388727616016, 1255647523519025280], 'label': '559872.lw.48.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BU', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126411
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6751, -1, 6107, -1], 'generators': [636847846747924549081, 35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.48.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.br1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126412
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1046, -1, 4259, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 636847846747924549081, 871108433886504447360, 6645229879800, 46288117478091007, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126413
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1198, -1, 4308, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 46995388727616016, 46288117477410607, 1255647523519025280], 'label': '559872.lw.48.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bt1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BX', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126414
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1349, -1, 4357, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126415
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2757, -1, 4813, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 6645229879800, 820016402241462860280, 1255647523519025280, 439230989398159008862, 726737487399552843502], 'label': '559872.lw.48.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.BZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126416
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2541, -1, 4743, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 726737487399552843502, 546278676798015591262, 1255647523519025280], 'label': '559872.lw.48.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126417
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [897, -1, 4210, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 636726912922779533422, 6645229879800, 820016402241462860280, 1255647523519025280, 439230989398159008862], 'label': '559872.lw.48.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126418
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7632, -1, 6393, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 46288117478091007, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.by1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126419
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1108, -1, 740, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 188032435611404269097, 12933043320, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.12.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.f1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.F', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126420
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7670, -1, 6405, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 636726912922779533422, 6645229879800, 46288117478091007, 546278676798015591262, 1255647523519025280], 'label': '559872.lw.48.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.bz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126421
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6782, -1, 6117, -1], 'generators': [820016402241462860280, 46287837780393007, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.ca1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CE', 'subgroup_fusion': None, 'weyl_group': '11664.bu'}
  • id: 227126422
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [6720, -1, 6097, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CF', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126423
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1463, -1, 4394, -1], 'generators': [820016402241462860280, 1089305682393623, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 6645229199400, 1255647523519025280], 'label': '559872.lw.48.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.cc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CG', 'subgroup_fusion': None, 'weyl_group': '11664.bu'}
  • id: 227126424
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6627, -1, 6067, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CH', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126425
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6929, -1, 6165, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 572644575773341708447, 32389886532326400, 871108433886504447360, 46995388727616016, 46284088116672007, 1255647523519025280], 'label': '559872.lw.48.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ce1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CI', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126426
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7005, -1, 6189, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288098357263287, 6812879759400, 1094530192041023, 51212988841832457242, 1255647523519025280], 'label': '559872.lw.48.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126427
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7859, -1, 6466, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280, 1094797475614103], 'label': '559872.lw.48.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126428
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4964, -1, 5528, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288098357263287, 6812879759400, 1094530192041023, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.48.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ch1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126429
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2890, -1, 4856, -1], 'generators': [820016402241462860280, 1094797475614103, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ci1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126430
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1460, -1, 854, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.12.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.G', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126431
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 3, 'diagramx': [5368, -1, 5659, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CN', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126432
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [5306, -1, 5639, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995388727616016, 46288117477410607, 6645229879800, 1255647523519025280], 'label': '559872.lw.48.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ck1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CO', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126433
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1160, -1, 4296, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 572644575773341708447, 32389886532326400, 871108433886504447360, 6645229199400, 46995388727616016, 1255647523519025280], 'label': '559872.lw.48.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CP', 'subgroup_fusion': None, 'weyl_group': '23328.bq'}
  • id: 227126434
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7465, -1, 6338, -1], 'generators': [636847846747924549081, 35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 6645229879800, 820016402241462860280, 1255647523519025280, 439230989398159008862], 'label': '559872.lw.48.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126435
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1083, -1, 4271, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 636847846747924549081, 871108433886504447360, 6645229879800, 46288117478091007, 546278676798015591262, 1255647523519025280], 'label': '559872.lw.48.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126436
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1236, -1, 4320, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 572644575773341708447, 32389886532326400, 871108433886504447360, 46995388727616016, 46288117477410607, 1255647523519025280], 'label': '559872.lw.48.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.co1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CS', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126437
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5202, -1, 5605, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280, 726737487399552843502], 'label': '559872.lw.48.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126438
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1387, -1, 4369, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 636726912922779533422, 6645229879800, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CU', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126439
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2501, -1, 4730, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 726737487399552843502, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126440
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [864, -1, 4200, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 439230989398159008862, 6645229879800, 734164596604266565081, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126441
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [447, -1, 526, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 51212988854246581922, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 6812879759400, 1255647523519025280, 32389973710617736], 'label': '559872.lw.12.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '12.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.H', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126442
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6332, -1, 5971, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 636726912922779533422, 6645229879800, 46288117478091007, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ct1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126443
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6279, -1, 5954, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 546278676798015591262, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126444
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.CZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1879, -1, 4529, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192041023, 820016402241462860280, 1255647523519025280, 46287837780393007, 327056278482747566040], 'label': '559872.lw.48.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.cv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.CZ', 'subgroup_fusion': None, 'weyl_group': '11664.bu'}
  • id: 227126445
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6689, -1, 6087, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 1094530192041023, 51212988841832457242, 1255647523519025280], 'label': '559872.lw.48.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126446
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [168, -1, 3975, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 180584409720, 1255647523519025280], 'label': '559872.lw.48.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126447
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [7595, -1, 6380, -1], 'generators': [820016402241462860280, 52064920385146934050, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.cy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126448
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6150, -1, 5912, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 546278676798015591262, 180584409720, 1255647523519025280], 'label': '559872.lw.48.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.cz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126449
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1576, -1, 4431, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 52064920658138251810, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.da1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126450
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1690, -1, 4467, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 1094530192041023, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.48.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.db1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126451
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1804, -1, 4504, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 51212989102409650082, 6812879759400, 12933849720, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '48.dc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126452
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [715, -1, 612, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 51212989102409650082, 12933849720, 6812879759400, 1255647523519025280, 32389973710617736], 'label': '559872.lw.12.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '12.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.I', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126453
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5164, -1, 5593, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46284101049715327, 6812879759400, 1094530192041023, 51212988841832457242, 1255647523519025280], 'label': '559872.lw.48.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126454
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1425, -1, 4381, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.48.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.de1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126455
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [932, -1, 4222, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 439230989398159008862, 6645229879800, 46288117478091007, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.48.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.df1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126456
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7708, -1, 6417, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 734042992041763141081, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126457
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6385, -1, 5988, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 546278676798015591262, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.48.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126458
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [206, -1, 3987, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280, 1094543125084103], 'label': '559872.lw.48.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.di1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126459
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6184, -1, 5923, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1094543125084103, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126460
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [600, -1, 4114, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46284101049715327, 6812879759400, 1094530192041023, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.48.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126461
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [340, -1, 4030, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280, 636848537100398477422], 'label': '559872.lw.48.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126462
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1842, -1, 4517, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280, 636726180724725829081], 'label': '559872.lw.48.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126463
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '2.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2.C', 'coset_action_label': None, 'count': 1, 'diagramx': [32, 2696, 18, 960], 'generators': [820016402241462860280, 163151836496911558923, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 46288117478091007, 1094530192041023, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.2.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.C', 'subgroup_fusion': None, 'weyl_group': '559872.lw'}
  • id: 227126464
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [485, -1, 538, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 327056278482747566040, 1255647523519025280, 32389973710617736], 'label': '559872.lw.12.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '12.j1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.J', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126465
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [638, -1, 4127, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 726859173037867083502, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126466
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2927, -1, 4868, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 6645229879800, 820016402241462860280, 1255647523519025280, 439230989398159008862, 636848537100398477422], 'label': '559872.lw.48.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.do1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DS', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126467
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6227, -1, 5937, -1], 'generators': [820016402241462860280, 35700769812329758080, 636848537100398477422, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126468
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [241, -1, 3998, -1], 'generators': [820016402241462860280, 35700769812329758080, 636848537100398477422, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 546278676798015591262, 1255647523519025280], 'label': '559872.lw.48.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DU', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126469
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2723, -1, 4802, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 726859173037867083502, 32389886532326400, 871108433886504447360, 439230989398159008862, 6645229879800, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126470
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [6050, -1, 5880, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 46288117478091007, 871108433886504447360, 6645229879800, 820016402241462860280, 1255647523519025280, 439230989398159008862, 636726180724725829081], 'label': '559872.lw.48.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ds1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126471
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [408, -1, 4052, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 636726180724725829081, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dt1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126472
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [490, -1, 4079, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 726859173037867083502, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.du1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126473
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.DZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [530, -1, 4092, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 726859173037867083502, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 546278676798015591262, 1255647523519025280], 'label': '559872.lw.48.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.DZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126474
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 6, 'diagramx': [449, -1, 4065, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 546278676798015591262, 636726180724725829081, 1255647523519025280], 'label': '559872.lw.48.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126475
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [1226, -1, 778, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 188032435611404269097, 734164596604266565081, 12933043320, 1255647523519025280], 'label': '559872.lw.12.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.k1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.K', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126476
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [1311, -1, 4345, -1], 'generators': [820016402241462860280, 51213029652729223322, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6812879759400, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126477
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [130, -1, 3962, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126478
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.ED', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [306, -1, 4019, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 51212989102409327522, 6812879759400, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.dz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ED', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126479
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [6116, -1, 5902, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1094530192041023, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ea1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126480
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [1728, -1, 4480, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1094530192041023, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.48.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.eb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EF', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126481
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1500, -1, 4406, -1], 'generators': [820016402241462860280, 1089305682393623, 186811430400, 35700769812329758080, 1466521590431963520, 572644575773341708447, 32389886532326400, 871108433886504447360, 6645229199400, 1255647523519025280], 'label': '559872.lw.48.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.ec1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EG', 'subgroup_fusion': None, 'weyl_group': '11664.bu'}
  • id: 227126482
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [6658, -1, 6077, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 572644575773341708447, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.EH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ed1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EH', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126483
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1273, -1, 4332, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 51212989102409327522, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.EI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ee1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126484
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [92, -1, 3950, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.EJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ef1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126485
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [273, -1, 4008, -1], 'generators': [52064920397561381290, 820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.EK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.eg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126486
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [161, -1, 433, -1], 'generators': [820016402241462860280, 46283920466112007, 540918822857334411721, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.12.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.l1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.L', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126487
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [6083, -1, 5891, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 546278676798015591262, 1255647523519025280], 'label': '559872.lw.48.EL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.eh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126488
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1766, -1, 4492, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192041023, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.48.EM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.ei1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126489
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [1615, -1, 4443, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.48.EN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ej1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EN', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126490
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 3, 'diagramx': [1653, -1, 4455, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 585065871214518371903, 871108433886504447360, 6645229879800, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.EO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.ek1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EO', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126491
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5241, -1, 5618, -1], 'generators': [820016402241462860280, 46999386035164216, 46287837780393007, 35700769812329758080, 1466521590431963520, 51213029640314695202, 32389886532326400, 871108433886504447360, 12933849720, 1255647523519025280], 'label': '559872.lw.48.EP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '48.el1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126492
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [676, -1, 4139, -1], 'generators': [820016402241462860280, 46999386035164216, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933849720, 51213029652728820122, 1255647523519025280], 'label': '559872.lw.48.EQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '48.em1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126493
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.ER', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1538, -1, 4418, -1], 'generators': [820016402241462860280, 35700769812329758080, 46995375794572936, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 46288117477410607, 52064838262242571693, 1255647523519025280], 'label': '559872.lw.48.ER', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '48.en1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ER', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126494
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.ES', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [373, -1, 4041, -1], 'generators': [820016402241462860280, 35700769812329758080, 46995375794572936, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 46288117477410607, 51212989102409650082, 1255647523519025280], 'label': '559872.lw.48.ES', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '48.eo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ES', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126495
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.ET', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4534, -1, 5389, -1], 'generators': [820016402241462860280, 806400, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46284088115865607, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.ET', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.ep1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ET', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126496
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4503, -1, 5379, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995288615475216, 12933043320, 6812880439800, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.EU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '48.eq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EU', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126497
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1546, -1, 882, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 183166628979702253097, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280], 'label': '559872.lw.12.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.m1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.M', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126498
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5085, -1, 5567, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995288615475216, 12933043320, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.EV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '48.er1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126521
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5956, -1, 5849, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 46288098357943687, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.FQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.fm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126499
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [752, -1, 4164, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6632296836480, 545784629489036427721, 46995288615475216, 820016402241462860280, 1255647523519025280, 46284088115865607], 'label': '559872.lw.48.EW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '48.es1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EW', 'subgroup_fusion': None, 'weyl_group': '2592.lv'}
  • id: 227126500
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [27, -1, 3929, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995388727616016, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.EX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.et1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EX', 'subgroup_fusion': None, 'weyl_group': '5184.bv'}
  • id: 227126501
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [58, -1, 3939, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995288615475216, 12933043320, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.EY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '48.eu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EY', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126502
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.EZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 2, 'diagramx': [7509, -1, 6352, -1], 'generators': [820016402241462860280, 35700769812329758080, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995288615475216, 12933043320, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.EZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '48.ev1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.EZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126503
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 8, 'diagramx': [2454, -1, 4715, -1], 'generators': [163169287395106381323, 1466521590431963520, 34189081155494057520, 6632296836480, 821272049764981885560, 1466647221095521920, 806400, 872364080008464791040, 871152539034662040976, 46284088115865607], 'label': '559872.lw.48.FA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.A', 'old_label': '48.ew1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FA', 'subgroup_fusion': None, 'weyl_group': '23328.hd'}
  • id: 227126504
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 16, 'diagramx': [7554, -1, 6367, -1], 'generators': [1466521590431963520, 34189081155494057520, 163151836496911558923, 6632296836480, 821272049764981885560, 1466647221095521920, 806400, 872364080008464791040, 871152539034662040976, 46284088115865607], 'label': '559872.lw.48.FB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.A', 'old_label': '48.ex1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FB', 'subgroup_fusion': None, 'weyl_group': '23328.hd'}
  • id: 227126505
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 48, 'diagramx': [4822, -1, 5482, -1], 'generators': [52137487339274616482, 1500440155006504336, 34189081155494057520, 871108433886504447360, 540918822857334411721, 1466647221095521920, 821528223155031214200, 1268530712751415680, 163151836409733510963, 46284088115865607], 'label': '559872.lw.48.FC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FC', 'old_label': '48.ey1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FC', 'subgroup_fusion': None, 'weyl_group': '11664.fz'}
  • id: 227126506
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 48, 'diagramx': [7423, -1, 6325, -1], 'generators': [32416133904000000, 51212988854246904482, 1500440155006504336, 34189081155494057520, 871108433886504447360, 540918822857334411721, 1466647221095521920, 423478804663928901723, 821528223155031214200, 46284088115865607], 'label': '559872.lw.48.FD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FD', 'old_label': '48.ez1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FD', 'subgroup_fusion': None, 'weyl_group': '11664.fn'}
  • id: 227126507
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 96, 'diagramx': [4874, -1, 5499, -1], 'generators': [32416133904000000, 1500440155006504336, 51879946246096269602, 34189081155494057520, 871108433886504447360, 540918822857334411721, 535398512422526984163, 1466647221095521920, 821528223155031214200, 46284088115865607], 'label': '559872.lw.48.FE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.FE', 'old_label': '48.fa1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FE', 'subgroup_fusion': None, 'weyl_group': '11664.fg'}
  • id: 227126508
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1503, -1, 868, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 12933043320, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.12.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.n1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.N', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126509
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2684, -1, 4790, -1], 'generators': [738908420743158680281, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 540918822857334411721, 46995288615475216, 820016402241462860280, 1255647523519025280, 46284088115865607], 'label': '559872.lw.48.FF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EE', 'old_label': '48.fb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126510
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [566, -1, 4103, -1], 'generators': [820016402241462860280, 46287837780393007, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 46284088115865607, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.FG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.fc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FG', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126511
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4111, -1, 5252, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995388727616016, 46288117477410607, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.FH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FH', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126512
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2799, -1, 4827, -1], 'generators': [51213029652729223322, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 1094530192041023, 820016402241462860280, 1255647523519025280, 46287837780393007, 46284088115865607], 'label': '559872.lw.48.FI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.fe1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126513
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4644, -1, 5425, -1], 'generators': [820016402241462860280, 1094803702635023, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.FJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.ff1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126514
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2582, -1, 4756, -1], 'generators': [820016402241462860280, 1094803702635023, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.FK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.fg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126515
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [5127, -1, 5581, -1], 'generators': [820016402241462860280, 1094803702635023, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288117478091007, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.48.FL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.fh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FL', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126516
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7314, -1, 6290, -1], 'generators': [820016402241462860280, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 51212989102409327522, 46284088115865607, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.FM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.fi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126517
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2845, -1, 4842, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995288615475216, 12933849720, 46284088115865607, 51212988841832457242, 1255647523519025280], 'label': '559872.lw.48.FN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '48.fj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126518
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7372, -1, 6308, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 51212988854246581922, 32389886532326400, 871108433886504447360, 46995288615475216, 12933849720, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.FO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '48.fk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126519
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1588, -1, 895, -1], 'generators': [820016402241462860280, 46283920466112007, 540918822857334411721, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280], 'label': '559872.lw.12.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.o1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.O', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126520
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 2, 'diagramx': [4080, -1, 5242, -1], 'generators': [820016402241462860280, 6819106780080, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46995288615475216, 6812880439800, 46284088115865607, 1255647523519025280], 'label': '559872.lw.48.FP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '48.fl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FP', 'subgroup_fusion': None, 'weyl_group': '69984.p'}
  • id: 227126522
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3648, -1, 5102, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.FR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.fn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126523
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3447, -1, 5037, -1], 'generators': [820016402241462860280, 46999386035164216, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 1255647523519025280], 'label': '559872.lw.48.FS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '48.fo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FS', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126524
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3983, -1, 5210, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 734164596604266565081, 1255647523519025280], 'label': '559872.lw.48.FT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.fp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FT', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126525
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [970, -1, 4234, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 734164596604266565081, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.FU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.fq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FU', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126526
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3246, -1, 4971, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.48.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FV', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126527
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7191, -1, 6249, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 541412874089333050462, 32389886532326400, 871108433886504447360, 6645229879800, 46288098357943687, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.FW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '48.fs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126528
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4378, -1, 5338, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 46288098357943687, 444096792106841549662, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.FX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '48.ft1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FX', 'subgroup_fusion': None, 'weyl_group': '20784.b'}
  • id: 227126529
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7267, -1, 6274, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 46288117478091007, 1255647523519025280, 6632296836480, 545784629489036427721], 'label': '559872.lw.48.FY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '48.fu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126530
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [33, -1, 391, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 636726196416785585897, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.12.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.p1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.P', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126531
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.FZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4466, -1, 5367, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 6812880439800, 46288117478091007, 444096792106841549662, 1255647523519025280], 'label': '559872.lw.48.FZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '48.fv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.FZ', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126532
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 806400, 820016402241462860280, 1255647523519025280, 46287837780393007, 1094543125084103], 'label': '559872.lw.48.GA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.fwB', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126533
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192721423, 820016402241462860280, 1255647523519025280, 46287837780393007, 1094543125084103], 'label': '559872.lw.48.GB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.fwC', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126534
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [5801, -1, 5799, -1], 'generators': [46995388726809616, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 820016402241462860280, 1255647523519025280, 1094543125084103], 'label': '559872.lw.48.GC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.fx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GC', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126535
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 806400, 46283920466112007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.GD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '48.fyB', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GD', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126536
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 6812880439800, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.GE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.fyC', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126537
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [5863, -1, 5819, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 6812880439800, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.GF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '48.fz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126538
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3681, -1, 5113, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 572644575773341708447, 32389886532326400, 871108433886504447360, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.GG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.ga1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GG', 'subgroup_fusion': None, 'weyl_group': '11664.bu'}
  • id: 227126539
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4017, -1, 5221, -1], 'generators': [35700769812329758080, 12933043320, 1466521590431963520, 32389886532326400, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280, 726737422009614680286], 'label': '559872.lw.48.GH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.gb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GH', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126540
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1008, -1, 4246, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 726737422009614680286, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.GI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.gc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GI', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126541
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1750, -1, 948, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 188032435611404269097, 12933043320, 631982000885991493081, 1255647523519025280], 'label': '559872.lw.12.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.q1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Q', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126542
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3481, -1, 5047, -1], 'generators': [820016402241462860280, 46999386035164216, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 316716424025208450607, 1255647523519025280], 'label': '559872.lw.48.GJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.G', 'old_label': '48.gd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GJ', 'subgroup_fusion': None, 'weyl_group': '23328.bg'}
  • id: 227126543
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3548, -1, 5069, -1], 'generators': [820016402241462860280, 1089305682393623, 1094803702635023, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933849720, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.48.GK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.ge1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GK', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126544
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3134, -1, 4935, -1], 'generators': [35700769812329758080, 12933043320, 1466521590431963520, 32389886532326400, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280, 46287837780393007], 'label': '559872.lw.48.GL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GL', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126545
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4713, -1, 5447, -1], 'generators': [820016402241462860280, 46287837780393007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.48.GM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '48.gg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GM', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126546
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2183, -1, 4627, -1], 'generators': [820016402241462860280, 1089305682393623, 1094803702635023, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 51212989102409650082, 12933849720, 1255647523519025280], 'label': '559872.lw.48.GN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.D', 'old_label': '48.gh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GN', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126547
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3848, -1, 5167, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 6812879759400, 51213029652728820122, 1255647523519025280], 'label': '559872.lw.48.GO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.V', 'old_label': '48.gi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126548
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2296, -1, 4664, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 51212989102409650082, 12933043320, 6812879759400, 1255647523519025280], 'label': '559872.lw.48.GP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.V', 'old_label': '48.gj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GP', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126549
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [3279, -1, 4982, -1], 'generators': [820016402241462860280, 806400, 186811430400, 317068910272678557016, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.48.GQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GQ', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126550
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [3313, -1, 4993, -1], 'generators': [820016402241462860280, 806400, 584944247036899427903, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.48.GR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.gl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GR', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126551
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [3514, -1, 5058, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.48.GS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GS', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126552
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.B', 'coset_action_label': None, 'count': 6, 'diagramx': [371, -1, 501, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 326922163405792506840, 6645229879800, 1255647523519025280], 'label': '559872.lw.12.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.r1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.R', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126553
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [3097, -1, 4923, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.48.GT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GT', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126554
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1993, -1, 4566, -1], 'generators': [46995388726809616, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 820016402241462860280, 1255647523519025280, 327056278482747566040], 'label': '559872.lw.48.GU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.go1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GU', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126555
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1917, -1, 4541, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.48.GV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GV', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126556
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [4680, -1, 5436, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.48.GW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GW', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126557
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1955, -1, 4553, -1], 'generators': [820016402241462860280, 806400, 316703995894241913736, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.48.GX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.gr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GX', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126558
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [2145, -1, 4615, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 51212989102409650082, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.48.GY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '48.gs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GY', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126559
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.GZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3172, -1, 4948, -1], 'generators': [820016402241462860280, 1089305682393623, 540918822857334411721, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.GZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '48.gt1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.GZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126560
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4746, -1, 5458, -1], 'generators': [820016402241462860280, 1089305682393623, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288117478091007, 1255647523519025280, 6632296836480, 545784629489036427721], 'label': '559872.lw.48.HA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '48.gu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126561
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3916, -1, 5189, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 51212988854246581922, 32389886532326400, 871108433886504447360, 12933043320, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '48.gv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HB', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126562
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2410, -1, 4701, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 52064920645724126890, 32389886532326400, 871108433886504447360, 12933043320, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '48.gw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HC', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126563
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [1828, -1, 973, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1800761010854543, 1255647523519025280, 545784629489036427721, 32389973710617736], 'label': '559872.lw.12.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '12.s1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.S', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126564
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 12, 'diagramx': [3210, -1, 4960, -1], 'generators': [820016402241462860280, 540918822857334411721, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '48.gx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126565
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 12, 'diagramx': [4780, -1, 5468, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288117478091007, 1094530192041023, 1255647523519025280, 6632296836480, 545784629489036427721], 'label': '559872.lw.48.HE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '48.gy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126566
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5925, -1, 5840, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288098357943687, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.gz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126567
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6018, -1, 5869, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288098357943687, 46284088116672007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.ha1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126572
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [5894, -1, 5829, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.HL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.hd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HL', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126573
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '48.heB', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126574
    {'ambient': '559872.lw', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.A', 'coset_action_label': None, 'count': 3, 'diagramx': [34, -1, 56, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32395191994731016, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 46284088115865607, 631982000885991493081, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.3.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126575
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [1377, -1, 827, -1], 'generators': [820016402241462860280, 806400, 438736938339558949321, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1800761010854543, 1255647523519025280, 32389973710617736], 'label': '559872.lw.12.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '12.t1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.T', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126576
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 12933043320, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.heC', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126577
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [5832, -1, 5809, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '48.hf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HO', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126578
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7155, -1, 6238, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.48.HP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '48.hg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126579
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4334, -1, 5324, -1], 'generators': [820016402241462860280, 806400, 438736938339558949321, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.48.HQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '48.hh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HQ', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126580
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7229, -1, 6262, -1], 'generators': [820016402241462860280, 438736938339558949321, 35700769812329758080, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.HR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '48.hi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126581
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4423, -1, 5353, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 541412874089333050462, 32389886532326400, 871108433886504447360, 46288117478091007, 1255647523519025280, 6632296836480], 'label': '559872.lw.48.HS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '48.hj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HS', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126582
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [5987, -1, 5860, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288117477410607, 46288098357943687, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.A', 'old_label': '48.hk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126583
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 2, 'diagramx': [5740, -1, 5779, -1], 'generators': [820016402241462860280, 35700769812329758080, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933043320, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '48.hl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HU', 'subgroup_fusion': None, 'weyl_group': '69984.m'}
  • id: 227126584
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6561, -1, 6045, -1], 'generators': [820016402241462860280, 1089305682393623, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 636847846747924549081, 871108433886504447360, 46288117478091007, 1255647523519025280], 'label': '559872.lw.48.HV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CF', 'old_label': '48.hm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HV', 'subgroup_fusion': None, 'weyl_group': '20000.z'}
  • id: 227126585
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 24, 'diagramx': [6595, -1, 6056, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 636847846747924549081, 871108433886504447360, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.CF', 'old_label': '48.hn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HW', 'subgroup_fusion': None, 'weyl_group': '20000.z'}
  • id: 227126586
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [333, -1, 489, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.12.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.u1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.U', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126587
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3715, -1, 5123, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 6645229199400, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.HX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.ho1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HX', 'subgroup_fusion': None, 'weyl_group': '11664.bu'}
  • id: 227126588
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3581, -1, 5080, -1], 'generators': [820016402241462860280, 46999386035164216, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 46284088116672007, 1255647523519025280], 'label': '559872.lw.48.HY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.hp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HY', 'subgroup_fusion': None, 'weyl_group': '11664.bu'}
  • id: 227126589
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.HZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 734164596604266565081, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280, 46287837780393007], 'label': '559872.lw.48.HZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.hqB', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.HZ', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126590
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 636726886763072410206, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280, 46287837780393007], 'label': '559872.lw.48.IA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.hqC', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IA', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126591
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6528, -1, 6035, -1], 'generators': [636847846747924549081, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 540918822857334411721, 180584409720, 6645229879800, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.48.IB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.hr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IB', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126592
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3061, -1, 4912, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 180584409720, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.IC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.hs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IC', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126593
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.ID', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3346, -1, 5004, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.ID', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.ht1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ID', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126594
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6428, -1, 6002, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 1255647523519025280], 'label': '559872.lw.48.IE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.hu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IE', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126595
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3748, -1, 5134, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 572644575773341708447, 32389886532326400, 871108433886504447360, 6645229199400, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.IF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.hv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IF', 'subgroup_fusion': None, 'weyl_group': '10000.ej'}
  • id: 227126596
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3614, -1, 5091, -1], 'generators': [820016402241462860280, 46999386035164216, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 46284088116672007, 316716424025208450607, 1255647523519025280], 'label': '559872.lw.48.IG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '48.hw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126597
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [409, -1, 513, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 51212989102409650082, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.12.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.v1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.V', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126598
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3883, -1, 5178, -1], 'generators': [820016402241462860280, 35700769812329758080, 46995375794572936, 1466521590431963520, 32389886532326400, 871108433886504447360, 52064840617010848930, 46288117477410607, 6812879759400, 1255647523519025280], 'label': '559872.lw.48.IH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.V', 'old_label': '48.hx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IH', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126599
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.II', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2334, -1, 4676, -1], 'generators': [820016402241462860280, 35700769812329758080, 46995375794572936, 1466521590431963520, 32389886532326400, 871108433886504447360, 52064920397561058730, 46288117477410607, 6812879759400, 1255647523519025280], 'label': '559872.lw.48.II', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.V', 'old_label': '48.hy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.II', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126600
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [3380, -1, 5015, -1], 'generators': [820016402241462860280, 584944247036899427903, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.IJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.hz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IJ', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126601
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [3414, -1, 5026, -1], 'generators': [820016402241462860280, 186811430400, 317068910272678557016, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.IK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.ia1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IK', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126602
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [2069, -1, 4590, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 585065871214518371903, 871108433886504447360, 6645229879800, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.IL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.ib1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126603
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [2031, -1, 4578, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 327056278482747566040, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.IM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.ic1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IM', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126604
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [2107, -1, 4602, -1], 'generators': [820016402241462860280, 316703995894241913736, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1094530192721423, 1255647523519025280], 'label': '559872.lw.48.IN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '48.id1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IN', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126605
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3782, -1, 5145, -1], 'generators': [820016402241462860280, 46283920466112007, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933849720, 1094530192041023, 51212988841832457242, 1255647523519025280], 'label': '559872.lw.48.IO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '48.ie1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126606
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2221, -1, 4639, -1], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 51212989102409650082, 1094530192041023, 820016402241462860280, 1255647523519025280, 46283920466112007, 6819107460480], 'label': '559872.lw.48.IP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '48.if1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IP', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126607
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3950, -1, 5199, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 51212989102409650082, 180584409720, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.IQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '48.ig1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126608
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1791, -1, 961, -1], 'generators': [820016402241462860280, 540918822857334411721, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 32389973710617736], 'label': '559872.lw.12.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.w1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.W', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126609
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2372, -1, 4688, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 52064920397561058730, 180584409720, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.IR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '48.ih1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IR', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126610
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 12, 'diagramx': [3815, -1, 5156, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933849720, 46288117478091007, 1094530192041023, 51212988841832457242, 1255647523519025280], 'label': '559872.lw.48.IS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '48.ii1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IS', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126611
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 12, 'diagramx': [2258, -1, 4652, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 51212988854246581922, 32389886532326400, 871108433886504447360, 12933849720, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.IT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.H', 'old_label': '48.ij1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IT', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126612
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 2, 'diagramx': [5771, -1, 5790, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 46288117477410607, 6645229879800, 1094543125084103, 1255647523519025280], 'label': '559872.lw.48.IU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '48.ik1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IU', 'subgroup_fusion': None, 'weyl_group': '69984.h'}
  • id: 227126613
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 2, 'diagramx': [5709, -1, 5769, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 46288117478091007, 180584409720, 1094530192041023, 1255647523519025280], 'label': '559872.lw.48.IV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '48.il1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IV', 'subgroup_fusion': None, 'weyl_group': '69984.p'}
  • id: 227126614
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6495, -1, 6024, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 180584409720, 726737422009614680286, 1255647523519025280, 443602744971260965321], 'label': '559872.lw.48.IW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.im1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IW', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126615
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3028, -1, 4901, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 636726886763072410206, 180584409720, 1255647523519025280], 'label': '559872.lw.48.IX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.in1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IX', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126616
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2995, -1, 4890, -1], 'generators': [35700769812329758080, 734042992041763141081, 1466521590431963520, 32389886532326400, 871108433886504447360, 540918822857334411721, 6645229879800, 820016402241462860280, 1255647523519025280, 46287837780393007], 'label': '559872.lw.48.IY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.io1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IY', 'subgroup_fusion': None, 'weyl_group': '23328.bq'}
  • id: 227126617
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.IZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [6461, -1, 6013, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 636726886763072410206, 1255647523519025280], 'label': '559872.lw.48.IZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.ip1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.IZ', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126618
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '48.JA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 24, 'diagramx': [2962, -1, 4879, -1], 'generators': [820016402241462860280, 35700769812329758080, 540918822857334411721, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.48.JA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.E', 'old_label': '48.iq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.JA', 'subgroup_fusion': None, 'weyl_group': '10000.eo'}
  • id: 227126619
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [676, -1, 600, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 51821612137943989933, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.12.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.x1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.X', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126620
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [285, -1, 6575, -1], 'generators': [820016402241462860280, 156276420197455355161, 820061596862952601087, 35700769812330206640, 1466521590431963520, 35700769999140830640, 32389886532326400, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280], 'label': '559872.lw.54.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.A', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126621
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [560, -1, 6664, -1], 'generators': [820016402241462860280, 820061596862952601087, 35700769812330206640, 1466521590431963520, 35700769999140830640, 32389886532326400, 6645229879800, 12933043320, 734042533029422456297, 156891058709895902897, 1255647523519025280], 'label': '559872.lw.54.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.B', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126622
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [161, -1, 6535, -1], 'generators': [820016402241462860280, 820061596862952601087, 35700769812330206640, 1466521590431963520, 35700769999140830640, 32389886532326400, 6645229879800, 12933043320, 631982000885991493081, 156891058709895902897, 1255647523519025280], 'label': '559872.lw.54.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.C', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126623
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [204, -1, 6548, -1], 'generators': [820016402241462860280, 156276420197455355161, 820061596862952601087, 35700769812330206640, 1466521590431963520, 32389886532326400, 35700769999140830640, 6645229879800, 12933043320, 734042533029422456297, 1255647523519025280], 'label': '559872.lw.54.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.D', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126624
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 27, 'diagramx': [517, -1, 6650, -1], 'generators': [820016402241462860280, 820061596862952601087, 540918822857334411721, 1466521590431963520, 32389886532326400, 32395191994731016, 6645229879800, 12933043320, 30578870934446647680, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.54.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.E', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126625
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 27, 'diagramx': [33, -1, 6493, -1], 'generators': [820016402241462860280, 156276420197455355161, 820061596862952601087, 1466521590431963520, 35700769999140830640, 32395191994731016, 32389886532326400, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280], 'label': '559872.lw.54.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.f1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.F', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126626
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 27, 'diagramx': [118, -1, 6521, -1], 'generators': [820016402241462860280, 156276420197455355161, 820061596862952601087, 1466521590431963520, 32389886532326400, 631981934801461092961, 35700769999140830640, 32395191994731016, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.54.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.G', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126627
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 27, 'diagramx': [76, -1, 6507, -1], 'generators': [820016402241462860280, 820061596862952601087, 540918822857334411721, 1466521590431963520, 32389886532326400, 32395191994731016, 738908791434283196881, 6645229879800, 12933043320, 30578870934446647680, 1255647523519025280], 'label': '559872.lw.54.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.H', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126628
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 27, 'diagramx': [363, -1, 6600, -1], 'generators': [820016402241462860280, 806400, 34189081155494057520, 32395191994731000, 32389873599283320, 32395191994731016, 125630663558400, 871108433886504447360, 1089473332147207, 327056278482747566040, 32389960778380800], 'label': '559872.lw.54.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.I', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126629
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 54, 'diagramx': [245, -1, 6562, -1], 'generators': [820016402241462860280, 156276420197455355161, 126951271735816, 34234248408709270320, 32389886532326400, 871108433886504447360, 178978526540429696763, 12933043320, 45300643225649400, 46284088115865607, 34234248221898646320], 'label': '559872.lw.54.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.J', 'old_label': '54.j1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.J', 'subgroup_fusion': None, 'weyl_group': '10368.ke'}
  • id: 227126630
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [1339, -1, 815, -1], 'generators': [820016402241462860280, 806400, 46283920465305607, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 188032435611404269097, 12933849720, 1255647523519025280], 'label': '559872.lw.12.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.y1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Y', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126631
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 54, 'diagramx': [477, -1, 6637, -1], 'generators': [806400, 186811430400, 1466521590431963520, 32395191994731016, 32389886532326400, 1089473332147200, 51212989102409650082, 6645229879800, 12933043320, 46284088115865607, 1255647523519025280], 'label': '559872.lw.54.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.K', 'old_label': '54.k1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.K', 'subgroup_fusion': None, 'weyl_group': '25000.de'}
  • id: 227126632
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 27, 'diagramx': [439, -1, 6625, -1], 'generators': [820016402241462860280, 806400, 34189081155494057520, 186811430400, 125630663558400, 871108433886504447360, 1089473332147207, 51212989102409650082, 6645229879800, 12933043320, 6645229879816], 'label': '559872.lw.54.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.l1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.L', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126633
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 27, 'diagramx': [401, -1, 6612, -1], 'generators': [820016402241462860280, 806400, 156276420197455355161, 820061596862952601087, 186811430400, 1466521590431963520, 32395191994731016, 32389886532326400, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.54.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.m1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.M', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126634
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '54.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 54, 'diagramx': [326, -1, 6588, -1], 'generators': [820016402241462860280, 30668147009801285176, 35700769812330206640, 30713341624585003560, 35700769999140830640, 32389886532326400, 871108433886504447360, 29355639470587226160, 12933043320, 46284088115865607, 545784629489036427721], 'label': '559872.lw.54.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.N', 'old_label': '54.n1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.N', 'subgroup_fusion': None, 'weyl_group': '2592.lx'}
  • id: 227126635
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '64.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [272, -1, 6755, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 32389886532326416, 1255647523519025280], 'label': '559872.lw.64.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.B', 'old_label': '64.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.A', 'subgroup_fusion': None, 'weyl_group': '3888.gj'}
  • id: 227126636
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '64.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': [29, -1, 6677, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 1466521590431963520, 45194808300364816, 32389886532326400, 871108433886504447360, 1800761010048143, 1255647523519025280], 'label': '559872.lw.64.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.D', 'old_label': '64.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.B', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126637
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '64.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': [101, -1, 6700, -1], 'generators': [51212988841832457242, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 163164641150917702923, 438743340800442968521, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.64.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.C', 'old_label': '64.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.C', 'subgroup_fusion': None, 'weyl_group': '82944.bd'}
  • id: 227126638
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '64.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': [67, -1, 6689, -1], 'generators': [1089479559168143, 35700769812329758080, 1466521590431963520, 32389886532326400, 163151836496911558923, 871108433886504447360, 32389973710617736, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.64.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.D', 'old_label': '64.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.D', 'subgroup_fusion': None, 'weyl_group': '2880.hw'}
  • id: 227126639
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '64.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 16, 'diagramx': [130, -1, 6709, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.64.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.I', 'old_label': '64.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.E', 'subgroup_fusion': None, 'weyl_group': '34992.z'}
  • id: 227126640
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '64.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 16, 'diagramx': [156, -1, 6718, -1], 'generators': [1806085152834623, 35700769812329758080, 1466521590431963520, 32389886532326400, 163151836496911558923, 871108433886504447360, 45194808301171216, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.64.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.H', 'old_label': '64.f1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.F', 'subgroup_fusion': None, 'weyl_group': '36000.o'}
  • id: 227126641
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [1189, -1, 766, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 180584409720, 438743340800442968521, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.12.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.z1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Z', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126642
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '64.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [207, -1, 6735, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 1466521590431963520, 32389886532326400, 45199952299313416, 871108433886504447360, 1800767237875223, 1255647523519025280], 'label': '559872.lw.64.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.F', 'old_label': '64.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.G', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126643
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '64.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': [181, -1, 6726, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933849720, 6812880439800, 1255647523519025280], 'label': '559872.lw.64.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.L', 'old_label': '64.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.H', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126644
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '64.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': [234, -1, 6743, -1], 'generators': [820016402241462860280, 163151836496911558923, 1094803701954623, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 1255647523519025280, 32389973711424136], 'label': '559872.lw.64.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.I', 'old_label': '64.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.I', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126645
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3330, -1, 7840, -1], 'generators': [806400, 872620233870097889280, 186811430400, 35700769812329758080, 1466521590431963520, 1089473332953623, 32389886532326400, 326922163405792506840, 32395298292489016, 821272049764981885560], 'label': '559872.lw.72.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126646
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3368, -1, 7851, -1], 'generators': [806400, 872364080008464791040, 186811430400, 35700769812329758080, 1466521590431963520, 1089473332953623, 32389886532326400, 321934720733499697320, 32395298292489016, 821528223155031214200], 'label': '559872.lw.72.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.B', 'subgroup_fusion': None, 'weyl_group': '3888.dc'}
  • id: 227126647
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3292, -1, 7827, -1], 'generators': [820016402241462860280, 820016402254395903383, 186811430400, 1466521590431963520, 45194808301171216, 326934612459548846040, 32389886532326400, 906809203692128183040, 6645229879800, 1255647523519025280], 'label': '559872.lw.72.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.C', 'subgroup_fusion': None, 'weyl_group': '3888.dc'}
  • id: 227126648
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3406, -1, 7864, -1], 'generators': [820016402241462860280, 806400, 820016402254395903383, 872364080008464791040, 35700769812329758080, 1466521590431963520, 51212988854246581922, 32389886532326400, 12933849720, 871108438943364341160], 'label': '559872.lw.72.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '72.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.D', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126649
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9104, -1, 9710, -1], 'generators': [820016402241462860280, 806400, 820016402254395903383, 872364080008464791040, 35700769812329758080, 1466521590431963520, 32389886532326400, 6812879759400, 12933849720, 90876406985856702013], 'label': '559872.lw.72.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '72.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.E', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126650
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3255, -1, 7815, -1], 'generators': [820016402241462860280, 820016402254395903383, 186811430400, 1466521590431963520, 45194808301171216, 32389886532326400, 906809203692128183040, 6645229879800, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.72.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Y', 'old_label': '72.f1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.F', 'subgroup_fusion': None, 'weyl_group': '3888.dc'}
  • id: 227126651
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5113, -1, 8417, -1], 'generators': [820016402241462860280, 806400, 820016402254395903383, 872364080008464791040, 35700769812329758080, 871153632263367498256, 1466521590431963520, 51212988854246581922, 32389886532326400, 12933849720], 'label': '559872.lw.72.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '72.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.G', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126652
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 6, 'diagramx': [599, -1, 575, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 180584409720, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.12.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.ba1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126653
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8666, -1, 9568, -1], 'generators': [820016402241462860280, 806400, 872620233870097889280, 820016402254395903383, 35700769812329758080, 1466521590431963520, 32389886532326400, 87834899914727980322, 12933849720, 45200132882916496], 'label': '559872.lw.72.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '72.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.H', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126654
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4454, -1, 8203, -1], 'generators': [820016402241462860280, 32395211114197696, 156276420197455355161, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229199400, 12933849720, 1255647523519025280], 'label': '559872.lw.72.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BE', 'old_label': '72.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.I', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126655
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9836, -1, 9947, -1], 'generators': [1089479559168143, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 12933849720, 871108433886504447360, 32389973710617736, 6645229199400, 820016402241462860280], 'label': '559872.lw.72.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.j1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.J', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126656
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9898, -1, 9967, -1], 'generators': [820016402241462860280, 806400, 186811430400, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.k1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.K', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126657
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9867, -1, 9957, -1], 'generators': [1089479559168143, 186811430400, 1466521590431963520, 34189081155494057520, 12933849720, 871108433886504447360, 1466647401679125256, 1466647221095521920, 6645229199400, 820016402241462860280], 'label': '559872.lw.72.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.l1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.L', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126658
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9588, -1, 9866, -1], 'generators': [1089479559168143, 186811430400, 1466521590431963520, 34189081155494057520, 871108433886504447360, 1466647401679125256, 1466647221095521920, 6645229879800, 806400, 820016402241462860280], 'label': '559872.lw.72.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.m1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.M', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126659
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8227, -1, 9426, -1], 'generators': [820016402241462860280, 1466521590431963520, 871152539040889061887, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 734042992041763141081, 545785340919656389321, 1255647523519025280], 'label': '559872.lw.72.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.n1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.N', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126660
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3089, -1, 7761, -1], 'generators': [820016402241462860280, 901687304653300983600, 871152539040889061887, 1466521590431963520, 32389886532326400, 6645229879800, 12933043320, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.o1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.O', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126661
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9149, -1, 9724, -1], 'generators': [187943847086324691497, 820016402241462860280, 901687304653300983600, 871152539040889061887, 1466521590431963520, 32389886532326400, 6645229879800, 12933043320, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.72.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.p1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.P', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126662
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6858, -1, 8982, -1], 'generators': [820016402241462860280, 183166629153579833777, 871152539040889061887, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.72.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.q1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.Q', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126663
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1708, -1, 934, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 438743340800442968521, 734042992041763141081, 1255647523519025280, 32389973711424136], 'label': '559872.lw.12.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.bb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126664
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2747, -1, 7650, -1], 'generators': [806400, 872620233870097889280, 1094803701954623, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 326922163405792506840, 821272049764981885560], 'label': '559872.lw.72.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.r1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.R', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126665
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3051, -1, 7748, -1], 'generators': [820016402241462860280, 1466521590431963520, 871152539040889061887, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.s1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.S', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126666
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5655, -1, 8592, -1], 'generators': [820016402241462860280, 901687304653300983600, 871152539040889061887, 1466521590431963520, 32389886532326400, 6645229879800, 12933043320, 737198985574543056601, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.t1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.T', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126667
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8131, -1, 9394, -1], 'generators': [820016402241462860280, 183166629153579833777, 901687304653300983600, 871152539040889061887, 1466521590431963520, 32389886532326400, 6645229879800, 622845472210905339497, 12933043320, 1255647523519025280], 'label': '559872.lw.72.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.u1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.U', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126668
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1465, -1, 7235, -1], 'generators': [820016402241462860280, 871152539040889061887, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 188026744842196083497, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.72.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.v1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.V', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126669
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2785, -1, 7663, -1], 'generators': [806400, 1094803701954623, 872364080008464791040, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 321934720733499697320, 821528223155031214200], 'label': '559872.lw.72.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.w1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.W', 'subgroup_fusion': None, 'weyl_group': '8000.eh'}
  • id: 227126670
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2899, -1, 7699, -1], 'generators': [806400, 872620233870097889280, 186811430400, 35700769812329758080, 1466521590431963520, 45194808301171216, 32389886532326400, 326922163405792506840, 6645229879800, 821272049764981885560], 'label': '559872.lw.72.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.x1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.X', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126671
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [550, -1, 6938, -1], 'generators': [1089479559168143, 872620233870097889280, 1466521590431963520, 34189081155494057520, 12933849720, 821272049764981885560, 1466647221095521920, 6645229199400, 820050241037901038776, 545792454581040018121], 'label': '559872.lw.72.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '72.y1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.Y', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126672
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6144, -1, 8751, -1], 'generators': [1089479559168143, 1466521590431963520, 34189081155494057520, 12933849720, 1466647221095521920, 545784629489036427721, 6645229199400, 872364080008464791040, 821528223155031214200, 871140827696059963456], 'label': '559872.lw.72.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '72.z1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.Z', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126673
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1423, -1, 7221, -1], 'generators': [820016402241462860280, 32395211114197696, 820016402254395903383, 35700769812329758080, 1466521590431963520, 32389886532326400, 6645229199400, 12933849720, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.72.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BH', 'old_label': '72.ba1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126674
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 6, 'diagramx': [118, -1, 419, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 438743340800442968521, 1255647523519025280, 32389973711424136], 'label': '559872.lw.12.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.bc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126675
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9805, -1, 9937, -1], 'generators': [820016402241462860280, 806400, 820016402254395903383, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 12933849720, 45200132882916496, 1255647523519025280], 'label': '559872.lw.72.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.bb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BB', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126676
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9774, -1, 9927, -1], 'generators': [1089479559168143, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 12933849720, 1089473332147200, 806400, 1255647523519025280, 45200132882916496], 'label': '559872.lw.72.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.bc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BC', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126677
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1806, -1, 7345, -1], 'generators': [820016402241462860280, 871152539040889061887, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 188026744842196083497, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.72.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126678
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5252, -1, 8461, -1], 'generators': [820016402241462860280, 183166629153579833777, 901687304653300983600, 871152539040889061887, 1466521590431963520, 32389886532326400, 6645229879800, 12933043320, 737198985574543056601, 1255647523519025280], 'label': '559872.lw.72.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.be1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126679
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4961, -1, 8367, -1], 'generators': [820016402241462860280, 871152539040889061887, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 636726196416785585897, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126680
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3455, -1, 7879, -1], 'generators': [820016402241462860280, 901687304653300983600, 871152539040889061887, 1466521590431963520, 32389886532326400, 6645229879800, 12933043320, 636726196416785585897, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126681
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5212, -1, 8449, -1], 'generators': [820016402241462860280, 183166629153579833777, 1466521590431963520, 871152539040889061887, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 737198985574543056601, 1255647523519025280], 'label': '559872.lw.72.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126682
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5366, -1, 8499, -1], 'generators': [187943847086324691497, 820016402241462860280, 901687304653300983600, 871152539040889061887, 1466521590431963520, 32389886532326400, 6645229879800, 12933043320, 737198985574543056601, 1255647523519025280], 'label': '559872.lw.72.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.bi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126683
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8471, -1, 9505, -1], 'generators': [820016402241462860280, 901687304653300983600, 871152539040889061887, 1466521590431963520, 32389886532326400, 6645229879800, 622845472210905339497, 12933043320, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126684
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9373, -1, 9797, -1], 'generators': [820016402241462860280, 1466521590431963520, 871152539040889061887, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 636726196416785585897, 545785340919656389321, 1255647523519025280], 'label': '559872.lw.72.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.bk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126685
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '4.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.A', 'coset_action_label': None, 'count': 1, 'diagramx': [108, 2696, 93, 2940], 'generators': [820016402241462860280, 163151836496911558923, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 46288117478091007, 1094530192041023, 1255647523519025280], 'label': '559872.lw.4.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.A', 'subgroup_fusion': None, 'weyl_group': '559872.lw'}
  • id: 227126686
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1262, -1, 790, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 12933043320, 438743340800442968521, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.12.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.bd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126687
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4809, -1, 8318, -1], 'generators': [820016402241462860280, 34189081155494057520, 1089473332147223, 1268452252289335680, 871108433886504447360, 6812879759400, 6632296156080, 51212989114823775002, 1499016252856590736, 1268530712751415680], 'label': '559872.lw.72.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126688
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8395, -1, 9480, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1255621276147351680, 1089473332147223, 871108433886504447360, 6812879759400, 6632296156080, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.72.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126689
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2596, -1, 7601, -1], 'generators': [30546481160479697296, 820016402241462860280, 30580315927556331023, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.bn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126690
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2634, -1, 7614, -1], 'generators': [820016402241462860280, 820017491534212210583, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 871153628333638412176, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126691
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1050, -1, 7101, -1], 'generators': [156282822397283502361, 820016402241462860280, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1800761010854543, 1255647523519025280], 'label': '559872.lw.72.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.bp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126692
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5576, -1, 8567, -1], 'generators': [820016402241462860280, 156276420197455355161, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1800761010854543, 1255647523519025280], 'label': '559872.lw.72.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.bq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126693
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [855, -1, 7038, -1], 'generators': [820016402241462860280, 1466521590431963520, 45194808301171216, 32389886532326400, 906809203692128183040, 6645229879800, 871107344593756709903, 12933043320, 545785340919656389321, 1255647523519025280], 'label': '559872.lw.72.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.br1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126694
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2936, -1, 7712, -1], 'generators': [317081359326433454783, 872620233870097889280, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 821272049764981885560, 45194808301171216, 6645229879800, 806400], 'label': '559872.lw.72.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BS', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126695
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2975, -1, 7724, -1], 'generators': [820016402241462860280, 34189081155494057520, 186811430400, 1089479559974543, 1268452252289335680, 871108433886504447360, 6645229879800, 12933849720, 51212989114823775002, 1268530712751415680], 'label': '559872.lw.72.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bt1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126696
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2391, -1, 7535, -1], 'generators': [820016402241462860280, 540918822857334411721, 1466521590431963520, 32389886532326400, 871108433886504447360, 30547570279350660487, 6645229879800, 12933043320, 30578870934446647680, 1255647523519025280], 'label': '559872.lw.72.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.bu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BU', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126697
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1418, -1, 840, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 32389886532326416, 545791031688864574921, 6645229879800, 12933043320, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.12.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.be1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126698
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2429, -1, 7547, -1], 'generators': [820016402241462860280, 46283920466112007, 540918822857334411721, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 871108433718854693760, 1255647523519025280], 'label': '559872.lw.72.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126699
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [893, -1, 7049, -1], 'generators': [820016402241462860280, 46283920466112007, 186811430400, 1466521590431963520, 411859534130845926497, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.72.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.bw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126700
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5614, -1, 8579, -1], 'generators': [820016402241462860280, 156276420197455355161, 46283920466112007, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.72.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.bx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126701
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8947, -1, 9659, -1], 'generators': [820016402241462860280, 1512889476046139663, 34189081155494057520, 51821612150358114853, 1511821106566485120, 1268452252289335680, 871108433886504447360, 1511822233657209720, 1511820925982882040, 1268530712751415680], 'label': '559872.lw.72.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.by1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126702
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [931, -1, 7062, -1], 'generators': [820016402241462860280, 46283920466112007, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 871108433718854693760, 188026744842196083497, 1255647523519025280], 'label': '559872.lw.72.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.bz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.BZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126703
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7416, -1, 9163, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 6645229879800, 12933043320, 871107344599982924183, 438743340800442968521, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.ca1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126704
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6182, -1, 8763, -1], 'generators': [820016402241462860280, 35700769812329758080, 438736938339558949321, 1466521590431963520, 32389886532326400, 6645229879800, 12933043320, 871107344599982924183, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.cb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126705
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5831, -1, 8649, -1], 'generators': [35700769812329758080, 12933043320, 1466521590431963520, 32389886532326400, 32389973710617736, 6645229879800, 820016402241462860280, 1255647523519025280, 871107344599982924183, 545791031688864574921], 'label': '559872.lw.72.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.cc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CC', 'subgroup_fusion': None, 'weyl_group': '5184.ga'}
  • id: 227126706
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5889, -1, 8668, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 6645229879800, 12933043320, 871107344599982924183, 1255647523519025280, 32389973710617736, 545784629489036427721], 'label': '559872.lw.72.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.cd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CD', 'subgroup_fusion': None, 'weyl_group': '25000.de'}
  • id: 227126707
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7838, -1, 9299, -1], 'generators': [820016402241462860280, 541411953575178396241, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 35444779584389159040, 1800767237068823, 32389973710617736, 1268530712751415680], 'label': '559872.lw.72.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '72.ce1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126708
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1942, -1, 1010, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332953623, 32389886532326400, 871108433886504447360, 326922163405792506840, 6645229879800, 1255647523519025280], 'label': '559872.lw.12.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BF', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126709
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5937, -1, 8683, -1], 'generators': [872620233870097889280, 1466521590431963520, 34189081155494057520, 820049881507922828287, 821272049764981885560, 1466647221095521920, 183166629153579833777, 871108439216874935160, 806400, 871108433892732274680], 'label': '559872.lw.72.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '72.cf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126710
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9681, -1, 9897, -1], 'generators': [820016402241462860280, 806400, 34189081155494057520, 1512889476045736463, 1466521590431963520, 1511821106566485120, 1466647221095521920, 871108433886504447360, 1511820925982882040, 45200132882916496], 'label': '559872.lw.72.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.cg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CG', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126711
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9712, -1, 9907, -1], 'generators': [820016402241462860280, 806400, 34189081155494057520, 186811430400, 1089479559168143, 32389886532326400, 871108433886504447360, 32416133904000000, 12933849720, 45200132882916496], 'label': '559872.lw.72.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.ch1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CH', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126712
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9743, -1, 9916, -1], 'generators': [820016402241462860280, 806400, 186811430400, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 45200132882916496, 1255647523519025280], 'label': '559872.lw.72.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.ci1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CI', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126713
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9650, -1, 9887, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 45200132882916496], 'label': '559872.lw.72.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.cj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CJ', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126714
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7875, -1, 9312, -1], 'generators': [820016402241462860280, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1800767237068823, 438743340800442968521, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.ck1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126715
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2225, -1, 7481, -1], 'generators': [820016402241462860280, 438736938339558949321, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1800767237068823, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.cl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126716
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7294, -1, 9123, -1], 'generators': [820016402241462860280, 806400, 438736938339558949321, 35700769812329758080, 1466521590431963520, 32389886532326400, 871139734299705432967, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.72.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '72.cm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126717
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7332, -1, 9136, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871139734299705432967, 6645229879800, 12933849720, 188032435611404269097, 1255647523519025280], 'label': '559872.lw.72.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '72.cn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126718
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9619, -1, 9877, -1], 'generators': [820016402241462860280, 806400, 1094797475614103, 34189081155494057520, 186811430400, 1466521590431963520, 1466647221095521920, 871108433886504447360, 12933849720, 1466647401679125256], 'label': '559872.lw.72.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.co1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CO', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126719
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [999, -1, 705, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 51212988854246581922, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 6812879759400, 45200132882916496, 1255647523519025280], 'label': '559872.lw.12.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '12.bg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126720
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9929, -1, 9977, -1], 'generators': [820016402241462860280, 806400, 34189081155494057520, 186811430400, 1466521590431963520, 1466647221095521920, 871108433886504447360, 6645229879800, 12933849720, 1466647401679125256], 'label': '559872.lw.72.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.cp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CP', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126721
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9557, -1, 9857, -1], 'generators': [820016402241462860280, 806400, 1094797475614103, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 12933849720, 32389973710617736], 'label': '559872.lw.72.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.cq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CQ', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126722
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9526, -1, 9846, -1], 'generators': [1089479559168143, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 45194808301171216, 6645229879800, 806400, 820016402241462860280], 'label': '559872.lw.72.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.cr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CR', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126723
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1864, -1, 7364, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 45194627716761736, 734042992041763141081, 545785340919656389321, 1255647523519025280], 'label': '559872.lw.72.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.cs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CS', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126724
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5075, -1, 8404, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 737198985574543056601, 45194627716761736, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ct1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126725
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5328, -1, 8486, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 636726180724725829081, 45194627716761736, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.cu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CU', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126726
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3512, -1, 7898, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 636726180724725829081, 45194627716761736, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.cv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126727
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2861, -1, 7687, -1], 'generators': [872364080008464791040, 186811430400, 35700769812329758080, 1466521590431963520, 45194808301171216, 1089473332953623, 32389886532326400, 6645229199400, 321934720733499697320, 821528223155031214200], 'label': '559872.lw.72.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.cw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CW', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126728
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3129, -1, 7774, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 871141179367060364287, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280, 820018203002473714560], 'label': '559872.lw.72.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.cx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126729
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5698, -1, 8606, -1], 'generators': [820016402241462860280, 871108433705921650680, 1466521590431963520, 32389886532326400, 33479179281676927, 906809203692128183040, 6645229879800, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.cy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126730
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1667, -1, 921, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 51212989102409650082, 12933849720, 6812879759400, 45200132882916496, 1255647523519025280], 'label': '559872.lw.12.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '12.bh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126731
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.CZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8177, -1, 9409, -1], 'generators': [820016402241462860280, 871108433705921650680, 1466521590431963520, 32389886532326400, 33479179281676927, 906809203692128183040, 6645229879800, 188026744842196083497, 636847820594404529897, 1255647523519025280], 'label': '559872.lw.72.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.cz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.CZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126732
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1511, -1, 7250, -1], 'generators': [187943847086324691497, 820016402241462860280, 871108433705921650680, 901687304653300983600, 1466521590431963520, 32389886532326400, 33479179281676927, 6645229879800, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.72.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.da1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126733
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5290, -1, 8474, -1], 'generators': [820016402241462860280, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871107344593756709903, 734042992041763141081, 545785340919656389321, 1255647523519025280, 32389973711424136], 'label': '559872.lw.72.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.db1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126734
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8569, -1, 9536, -1], 'generators': [820016402241462860280, 901687304653300983600, 820050237195350924176, 1466521590431963520, 32389886532326400, 6645229879800, 737198985574543056601, 438743340800442968521, 1800761010854543, 1255647523519025280], 'label': '559872.lw.72.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126735
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5404, -1, 8511, -1], 'generators': [820016402241462860280, 820017491534212210583, 1466521590431963520, 32389886532326400, 871140823592453977096, 906809203692128183040, 6645229879800, 636726180724725829081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126736
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9415, -1, 9810, -1], 'generators': [820016402241462860280, 820017491534212210583, 901687304653300983600, 1466521590431963520, 32389886532326400, 871140823592453977096, 6645229879800, 636726180724725829081, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.de1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126737
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4999, -1, 8379, -1], 'generators': [820016402241462860280, 1466521590431963520, 45194808301171216, 32389886532326400, 906809203692128183040, 6645229879800, 871107344599983730583, 734042992041763141081, 545785340919656389321, 1255647523519025280], 'label': '559872.lw.72.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.df1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126738
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2556, -1, 7588, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 820063397630190476296, 6645229879800, 737198985574543056601, 438743340800442968521, 1800767237875223, 1255647523519025280], 'label': '559872.lw.72.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126739
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8621, -1, 9553, -1], 'generators': [820016402241462860280, 820017491547145253903, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 636726180724725829081, 871153628333638412176, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126740
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1011, -1, 7088, -1], 'generators': [820016402241462860280, 820017491547145253903, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 636726180724725829081, 871153628333638412176, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.di1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126741
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [961, -1, 692, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280, 51212989114823775002, 32389973710617736], 'label': '559872.lw.12.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126742
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5037, -1, 8392, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 737198985574543056601, 45194627716761736, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126743
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7492, -1, 9188, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 737198985574543056601, 45194627716761736, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.dk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126744
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3911, -1, 8027, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 45194627716761736, 438743340800442968521, 1255647523519025280, 622845435596059323481], 'label': '559872.lw.72.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126745
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1601, -1, 7279, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 636726180724725829081, 45194627716761736, 545785340919656389321, 1255647523519025280], 'label': '559872.lw.72.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.dm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126746
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2823, -1, 7675, -1], 'generators': [872620233870097889280, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332953623, 32389886532326400, 326922163405792506840, 6645229199400, 821272049764981885560], 'label': '559872.lw.72.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DN', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126747
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2469, -1, 7560, -1], 'generators': [820016402241462860280, 871108433705921650680, 1466521590431963520, 32389886532326400, 33479179281676927, 906809203692128183040, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.do1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126748
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [591, -1, 6952, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 871141179367060364287, 32389886532326400, 6645229879800, 438743340800442968521, 738908776443002781001, 1255647523519025280, 820018203002473714560], 'label': '559872.lw.72.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126749
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3716, -1, 7965, -1], 'generators': [187943847086324691497, 820016402241462860280, 871108433705921650680, 901687304653300983600, 1466521590431963520, 32389886532326400, 33479179281676927, 6645229879800, 636847820594404529897, 1255647523519025280], 'label': '559872.lw.72.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126750
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4282, -1, 8148, -1], 'generators': [820016402241462860280, 871108433705921650680, 1466521590431963520, 32389886532326400, 33479179281676927, 906809203692128183040, 6645229879800, 188026744842196083497, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.72.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126751
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6640, -1, 8911, -1], 'generators': [820016402241462860280, 820017491534212210583, 1466521590431963520, 32389886532326400, 871140823592453977096, 906809203692128183040, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ds1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DS', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126752
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1866, -1, 985, -1], 'generators': [820016402241462860280, 540918822857334411721, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 32389973711424136], 'label': '559872.lw.12.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126753
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7997, -1, 9351, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 871107344593756709903, 737198985574543056601, 545702443163784997321, 1255647523519025280, 32389973711424136], 'label': '559872.lw.72.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dt1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126754
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4127, -1, 8097, -1], 'generators': [820016402241462860280, 901687304653300983600, 820050237195350924176, 1466521590431963520, 32389886532326400, 6645229879800, 438743340800442968521, 1800761010854543, 1255647523519025280, 622845435596059323481], 'label': '559872.lw.72.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.du1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DU', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126755
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [781, -1, 7013, -1], 'generators': [820016402241462860280, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871107344593756709903, 636726180724725829081, 545785340919656389321, 1255647523519025280, 32389973711424136], 'label': '559872.lw.72.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126756
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3214, -1, 7802, -1], 'generators': [820016402241462860280, 820017491547145253903, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 737198985574543056601, 871153628333638412176, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126757
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6687, -1, 8926, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 45194808301171216, 32389886532326400, 6645229879800, 737198985574543056601, 871107344599983730583, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126758
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6733, -1, 8942, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 820063397630190476296, 6645229879800, 438743340800442968521, 1800767237875223, 1255647523519025280, 622845435596059323481], 'label': '559872.lw.72.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126759
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.DZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9065, -1, 9697, -1], 'generators': [820016402241462860280, 1466521590431963520, 45194808301171216, 32389886532326400, 906809203692128183040, 6645229879800, 871107344599983730583, 636726180724725829081, 545785340919656389321, 1255647523519025280], 'label': '559872.lw.72.DZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.dz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.DZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126760
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2709, -1, 7638, -1], 'generators': [820016402241462860280, 820016402254395903383, 186811430400, 1466521590431963520, 326934612459548846040, 32389886532326400, 906809203692128183040, 6645229879800, 1255647523519025280, 32389973711424136], 'label': '559872.lw.72.EA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ea1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EA', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126761
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3172, -1, 7788, -1], 'generators': [820016402241462860280, 46283920466112007, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871108433718854693760, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.EB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.eb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126762
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2513, -1, 7574, -1], 'generators': [820016402241462860280, 871154339801899916167, 901687304653300983600, 1466521590431963520, 32389886532326400, 820018203008700735480, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.EC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ec1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126763
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [560, -1, 562, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332953623, 32389886532326400, 871108433886504447360, 6645229879800, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.12.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BK', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126764
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.ED', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9024, -1, 9684, -1], 'generators': [820016402241462860280, 46283920466112007, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871108433718854693760, 188026744842196083497, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.72.ED', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ed1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ED', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126765
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [970, -1, 7075, -1], 'generators': [187943847086324691497, 820016402241462860280, 46283920466112007, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 871108433718854693760, 636726196416785585897, 1255647523519025280], 'label': '559872.lw.72.EE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ee1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126766
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1922, -1, 7383, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 636847846747924549081, 6645229879800, 45194627716761736, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.EF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ef1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126767
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3980, -1, 8050, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 636847846747924549081, 906809203692128183040, 6645229879800, 45194627716761736, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.EG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.eg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126768
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8912, -1, 9647, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 45194627716761736, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.EH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.eh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126769
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8082, -1, 9379, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 734164596604266565081, 45194627716761736, 545785340919656389321, 1255647523519025280], 'label': '559872.lw.72.EI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ei1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126770
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4013, -1, 8060, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 624555287925214343881, 45194627716761736, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.EJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ej1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126771
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7531, -1, 9200, -1], 'generators': [636847846747924549081, 1466521590431963520, 32389886532326400, 45194627716761736, 820016402254395903383, 545785340919656389321, 6645229879800, 820016402241462860280, 1255647523519025280, 906809203692128183040], 'label': '559872.lw.72.EK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.ek1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126772
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1385, -1, 7209, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 45194627716761736, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.EL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.el1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126773
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5441, -1, 8523, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 45194627716761736, 545702443163784997321, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.EM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.em1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126774
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1904, -1, 998, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 1255647523519025280, 545784629489036427721, 32389973711424136], 'label': '559872.lw.12.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126775
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3013, -1, 7736, -1], 'generators': [820016402241462860280, 34189081155494057520, 1268452426166916616, 1089479559974543, 1268452252289335680, 871108433886504447360, 6812879759400, 12933849720, 51212988841832457242, 1268530712751415680], 'label': '559872.lw.72.EN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.en1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126776
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6816, -1, 8969, -1], 'generators': [30546481160479697296, 820016402241462860280, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 30578870947379691000, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.EO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '72.eo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126777
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6348, -1, 8817, -1], 'generators': [820016402241462860280, 871108433705921650680, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871153628333638412176, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.EP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ep1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126778
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6386, -1, 8829, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 1466521590431963520, 32389886532326400, 820063397630190476296, 6645229879800, 438743340800442968521, 1255647523519025280, 820018203002473714560], 'label': '559872.lw.72.EQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.eq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126779
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.ER', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8985, -1, 9671, -1], 'generators': [820016402241462860280, 34189081155494057520, 1268452426166916616, 1089479559974543, 1268452252289335680, 871108433886504447360, 6812879759400, 12933849720, 51212989114823775002, 1268530712751415680], 'label': '559872.lw.72.ER', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.er1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ER', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126780
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.ES', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2672, -1, 7626, -1], 'generators': [820016402241462860280, 820016402254395903383, 186811430400, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 327056278482747566040, 1255647523519025280, 32389973711424136], 'label': '559872.lw.72.ES', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.es1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ES', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126781
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.ET', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4847, -1, 8330, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1255621363325643016, 1255621276147351680, 1089473332147223, 871108433886504447360, 6645229879800, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.72.ET', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.et1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ET', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126782
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8434, -1, 9492, -1], 'generators': [820016402241462860280, 34189081155494057520, 186811430400, 1268452426166916616, 1089473332147223, 1268452252289335680, 871108433886504447360, 6645229879800, 51212989114823775002, 1268530712751415680], 'label': '559872.lw.72.EU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.eu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EU', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126783
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6778, -1, 8956, -1], 'generators': [820016402241462860280, 30591675769036395016, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 30578870934446647680, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.EV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '72.ev1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126784
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6462, -1, 8854, -1], 'generators': [820016402241462860280, 820016402254395903383, 901687304653300983600, 820050237195350924176, 1466521590431963520, 32389886532326400, 820018203008700735480, 6645229879800, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.EW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ew1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126785
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1630, -1, 909, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 51212989102409650082, 6645229879800, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.12.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126786
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6424, -1, 8841, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 871140823592453977096, 906809203692128183040, 6645229879800, 871108433718854693760, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.EX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ex1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126787
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4885, -1, 8343, -1], 'generators': [820016402241462860280, 820048792215174284167, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 188026744842196083497, 180584409720, 734042992041763141081, 1255647523519025280], 'label': '559872.lw.72.EY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ey1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126788
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.EZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3873, -1, 8015, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 871141179367060364287, 624555242156578804697, 6645229879800, 438743340800442968521, 1255647523519025280, 820018203002473714560], 'label': '559872.lw.72.EZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ez1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.EZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126789
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7569, -1, 9212, -1], 'generators': [820016402241462860280, 871108433705921650680, 1466521590431963520, 32389886532326400, 33479179281676927, 906809203692128183040, 6645229879800, 636726196416785585897, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.FA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fa1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126790
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1641, -1, 7292, -1], 'generators': [187943847086324691497, 820016402241462860280, 871108433705921650680, 901687304653300983600, 1466521590431963520, 32389886532326400, 33479179281676927, 6645229879800, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.FB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126791
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3947, -1, 8039, -1], 'generators': [820016402241462860280, 901687304653300983600, 820050237195350924176, 1466521590431963520, 32389886532326400, 6645229879800, 624555287925214343881, 438743340800442968521, 1800761010854543, 1255647523519025280], 'label': '559872.lw.72.FC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126792
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1347, -1, 7197, -1], 'generators': [820016402241462860280, 1466521590431963520, 32389886532326400, 636847846747924549081, 906809203692128183040, 6645229879800, 871107344593756709903, 545785340919656389321, 1255647523519025280, 32389973711424136], 'label': '559872.lw.72.FD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126793
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7607, -1, 9225, -1], 'generators': [820016402241462860280, 820017491534212210583, 1466521590431963520, 32389886532326400, 871140823592453977096, 906809203692128183040, 6645229879800, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.FE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fe1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126794
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5476, -1, 8535, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 871107344593756709903, 545702443163784997321, 738908776443002781001, 1255647523519025280, 32389973711424136], 'label': '559872.lw.72.FF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ff1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126795
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6501, -1, 8867, -1], 'generators': [187943847086324691497, 820016402241462860280, 871108433705921650680, 901687304653300983600, 1466521590431963520, 32389886532326400, 33479179281676927, 6645229879800, 737198985574543056601, 1255647523519025280], 'label': '559872.lw.72.FG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126796
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '4.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 4, 'diagramx': [32, -1, 69, -1], 'generators': [32389886532326400, 6645229879800, 35700769812329758080, 540918822857334411721, 1255647523519025280, 820016402241462860280, 1094530192041023, 46288117478091007, 1466521590431963520, 871108433886504447360, 163151878342488069003, 51212989102409327522, 186811430400], 'label': '559872.lw.4.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '4.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.B', 'subgroup_fusion': None, 'weyl_group': '139968.ii'}
  • id: 227126797
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [639, -1, 588, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 45194627717568136, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.12.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '12.bn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126798
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7958, -1, 9338, -1], 'generators': [820016402241462860280, 871108433705921650680, 1466521590431963520, 32389886532326400, 33479179281676927, 906809203692128183040, 6645229879800, 636847820594404529897, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.FH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126799
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4088, -1, 8085, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 871141179367060364287, 6645229879800, 622845472210905339497, 438743340800442968521, 1255647523519025280, 820018203002473714560], 'label': '559872.lw.72.FI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126800
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [673, -1, 6978, -1], 'generators': [820016402241462860280, 820048792215174284167, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 734164596604266565081, 188026744842196083497, 180584409720, 1255647523519025280], 'label': '559872.lw.72.FJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126801
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7454, -1, 9175, -1], 'generators': [820016402241462860280, 820017491534212210583, 901687304653300983600, 1466521590431963520, 32389886532326400, 636847846747924549081, 871140823592453977096, 6645229879800, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.FK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126802
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4242, -1, 8135, -1], 'generators': [820016402241462860280, 820017491534212210583, 1466521590431963520, 32389886532326400, 636847846747924549081, 906809203692128183040, 871140823592453977096, 6645229879800, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.FL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126803
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4166, -1, 8110, -1], 'generators': [820016402241462860280, 901687304653300983600, 820050237195350924176, 1466521590431963520, 32389886532326400, 6645229879800, 438743340800442968521, 738908776443002781001, 1800761010854543, 1255647523519025280], 'label': '559872.lw.72.FM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126804
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2142, -1, 7454, -1], 'generators': [871107344593756709903, 1466521590431963520, 32389886532326400, 734164596604266565081, 545785340919656389321, 6645229879800, 32389973711424136, 820016402241462860280, 1255647523519025280, 906809203692128183040], 'label': '559872.lw.72.FN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126805
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7645, -1, 9237, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 820063397630190476296, 6645229879800, 624555287925214343881, 438743340800442968521, 1800767237875223, 1255647523519025280], 'label': '559872.lw.72.FO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126806
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1557, -1, 7265, -1], 'generators': [820016402241462860280, 820017491547145253903, 901687304653300983600, 1466521590431963520, 32389886532326400, 636847846747924549081, 6645229879800, 871153628333638412176, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.FP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126807
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4206, -1, 8123, -1], 'generators': [636847846747924549081, 820017491547145253903, 1466521590431963520, 32389886532326400, 871153628333638412176, 6645229879800, 438743340800442968521, 820016402241462860280, 1255647523519025280, 906809203692128183040], 'label': '559872.lw.72.FQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126808
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [243, -1, 459, -1], 'generators': [820016402241462860280, 806400, 438736938339558949321, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 45194627717568136, 1255647523519025280], 'label': '559872.lw.12.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '12.bo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126809
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4375, -1, 8177, -1], 'generators': [636847846747924549081, 1466521590431963520, 32389886532326400, 545785340919656389321, 45194808301171216, 6645229879800, 820016402241462860280, 1255647523519025280, 871107344599983730583, 906809203692128183040], 'label': '559872.lw.72.FR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126810
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7374, -1, 9149, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 820063397630190476296, 6645229879800, 438743340800442968521, 738908776443002781001, 1800767237875223, 1255647523519025280], 'label': '559872.lw.72.FS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FS', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126811
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4329, -1, 8162, -1], 'generators': [820016402241462860280, 820017491547145253903, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871153628333638412176, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.FT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ft1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126812
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1123, -1, 7124, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 45194808301171216, 32389886532326400, 6645229879800, 871107344599983730583, 545702443163784997321, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.FU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FU', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126813
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5975, -1, 8696, -1], 'generators': [1466521590431963520, 32389886532326400, 734164596604266565081, 545785340919656389321, 45194808301171216, 6645229879800, 820016402241462860280, 1255647523519025280, 871107344599983730583, 906809203692128183040], 'label': '559872.lw.72.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126814
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4923, -1, 8355, -1], 'generators': [820016402241462860280, 186811430400, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 188026744842196083497, 734042992041763141081, 820061597049764031487, 1255647523519025280], 'label': '559872.lw.72.FW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126815
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6541, -1, 8880, -1], 'generators': [187943847086324691497, 820016402241462860280, 46283920466112007, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 871108433718854693760, 737198985574543056601, 1255647523519025280], 'label': '559872.lw.72.FX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126816
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8516, -1, 9519, -1], 'generators': [820016402241462860280, 46283920466112007, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871108433718854693760, 636726196416785585897, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.FY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126817
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.FZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6587, -1, 8895, -1], 'generators': [820016402241462860280, 871154339801899916167, 901687304653300983600, 1466521590431963520, 32389886532326400, 820018203008700735480, 6645229879800, 622845472210905339497, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.FZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.fz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.FZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126818
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5741, -1, 8620, -1], 'generators': [820016402241462860280, 871154339801899916167, 901687304653300983600, 1466521590431963520, 32389886532326400, 820018203008700735480, 6645229879800, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.GA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ga1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126819
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1976, -1, 1021, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 180584409720, 438743340800442968521, 734042992041763141081, 1255647523519025280, 32389973711424136], 'label': '559872.lw.12.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.bp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126820
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1682, -1, 7305, -1], 'generators': [187943847086324691497, 820016402241462860280, 46283920466112007, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 871108433718854693760, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.GB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.gb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126821
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [633, -1, 6965, -1], 'generators': [820016402241462860280, 46283920466112007, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871108433718854693760, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.GC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.gc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126822
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [709, -1, 6990, -1], 'generators': [820016402241462860280, 186811430400, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 734164596604266565081, 188026744842196083497, 820061597049764031487, 1255647523519025280], 'label': '559872.lw.72.GD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.gd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126823
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1159, -1, 7136, -1], 'generators': [820016402241462860280, 871154339801899916167, 901687304653300983600, 1466521590431963520, 32389886532326400, 624555242156578804697, 820018203008700735480, 6645229879800, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.GE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ge1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126824
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [745, -1, 7002, -1], 'generators': [820016402241462860280, 46283920466112007, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871108433718854693760, 636847820594404529897, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.GF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.gf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GF', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126825
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1088, -1, 7113, -1], 'generators': [187943847086324691497, 820016402241462860280, 46283920466112007, 901687304653300983600, 1466521590431963520, 32389886532326400, 6645229879800, 871108433718854693760, 636847820594404529897, 1255647523519025280], 'label': '559872.lw.72.GG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.gg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126826
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5782, -1, 8633, -1], 'generators': [820016402241462860280, 46283920466112007, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871108433718854693760, 188026744842196083497, 636847820594404529897, 1255647523519025280], 'label': '559872.lw.72.GH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.gh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126827
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [437, -1, 6902, -1], 'generators': [872620233870097889280, 1466521590431963520, 45194627717568136, 34189081155494057520, 821272049764981885560, 1466647221095521920, 820018208158965134640, 820018202921522444160, 545792454581040018121, 1094797475614103], 'label': '559872.lw.72.GI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '72.gi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126828
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [475, -1, 6914, -1], 'generators': [820016402241462860280, 1094797475614103, 156276420197455355161, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 12933849720, 45194627717568136, 1255647523519025280], 'label': '559872.lw.72.GJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BE', 'old_label': '72.gj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126829
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 72, 'diagramx': [513, -1, 6927, -1], 'generators': [872620233870097889280, 35700769812329758080, 545701731795634827721, 1466521590431963520, 45194627717568136, 821272049764981885560, 1466647221095521920, 820018208158965134640, 820018202921522444160, 1094797475614103], 'label': '559872.lw.72.GK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.GK', 'old_label': '72.gk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126830
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [76, -1, 405, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 180584409720, 438743340800442968521, 1255647523519025280, 32389973711424136], 'label': '559872.lw.12.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.bq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126831
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [4049, -1, 8072, -1], 'generators': [820063397543012184976, 1466521590431963520, 34189081155494057520, 12933849720, 1466647221095521920, 545784629489036427721, 6645229199400, 872364080008464791040, 821528223155031214200, 1094797475614103], 'label': '559872.lw.72.GL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '72.gl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126832
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [4417, -1, 8191, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 6645229199400, 12933849720, 45194627717568136, 820016408873759696783, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.72.GM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BH', 'old_label': '72.gm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126833
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [6040, -1, 8717, -1], 'generators': [32416133904000000, 186811430400, 32389886532326400, 34189081155494057520, 12933849720, 871108433886504447360, 32389973710617736, 6645229199400, 820016402241462860280, 1089479559974543], 'label': '559872.lw.72.GN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.gn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GN', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126834
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [8817, -1, 9617, -1], 'generators': [820018202921521637760, 872620233870097889280, 1466521590431963520, 34189081155494057520, 820016402254395903383, 821272049764981885560, 820018208158965815040, 1466647221095521920, 438743340800442968521, 820050237108171826696], 'label': '559872.lw.72.GO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '72.go1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126835
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [9973, -1, 9991, -1], 'generators': [1089479559168143, 12933043320, 32389886532326400, 541405551027595087441, 871108433886504447360, 32389886532326416, 6645229879800, 820016402241462860280, 1268530712751415680, 35444779584389159040], 'label': '559872.lw.72.GP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '72.gp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GP', 'subgroup_fusion': None, 'weyl_group': '2592.lv'}
  • id: 227126836
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [6009, -1, 8707, -1], 'generators': [35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 12933849720, 871108433886504447360, 32389973710617736, 6645229199400, 820016402241462860280, 1089479559974543], 'label': '559872.lw.72.GQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.gq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GQ', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126837
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [6071, -1, 8727, -1], 'generators': [820016402241462860280, 806400, 34189081155494057520, 45194808301171216, 1466521590431963520, 1089473332953623, 1511821106566485120, 1466647221095521920, 871108433886504447360, 1511822233657209720], 'label': '559872.lw.72.GR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.gr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GR', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126838
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [4706, -1, 8285, -1], 'generators': [820016402241462860280, 820016402254395903383, 35700769812329758080, 186810624000, 1466521590431963520, 32389886532326400, 180583603320, 438743340800442968521, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.GS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BE', 'old_label': '72.gs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GS', 'subgroup_fusion': None, 'weyl_group': '2592.lv'}
  • id: 227126839
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [5526, -1, 8550, -1], 'generators': [806400, 872620233870097889280, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332953623, 32389886532326400, 326922163405792506840, 821272049764981885560], 'label': '559872.lw.72.GT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.gt1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126840
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9454, -1, 9823, -1], 'generators': [806400, 872364080008464791040, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332953623, 32389886532326400, 321934720733499697320, 821528223155031214200], 'label': '559872.lw.72.GU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.gu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GU', 'subgroup_fusion': None, 'weyl_group': '8000.eh'}
  • id: 227126841
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1152, -1, 754, -1], 'generators': [32389886532326400, 6645229879800, 35700769812329758080, 1255647523519025280, 734042992041763141081, 820016402241462860280, 1466521590431963520, 438743340800442968521, 871108433886504447360, 1089473332147223, 45194808301171216, 186811430400], 'label': '559872.lw.12.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.br1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126842
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [7772, -1, 9278, -1], 'generators': [35700769812329758080, 186811430400, 1466521590431963520, 12933849720, 871108433886504447360, 1466647401679125256, 1466647221095521920, 6645229199400, 820016402241462860280, 1089479559974543], 'label': '559872.lw.72.GV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '72.gv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126843
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [7803, -1, 9288, -1], 'generators': [186811430400, 1466521590431963520, 34189081155494057520, 12933849720, 871108433886504447360, 1466647401679125256, 1466647221095521920, 6645229199400, 820016402241462860280, 1089479559974543], 'label': '559872.lw.72.GW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.gw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GW', 'subgroup_fusion': None, 'weyl_group': '3888.js'}
  • id: 227126844
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1979, -1, 7402, -1], 'generators': [820016402241462860280, 34189081155494057520, 1268452426166916616, 1089473332147223, 1268452252289335680, 871108433886504447360, 6812879759400, 6632296156080, 51212989114823775002, 1268530712751415680], 'label': '559872.lw.72.GX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.gx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126845
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1234, -1, 7160, -1], 'generators': [820016402241462860280, 35700769812329758080, 1255621363325643016, 1255621276147351680, 1089473332147223, 871108433886504447360, 6812879759400, 6632296156080, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.72.GY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.gy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126846
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.GZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8703, -1, 9580, -1], 'generators': [820016402241462860280, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 12933043320, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.GZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.gz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.GZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126847
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8741, -1, 9592, -1], 'generators': [820016402241462860280, 820016402254395903383, 1466521590431963520, 32389886532326400, 906809203692128183040, 32389886532326416, 6645229879800, 12933043320, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.HA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ha1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HA', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126848
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4502, -1, 8219, -1], 'generators': [156282822397283502361, 820016402241462860280, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.72.HB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '72.hb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HB', 'subgroup_fusion': None, 'weyl_group': '25000.de'}
  • id: 227126849
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8866, -1, 9632, -1], 'generators': [820016402241462860280, 438736938339558949321, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 32389886532326416, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.72.HC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.hc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126850
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [818, -1, 7025, -1], 'generators': [820016402241462860280, 820016402254395903383, 35700769812329758080, 438736938339558949321, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 12933043320, 1255647523519025280], 'label': '559872.lw.72.HD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '72.hd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HD', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126851
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [4560, -1, 8238, -1], 'generators': [12933043320, 1466521590431963520, 32389886532326400, 820016402254395903383, 32389886532326416, 545785340919656389321, 6645229879800, 820016402241462860280, 1255647523519025280, 906809203692128183040], 'label': '559872.lw.72.HE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.he1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126852
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1299, -1, 802, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 734164596604266565081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.12.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.bs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BS', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126853
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7741, -1, 9268, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 45194808301171216, 1089473332953623, 32389886532326400, 871108433886504447360, 6645229879800], 'label': '559872.lw.72.HF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.hf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HF', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126854
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7711, -1, 9258, -1], 'generators': [806400, 872620233870097889280, 186811430400, 35700769812329758080, 1466521590431963520, 45194808301171216, 1089473332953623, 32389886532326400, 6645229879800, 821272049764981885560], 'label': '559872.lw.72.HG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.hg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HG', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126855
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2096, -1, 7439, -1], 'generators': [820016402241462860280, 806400, 820016402254395903383, 872364080008464791040, 35700769812329758080, 1466521590431963520, 51212988854246581922, 32389886532326400, 12933849720, 45194627717568136], 'label': '559872.lw.72.HH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '72.hh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126856
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1271, -1, 7172, -1], 'generators': [820016402241462860280, 806400, 872620233870097889280, 820016402254395903383, 35700769812329758080, 1466521590431963520, 32389886532326400, 87834899914727980322, 12933849720, 45194627717568136], 'label': '559872.lw.72.HI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '72.hi1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HI', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126857
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [4774, -1, 8307, -1], 'generators': [820016402241462860280, 806400, 34189081155494057520, 186811430400, 1466521590431963520, 1089479559168143, 1466647221095521920, 871108433886504447360, 12933849720, 1466647401679125256], 'label': '559872.lw.72.HJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.hj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HJ', 'subgroup_fusion': None, 'weyl_group': '1296.3538'}
  • id: 227126858
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4742, -1, 8297, -1], 'generators': [1089479559168143, 35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 12933849720, 32389973710617736, 1089473332147200, 806400, 1255647523519025280], 'label': '559872.lw.72.HK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '72.hk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HK', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 227126859
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2308, -1, 7508, -1], 'generators': [820016402241462860280, 186810624000, 1089479559168143, 32389886532326400, 871108433886504447360, 29355639470587226160, 180583603320, 438743340800442968521, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.HL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '72.hl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126860
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2266, -1, 7494, -1], 'generators': [820016402241462860280, 186810624000, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 180583603320, 438743340800442968521, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.HM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BH', 'old_label': '72.hm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HM', 'subgroup_fusion': None, 'weyl_group': '2592.lx'}
  • id: 227126861
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 72, 'diagramx': [2351, -1, 7522, -1], 'generators': [820016402241462860280, 186810624000, 1089479559168143, 32389886532326400, 871108433886504447360, 180583603320, 438743340800442968521, 35457479611512819840, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.HN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.HN', 'old_label': '72.hn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HN', 'subgroup_fusion': None, 'weyl_group': '1296.3574'}
  • id: 227126862
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1196, -1, 7148, -1], 'generators': [820016402241462860280, 186810624000, 541411953575178396241, 1089479559168143, 32389886532326400, 871108433886504447360, 180583603320, 35444779584389159040, 32389973710617736, 1268530712751415680], 'label': '559872.lw.72.HO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BN', 'old_label': '72.ho1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126863
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 12, 'diagramx': [760, -1, 627, -1], 'generators': [820016402241462860280, 46283920465305607, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.12.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.bt1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BT', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126864
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6907, -1, 8998, -1], 'generators': [820016402241462860280, 186810624000, 541411953575178396241, 1089479559168143, 32389886532326400, 871108433886504447360, 180583603320, 35655602745925975680, 163151700498773658123, 32389973710617736], 'label': '559872.lw.72.HP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EA', 'old_label': '72.hp1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HP', 'subgroup_fusion': None, 'weyl_group': '23328.gl'}
  • id: 227126865
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 48, 'diagramx': [4665, -1, 8272, -1], 'generators': [820016402241462860280, 163151836496911558923, 186810624000, 541411953575178396241, 1089479559168143, 32389886532326400, 871108433886504447360, 180583603320, 35655602745925975680, 32389973710617736], 'label': '559872.lw.72.HQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.EB', 'old_label': '72.hq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HQ', 'subgroup_fusion': None, 'weyl_group': '23328.gj'}
  • id: 227126866
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [5147, -1, 8428, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1089479559168143, 32389886532326400, 871108433886504447360, 32416133904000000, 12933849720, 32389973710617736], 'label': '559872.lw.72.HR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '72.hr1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HR', 'subgroup_fusion': None, 'weyl_group': '1296.3529'}
  • id: 227126867
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [5178, -1, 8438, -1], 'generators': [820016402241462860280, 806400, 34189081155494057520, 186811430400, 1089479559168143, 32389886532326400, 871108433886504447360, 32416133904000000, 12933849720, 32389973710617736], 'label': '559872.lw.72.HS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BJ', 'old_label': '72.hs1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HS', 'subgroup_fusion': None, 'weyl_group': '1296.3584'}
  • id: 227126868
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8269, -1, 9439, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 32389973710617736], 'label': '559872.lw.72.HT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '72.ht1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HT', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126869
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [9492, -1, 9835, -1], 'generators': [32389886532326400, 321934720733499697320, 35700769812329758080, 1466521590431963520, 872364080008464791040, 821528223155031214200, 1089473332147223, 6645229199400, 45194808301171216, 186811430400], 'label': '559872.lw.72.HU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.hu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HU', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126870
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2037, -1, 7420, -1], 'generators': [820016402241462860303, 734042992041763141081, 1466521590431963520, 32389886532326400, 32389886532326416, 545785340919656389321, 6645229879800, 820016402241462860280, 1255647523519025280, 906809203692128183040], 'label': '559872.lw.72.HV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.hv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126871
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8779, -1, 9604, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.HW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.hw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126872
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1309, -1, 7184, -1], 'generators': [820016402241462860280, 820016402241462860303, 1466521590431963520, 32389886532326400, 906809203692128183040, 32389886532326416, 6645229879800, 636726180724725829081, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.HX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.hx1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126873
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4617, -1, 8256, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 636726180724725829081, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.HY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.hy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126874
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 12, 'diagramx': [812, -1, 644, -1], 'generators': [820016402241462860280, 540918822857334411721, 46283920465305607, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933043320, 631982000885991493081, 1255647523519025280], 'label': '559872.lw.12.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.bu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BU', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126875
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.HZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 72, 'diagramx': [7916, -1, 9325, -1], 'generators': [438654396675113586121, 872620233870097889280, 35700769812329758080, 1089473332147223, 1268452252289335680, 32416133904000000, 6645229879800, 737198985574543056601, 871140823679631461776, 821272049764981885560], 'label': '559872.lw.72.HZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.HZ', 'old_label': '72.hz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.HZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126876
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6105, -1, 8738, -1], 'generators': [872620233870097889280, 32389886532326400, 35700769812329758080, 326922163405792506840, 821272049764981885560, 1466521590431963520, 1089473332147223, 6645229199400, 45194808301171216, 186811430400], 'label': '559872.lw.72.IA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ia1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IA', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126877
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3796, -1, 7990, -1], 'generators': [820016402241462860280, 820016402241462860303, 1466521590431963520, 32389886532326400, 906809203692128183040, 32389886532326416, 6645229879800, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.IB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ib1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126878
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [36, -1, 6772, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 737198985574543056601, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.IC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.ic1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126879
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.ID', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [279, -1, 6851, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 438743340800442968521, 1255647523519025280, 622845435596059323481], 'label': '559872.lw.72.ID', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.id1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ID', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126880
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9196, -1, 9740, -1], 'generators': [820016402241462860303, 1466521590431963520, 32389886532326400, 32389886532326416, 545785340919656389321, 6645229879800, 820016402241462860280, 1255647523519025280, 636726180724725829081, 906809203692128183040], 'label': '559872.lw.72.IE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.ie1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IE', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126881
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [7680, -1, 9248, -1], 'generators': [872620233870097889280, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 326934612459548846040, 1089473332147223, 32389886532326400, 6645229879800, 821272049764981885560], 'label': '559872.lw.72.IF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.if1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IF', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126882
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [3834, -1, 8003, -1], 'generators': [51212988841832457242, 35700769812329758080, 1466521590431963520, 820016402254396709783, 32389886532326400, 12933849720, 871108438943364341160, 872364080008464791040, 820016402241462860280, 871153632263367498256], 'label': '559872.lw.72.IG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '72.ig1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IG', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126883
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [9274, -1, 9765, -1], 'generators': [820016402241462860280, 820016402254396709783, 872364080008464791040, 35700769812329758080, 871153632263367498256, 1466521590431963520, 51212988854246581922, 32389886532326400, 12933849720, 871108438943364341160], 'label': '559872.lw.72.IH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '72.ih1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IH', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126884
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.II', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3758, -1, 7978, -1], 'generators': [51212988841832457242, 1255647504398197800, 6812879759400, 34189081155494057520, 871108433886504447360, 1268452252289335680, 1256735576171663423, 820016402241462860280, 1268530712751415680, 45200132882916496], 'label': '559872.lw.72.II', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ii1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.II', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126885
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.B', 'coset_action_label': None, 'count': 12, 'diagramx': [864, -1, 661, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 631982000885991493081, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.12.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.bv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BV', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126886
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [399, -1, 6889, -1], 'generators': [820016402241462860280, 30591675769036395016, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 30578870947379691000, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.IJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '72.ij1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IJ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126887
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [81, -1, 6787, -1], 'generators': [820016402241462860303, 1466521590431963520, 32389886532326400, 871140823592453977096, 6645229879800, 438743340800442968521, 820016402241462860280, 1255647523519025280, 871108433705921650680, 906809203692128183040], 'label': '559872.lw.72.IK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ik1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IK', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126888
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [119, -1, 6799, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 820050237195350924176, 32389886532326400, 6645229879800, 438743340800442968521, 1255647523519025280, 820018203002473714560], 'label': '559872.lw.72.IL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.il1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IL', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126889
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [9237, -1, 9753, -1], 'generators': [820016402241462860280, 1499017560530918416, 34189081155494057520, 1089479559974543, 1268452252289335680, 871108433886504447360, 6812879759400, 12933849720, 51212989114823775002, 1268530712751415680], 'label': '559872.lw.72.IM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.im1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IM', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126890
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6953, -1, 9013, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 624555287925214343881, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.IN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.in1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IN', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126891
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6227, -1, 8778, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 636847846747924549081, 32389886532326416, 6645229879800, 545702443163784997321, 1255647523519025280], 'label': '559872.lw.72.IO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.io1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IO', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126892
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6310, -1, 8805, -1], 'generators': [636847846747924549081, 820016402241462860303, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 438743340800442968521, 820016402241462860280, 1255647523519025280, 906809203692128183040], 'label': '559872.lw.72.IP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ip1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IP', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126893
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8307, -1, 9451, -1], 'generators': [636847846747924549081, 820016402241462860303, 1466521590431963520, 32389886532326400, 32389886532326416, 545785340919656389321, 6645229879800, 820016402241462860280, 1255647523519025280, 906809203692128183040], 'label': '559872.lw.72.IQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.iq1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IQ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126894
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2183, -1, 7468, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.IR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ir1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IR', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126895
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [8353, -1, 9466, -1], 'generators': [820016402241462860303, 1466521590431963520, 32389886532326400, 738908776443002781001, 32389886532326416, 6645229879800, 438743340800442968521, 820016402241462860280, 1255647523519025280, 906809203692128183040], 'label': '559872.lw.72.IS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.is1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IS', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126896
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '12.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 12, 'diagramx': [917, -1, 678, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 624676887256985797086, 12933849720, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.12.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '12.bw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BW', 'subgroup_fusion': None, 'weyl_group': '46656.y'}
  • id: 227126897
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [9323, -1, 9781, -1], 'generators': [820016402241462860303, 1466521590431963520, 32389886532326400, 734164596604266565081, 32389886532326416, 545785340919656389321, 6645229879800, 820016402241462860280, 1255647523519025280, 906809203692128183040], 'label': '559872.lw.72.IT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.it1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IT', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126898
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8036, -1, 9364, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 32389886532326416, 6645229879800, 545702443163784997321, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.IU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '72.iu1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IU', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126899
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1721, -1, 7318, -1], 'generators': [820016402241462860280, 1223238034843372920, 35700769812329758080, 45194808301171216, 1255621276147351680, 1089473332147223, 871108433886504447360, 1255647523519025280, 51212989114823775002, 1223231576424968880], 'label': '559872.lw.72.IV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.iv1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IV', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126900
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [234, -1, 6836, -1], 'generators': [820016402241462860280, 34189081155494057520, 186811430400, 1089473332147223, 1268452252289335680, 871108433886504447360, 6645229879800, 51212989114823775002, 1499016252856590736, 1268530712751415680], 'label': '559872.lw.72.IW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.iw1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IW', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126901
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [324, -1, 6865, -1], 'generators': [30546481160479697296, 820016402241462860280, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 30578870934446647680, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.IX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '72.ix1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IX', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126902
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [195, -1, 6824, -1], 'generators': [820016402241462860280, 820016402241462860303, 901687304653300983600, 1466521590431963520, 32389886532326400, 820018203008700735480, 820063397630190476296, 6645229879800, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.IY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.iy1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IY', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126903
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.IZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [157, -1, 6811, -1], 'generators': [820016402241462860280, 820016402241462860303, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 871108433718854693760, 871153628333638412176, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.IZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.iz1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.IZ', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126904
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [6272, -1, 8792, -1], 'generators': [820016402241462860280, 820016402241462860303, 186811430400, 1466521590431963520, 45194808301171216, 32389886532326400, 906809203692128183040, 6645229879800, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.72.JA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '72.ja1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JA', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126905
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1759, -1, 7330, -1], 'generators': [820016402241462860280, 820016402254396709783, 872620233870097889280, 35700769812329758080, 1466521590431963520, 32389886532326400, 87834899914727980322, 12933849720, 6812880439800, 45200132882236096], 'label': '559872.lw.72.JB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '72.jb1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JB', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126906
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 36, 'diagramx': [361, -1, 6878, -1], 'generators': [820016402241462860280, 820016402254396709783, 872364080008464791040, 35700769812329758080, 871153632263366817856, 1466521590431963520, 51212988854246581922, 32389886532326400, 12933849720, 871108438943365021560], 'label': '559872.lw.72.JC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '72.jc1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JC', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126907
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '4.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.B', 'coset_action_label': None, 'count': 8, 'diagramx': [70, -1, 81, -1], 'generators': [820016402241462860280, 163151836496911558923, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 51212989102409650082, 6645229879800, 12933043320, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.4.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '4.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.C', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126908
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': [113, -1, 1059, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 186810624000, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 180583603320, 1255647523519025280, 32389973710617736], 'label': '559872.lw.16.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.A', 'old_label': '16.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.A', 'subgroup_fusion': None, 'weyl_group': '23328.hd'}
  • id: 227126909
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3674, -1, 7951, -1], 'generators': [820016402241462860280, 901687304653300983600, 1466521590431963520, 32389886532326400, 871141179367060364287, 6645229879800, 12933043320, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.JD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.E', 'old_label': '72.jd1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JD', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126910
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3636, -1, 7938, -1], 'generators': [820016402241462860280, 1466521590431963520, 32389886532326400, 33479179281676927, 906809203692128183040, 6645229879800, 12933043320, 737198985574543056601, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.JE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.E', 'old_label': '72.je1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JE', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126911
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3598, -1, 7926, -1], 'generators': [820016402241462860280, 540918822857334411721, 1466521590431963520, 32389886532326400, 906809203692128183040, 6645229879800, 12933043320, 871108433718854693760, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.JF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.E', 'old_label': '72.jf1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JF', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126912
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6991, -1, 9025, -1], 'generators': [820016402241462860280, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 30579960240128234903, 30578870934446647680, 438743340800442968521, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.JG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '72.jg1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JG', 'subgroup_fusion': None, 'weyl_group': '20784.b'}
  • id: 227126913
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7143, -1, 9074, -1], 'generators': [820016402241462860280, 156276420197455355161, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 12933849720, 1800761010854543, 1255647523519025280, 32389973710617736], 'label': '559872.lw.72.JH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.I', 'old_label': '72.jh1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JH', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126914
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [3560, -1, 7914, -1], 'generators': [820016402241462860280, 1466521590431963520, 32389886532326400, 33479179281676927, 906809203692128183040, 6645229879800, 871108433718854693760, 438743340800442968521, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.72.JI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.E', 'old_label': '72.ji1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JI', 'subgroup_fusion': None, 'weyl_group': '80000.q'}
  • id: 227126915
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7029, -1, 9038, -1], 'generators': [820016402241462860280, 806400, 156276420197455355161, 46283920465305607, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.72.JJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '72.jj1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JJ', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126916
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7219, -1, 9099, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 32389886532326400, 871107351232279080263, 6645229199400, 12933849720, 45200132882916496, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.72.JK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.I', 'old_label': '72.jk1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JK', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126917
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7067, -1, 9050, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 32389886532326400, 6645229879800, 12933849720, 820061597049763225087, 1255647523519025280, 545784629489036427721], 'label': '559872.lw.72.JL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '72.jl1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JL', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126918
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7181, -1, 9087, -1], 'generators': [820016402241462860280, 156276420197455355161, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229199400, 1806091379855303, 12933849720, 45200132882916496, 1255647523519025280], 'label': '559872.lw.72.JM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.I', 'old_label': '72.jm1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JM', 'subgroup_fusion': None, 'weyl_group': '7776.cd'}
  • id: 227126919
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 16, 'diagramx': [354, -1, 1137, -1], 'generators': [820016402241462860280, 35700769812329758080, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 32389886532326416, 163164641150917702923, 51212988841832457242, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.16.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.B', 'old_label': '16.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.B', 'subgroup_fusion': None, 'weyl_group': '34992.ea'}
  • id: 227126920
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7105, -1, 9062, -1], 'generators': [820016402241462860280, 45194808300364816, 1466521590431963520, 32389886532326400, 871108433886504447360, 30579960227195191823, 6645229879800, 30578870934446647680, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.JN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '72.jn1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JN', 'subgroup_fusion': None, 'weyl_group': '20784.b'}
  • id: 227126921
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '72.JO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7256, -1, 9111, -1], 'generators': [30546481160479697296, 820016402241462860280, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 180583603320, 30579964237436866703, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.72.JO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.I', 'old_label': '72.jo1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.JO', 'subgroup_fusion': None, 'weyl_group': '20784.b'}
  • id: 227126922
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '96.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '139968.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2222, -1, 7187], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 326934612459548846040, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.96.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '96.a1.N', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.A', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126923
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '192.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6740, -1, 8728], 'generators': [35700769812329758080, 1089473332147223, 1466521590431963520, 32389886532326400, 871108433886504447360, 32389886532326416, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.192.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '192.a1.N', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.A', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 227126924
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '192.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '139968.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2022, -1, 7686], 'generators': [35700769812329758080, 186811430400, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.192.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '192.b1.N', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.B', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126925
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '192.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '139968.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 4081, -1, 8140], 'generators': [1806085152834623, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 45194808301171216, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.192.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '192.c1.N', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.C', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126926
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [209807598918537488164, 29323249584054899760, 820050237108171826680, 1468322264263720320, 34190854274239855920, 27555085958400, 29355639470587226160], 'label': '559872.lw.256.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.C', 'old_label': '256.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1', 'subgroup_fusion': None, 'weyl_group': '972.455'}
  • id: 227126927
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '729.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 729, 'diagramx': None, 'generators': [849372041699117320320, 412339763420549885521, 820048813037852797440, 424949616735876344883, 820016402422046463376, 52124682685268472482, 29355639544832751360, 820048792115062143383, 29323249584055176960], 'label': '559872.lw.729.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '729.A', 'old_label': '729.a1.M', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.A', 'subgroup_fusion': None, 'weyl_group': '768.1090070'}
  • id: 227126928
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '768.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1640, -1, 9251], 'generators': [35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 820016402241462860280, 1255647523519025280], 'label': '559872.lw.768.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '768.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '768.a1.N', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.A', 'subgroup_fusion': None, 'weyl_group': '192.955'}
  • id: 227126929
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '2187.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 2187, 'diagramx': None, 'generators': [23, 411769574036877779422, 1223238021910329616, 7, 622851873883831726702, 30546480973669073296, 412347223353642037342], 'label': '559872.lw.2187.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2187.a1', 'old_label': '2187.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2187.a1', 'subgroup_fusion': None, 'weyl_group': '64.202'}
  • id: 227126930
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': [31, -1, 1032, -1], 'generators': [820016402241462860280, 163151836496911558923, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.16.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.B', 'old_label': '16.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.C', 'subgroup_fusion': None, 'weyl_group': '139968.ii'}
  • id: 227126931
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '139968.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1421, -1, 9581], 'generators': [23, 16], 'label': '559872.lw.139968.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '139968.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '139968.a1.N', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '139968.A', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227126932
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '559872.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '559872.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1330, -1, 9891], 'generators': [], 'label': '559872.lw.559872.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '559872.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '559872.a1.N', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '559872.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227126933
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.A', 'coset_action_label': None, 'count': 8, 'diagramx': [68, -1, 1045, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 1466521590431963520, 1089479559974543, 32389886532326400, 871108433886504447360, 6812880439800, 12933849720, 45200132882236096, 1255647523519025280], 'label': '559872.lw.16.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.E', 'old_label': '16.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.D', 'subgroup_fusion': None, 'weyl_group': '69984.fi'}
  • id: 227126934
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 32, 'diagramx': [310, -1, 1123, -1], 'generators': [820016402241462860280, 163151836496911558923, 1094797475614103, 35700769812329758080, 186810624000, 1466521590431963520, 32389886532326400, 871108433886504447360, 32395298292489016, 180583603320, 1255647523519025280], 'label': '559872.lw.16.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.E', 'old_label': '16.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.E', 'subgroup_fusion': None, 'weyl_group': '34992.ba'}
  • id: 227126935
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 8, 'diagramx': [157, -1, 1073, -1], 'generators': [820016402241462860280, 163151836496911558923, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280], 'label': '559872.lw.16.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.C', 'old_label': '16.f1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.F', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126936
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 8, 'diagramx': [195, -1, 1086, -1], 'generators': [820016402241462860280, 163151836496911558923, 1094803701954623, 35700769812329758080, 186810624000, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 180583603320, 1255647523519025280], 'label': '559872.lw.16.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.I', 'old_label': '16.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.G', 'subgroup_fusion': None, 'weyl_group': '69984.m'}
  • id: 227126937
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 16, 'diagramx': [396, -1, 1151, -1], 'generators': [820016402241462860280, 35700769812329758080, 45194808301171216, 1466521590431963520, 32389886532326400, 871108433886504447360, 163164641150917702923, 1806085152834623, 51212988841832457242, 438743340800442968521, 1255647523519025280], 'label': '559872.lw.16.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.H', 'old_label': '16.h1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.H', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126938
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 16, 'diagramx': [429, -1, 1161, -1], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 163151878255309777683, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 438743340800442968521, 1255647523519025280, 51212989114823775002], 'label': '559872.lw.16.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.I', 'old_label': '16.i1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.I', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126939
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.B', 'coset_action_label': None, 'count': 8, 'diagramx': [272, -1, 1110, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 186811430400, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280, 32389973710617736], 'label': '559872.lw.16.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.J', 'old_label': '16.j1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.J', 'subgroup_fusion': None, 'weyl_group': '69984.h'}
  • id: 227126940
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '6.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.A', 'coset_action_label': None, 'count': 1, 'diagramx': [406, 2605, 227, 3600], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 327056278482747566040, 1255647523519025280, 32389973710617736], 'label': '559872.lw.6.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.A', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126941
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '16.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '192.C', 'coset_action_label': None, 'count': 8, 'diagramx': [234, -1, 1098, -1], 'generators': [820016402241462860280, 163151836496911558923, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 12933849720, 6812880439800, 1255647523519025280, 32389973710617736], 'label': '559872.lw.16.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '16.k1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.K', 'subgroup_fusion': None, 'weyl_group': '69984.p'}
  • id: 227126942
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '18.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [33, -1, 1174, -1], 'generators': [820016402241462860280, 820016402254395903383, 540918822857334411721, 1466521590431963520, 32389886532326400, 871140823592453977096, 906809203692128183040, 6645229879800, 12933043320, 871108433718854693760, 738908776443002781001, 1255647523519025280], 'label': '559872.lw.18.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.A', 'old_label': '18.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.A', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126943
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '18.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '139968.A', 'coset_action_label': None, 'count': 18, 'diagramx': [73, -1, 1187, -1], 'generators': [820016402241462860280, 806400, 156276420197455355161, 186811430400, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 1255647523519025280, 32389973710617736], 'label': '559872.lw.18.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '18.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.B', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126944
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 1, 'diagramx': [2525, 2332, 2007, 4739], 'generators': [820016402241462860280, 186811430400, 35700769812329758080, 45194808301171216, 1466521590431963520, 326934612459548846040, 1089473332147223, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.24.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.A', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126945
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.B', 'coset_action_label': None, 'count': 2, 'diagramx': [3654, 5428, 2373, 5424], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 32389886532326400, 871108433886504447360, 6645229879800, 12933849720, 327056278482747566040, 1255647523519025280], 'label': '559872.lw.24.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.B', 'subgroup_fusion': None, 'weyl_group': '139968.j'}
  • id: 227126946
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 24, 'diagramx': [3571, -1, 2346, -1], 'generators': [820016402241462860280, 806400, 186811430400, 35700769812329758080, 1466521590431963520, 1089473332953623, 32389886532326400, 871108433886504447360, 326922163405792506840, 32395298292489016, 1255647523519025280], 'label': '559872.lw.24.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '24.c1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.C', 'subgroup_fusion': None, 'weyl_group': '10000.ej'}
  • id: 227126947
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3381, -1, 2284, -1], 'generators': [820016402241462860280, 35700769812329758080, 186811430400, 1466521590431963520, 45194808301171216, 326934612459548846040, 1089479559168143, 32389886532326400, 871108433886504447360, 6645229879800, 1255647523519025280], 'label': '559872.lw.24.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.A', 'old_label': '24.d1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.D', 'subgroup_fusion': None, 'weyl_group': '23328.bc'}
  • id: 227126948
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3495, -1, 2321, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 51212988854246581922, 1089479559168143, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 1255647523519025280], 'label': '559872.lw.24.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '24.e1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.E', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126949
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [106, -1, 1223, -1], 'generators': [820016402241462860280, 806400, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 51821612137943989933, 871108433886504447360, 6812879759400, 12933849720, 1255647523519025280], 'label': '559872.lw.24.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '24.f1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.F', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 227126950
    {'ambient': '559872.lw', 'aut_centralizer_order': None, 'aut_label': '24.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '768.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1983, -1, 1832, -1], 'generators': [820016402241462860280, 806400, 52064923100088045613, 35700769812329758080, 1466521590431963520, 1089479559168143, 32389886532326400, 871108433886504447360, 6812879759400, 12933849720, 1255647523519025280], 'label': '559872.lw.24.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '24.g1', 'projective_image': '559872.lw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.G', 'subgroup_fusion': None, 'weyl_group': None}