-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.dk', 'ambient_counter': 89, 'ambient_order': 3888, 'ambient_tex': 'C_3^3:S_3^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 162, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.dk.24.a1', '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': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '3888.dk', 'aut_centralizer_order': 54, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '576.8399', 'aut_weyl_index': 108, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.a1', '12.g1', '12.k1'], 'contains': ['48.a1', '72.i1', '72.k1', '72.o1', '72.p1'], 'core': '24.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7516, 6053, 3436, 4952], 'generators': [627, 23, 100111334478, 101069337600, 56], 'label': '3888.dk.24.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['48.a1', '216.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '3888.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '144.115'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '18.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [3, 2, 3, 3, 3, 2], 'aut_gens': [[736, 2918, 757, 1027], [736, 3431, 757, 1027], [736, 2918, 784, 973], [736, 2972, 757, 1027], [736, 2918, 973, 1027], [5107, 5111, 757, 1027], [733, 2918, 757, 1027]], 'aut_group': '20736.pd', 'aut_hash': 2986519587559918118, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 20736, 'aut_permdeg': 17, 'aut_perms': [176625221068800, 4197015660316, 25113582144000, 5331894180480, 37249, 10855], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 1, 8, 1], [3, 2, 4, 1], [3, 2, 32, 1], [6, 9, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2:\\GL(2,3)\\times \\GL(2,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '48.29', 'autcent_hash': 29, 'autcent_nilpotent': False, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(2,3)', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '432.734', 'autcentquo_hash': 734, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 9, 1], [3, 1, 8], [3, 2, 36], [6, 9, 8]], 'center_label': '9.2', 'center_order': 9, 'central_product': True, 'central_quotient': '18.4', 'commutator_count': 1, 'commutator_label': '9.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 52, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['18.4', 1], ['3.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 1, 2, 4], [3, 2, 1, 4], [3, 2, 2, 16], [6, 9, 2, 4]], 'element_repr_type': 'GLZq', 'elementary': 1, 'eulerian_function': 91, 'exponent': 6, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '162.52', 'hash': 52, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [1, 2, 3, 3], 'inner_gens': [[736, 2918, 757, 1027], [736, 2918, 784, 1243], [736, 2945, 757, 1027], [736, 3458, 757, 1027]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 18, 'inner_split': False, 'inner_tex': 'C_3:S_3', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 18], [2, 36]], 'label': '162.52', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^2wrC2', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 54, 'number_divisions': 30, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 23, 'number_subgroup_classes': 160, 'number_subgroups': 344, 'old_label': None, 'order': 162, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 9], [3, 80], [6, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 6, 2, 6, 4, 4], 'outer_gen_pows': [730, 730, 2918, 2918, 730, 730], 'outer_gens': [[733, 5108, 1243, 784], [733, 2921, 1243, 1270], [736, 2918, 1216, 1000], [5110, 731, 1243, 757], [5104, 5105, 757, 1027], [5107, 731, 757, 1027]], 'outer_group': '1152.157461', 'outer_hash': 7371672288863537087, 'outer_nilpotent': False, 'outer_order': 1152, 'outer_permdeg': 12, 'outer_perms': [1, 18594004, 23, 7711327, 303055320, 44352840], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4\\times \\GL(2,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 12], [4, 16]], 'representations': {'PC': {'code': 14018986071, 'gens': [1, 2, 4, 5], 'pres': [5, -3, -2, -3, -3, -3, 26, 248, 909]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [24577758, 15477644, 24507118, 2939606, 36731395]}, 'GLZq': {'d': 2, 'q': 9, 'gens': [757, 733, 3220, 737, 2920]}, 'Perm': {'d': 12, 'gens': [40723336, 91451125, 325, 435, 130682595]}}, 'schur_multiplier': [3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2\\wr C_2', 'transitive_degree': 18, 'wreath_data': ['C_3^2', 'C_2', '2T1'], 'wreath_product': True}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [6, 3, 2, 2, 12], 'aut_gens': [[100115008562, 193121112394], [262492957494, 461322126948], [100115008614, 193121112822], [262975587842, 448428965521], [269198979894, 460839496548], [268240977313, 460843125354]], 'aut_group': '62208.l', 'aut_hash': 1820680360968750972, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 62208, 'aut_permdeg': 648, 'aut_perms': [514611385904689074666529849802732880383838636903602357108659763007433597633945845978647611266818128476650022576554118896214295029621794154865402891252680136760497723456387917790563694075182311549133269008773338674010512279874502512554586590571388153702528997841229237460877353984878727795470276861493919328455629523141448691401293065716867006049826329781006935753618652849820155597411039466868412796827500189047753865695331636555938333590766143085113265240597099491948530356525305688756098617878106523713957040919629128311986679482439916562096372161606699919916703408535528487126230583721431876041829742530481626337366999562202645076605322121753925791012723408639787338227181150886863449605134955924255634176508682799809808367085014963058571675841812656073567857526970967748995511373507672590129652817585515922680068597395784262323549524933108810916799527965466552217190469569799714013108140174717179334731038426692350280663921121487144267889432624762567836801557499377448936251495588349831591035757521222436562209960604969789731553123129047868276587405356024257654462373684718340958149089522946985829250643709165520096982224081635739768808004674507299475392728164529456743123398360710694088306720604744275536026433074683494468047969986270188843861461451483501231943578856278365927589698975074138045970954134504624010434613659846191535563198403303865567486915397883068856541949512137887505941905581741102450027046067569005074536066742793518931692322621277550590705610332897678018166914535646247785839882560625116735191665976441065419939876787, 957812441949806045392664118073368063463149890494351146063793363655016259818999542530562455304785869559732205004058323627481504364191850433075213863342333574427753903740262052545457175294975294013033605052231906482063292953404789872517001777151063279359028262818857303809210570688583745473296266383997590317467032304633282061683641323875694776093862996736769761306880001974942707275552538548790977969381667336138782531910503625433718896526600615567888727172099867400814392563627243862316472208886315467703225142039701477999953019253378506040346613895913491243232275718726227379028570697545496234987541757729103661594530493275622304033823888759316389844641577495940861674591621635392452940230596799424705643064069010348722716276559890353977092523711408613912170558167597649627883055939205135395270890072174411019370354954360998402258091683831627634682078913725955729100844422214089230137935360293427017893182348012878043115130806081247635745966116441744934675717785114120436010821898346401380671254292531362362427105833386124274046784923536915028756227718977791154681416446769317517436990881673384667049701781408966176380991806806079045537738737968026719719971360164785157274003692243058254930136477121233401923577456681168765402786719041434606503817561495356570920820997341242023207534765293312340829263170721012292054494011296543027685646132001935737396211475001229491242592862561623911898782625064970390343324742245748914887400742262437547335731238669336334350923430699850553332034738689679218521715403896859383185029684967798095774802067747, 817409238987370478779634357675646529503602881943434070917585286308620003904450165209280970827035889366325716486503776728611020642079033587065315341400530738700834885404753278620035565966864401155398278166502220338865563453344582872701183168337601161691599437516373935311745683720987879773455668616694016627962329258169668521751298203208450032443578815428892833050235021165256876375209927083749411986615430890687113775976984821932754030483293978167196859843023861589068702837999257816563419273099477863198729342486627358259542607617678608856825785976417641939065918049246774130523323221185333574269656002790191449740811029204076183609995040890909627919896934621236694718724361550483047666870804011337587629127445476688231142251005592064646369838941702070371934421966992436889094664284589297364423812307095446106030527255874342117954750153034754066050437488263551237650410212338545084429799156585522773477377612922930429606286084313313044847059819226530031301009869828211693428152929306212248894060729853092232539915674901812046323596921562648653141958418394782468883057631210249671376959077199830972476771699289410925464875279700133657818247159342214969203253101158863280167453711736236672285685119043721492457421439798255367947308994766566586844701941462944406547561266290152752039621308831576623749317685708822034369571231108458172578006061442494683558198370911118995666705517346612185648324232014038369916437180408851798862007308241579272799327523339928228274284235274304475335019561103943793131039660035144988694793284981943986095342776133, 1250358883731218308741492495758195058897848360201689386134716248747673585862422429407044157632949031230748319335954555037584473661810053447885987578917582348732662016296923787831892866919877806807167034869300385773193735602092727730802414153249332691616170328824465210914578611873404195211065224036010034571405359232964483030473761253171753909623555962569249575609741527855512502291031904772440447165922000104020782697534326706232626704518754634832081008040366135194366409516724836863431534768883367377632173390881085810908501237293765001420735297456049232026893068001205472280069847845842622373278885524263805032415560924878341801806924402191146066333432448315817787639590378084673281278026924259883882956499182239995757330142040399681864582117565311193488009081247855342083645512672864561475784576443350078989865357887892089795853753299254420396589369037598450850969703421035841678690386680244420227210782234343995036400585373461280490450965803286490372811703073052122179222467542319317538909742912934016524050731013461759643747802183474999302778791577113932318673925166859746020653119128833403392923019580650282832730022530088367104790745928820548696918472035725843804737648100818690631451468669112528522324786408691168976964054085218659963909613409105739374265875175925102784731890582897567148044574101622153584029543486584204371347331393390648518335587342277284371015236593221480957709037494687057047669589592887744088635662266390628241642764335795030946081839344433917419585700630204228632115073190100024493220090643281629098306371935825, 713699135909981819006972787181579056073717356343218396576465023289514744007497252486278591939164564222038699516358693167183823008827545921902273819787982522091997507763359176968860777733419004207660753411113851866455638327263599115673909766465923702137540543219402982779313950112875205150619455954935707706457417854843418648770668720931351487325363090486796773113631970144362527436349005667120706432894456266441775105607841077084509795946792754595358691918804806241490459335720535878566331090269636006953949796795433724450453012531800979598177051776815577932143185712214004416496377358311794736904048893405297768914132534718007589987924048087376278160097164801529286321197518166115719972999099300937903624706826360642465991196132951736148291858714757428742653606867950012303313987242843583309388002035422925006064656627032838636683320058301093936504013673210590259625024494103480848196939326894054629230010058742089165487813861104817698218681228689927181430850404470168795766047965074822654921235874277708931962075370617922638300344240825788521715953247351369096922125536040007385568539913355872715245291383596693311048660610500289618956609745127477778124347618141711799237024639874310639082241271198096926417807444921351013753450848739979137219333726943495747158876163310148461534267799000378063215258294727987002557729461754545403653490867979476807549202685822195459547995806124177845672731419082118815127172069510224315905346642044910527177907521333047698537846875249071017222177862785284823224514275202341187502753794562240254388863051663], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 2, 1], [2, 18, 2, 1], [2, 81, 1, 1], [3, 2, 1, 1], [3, 4, 2, 2], [3, 4, 4, 1], [3, 8, 2, 2], [3, 8, 4, 1], [3, 16, 1, 1], [3, 16, 2, 2], [3, 16, 4, 1], [4, 162, 4, 1], [6, 18, 2, 1], [6, 18, 4, 1], [6, 36, 2, 2], [6, 36, 4, 2], [6, 36, 8, 1], [6, 72, 2, 2], [6, 72, 4, 1], [6, 162, 1, 1], [12, 324, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3^5.D_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '62208.l', 'autcentquo_hash': 1820680360968750972, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3^5.D_4', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 18, 2], [2, 81, 1], [3, 2, 1], [3, 4, 8], [3, 8, 8], [3, 16, 9], [4, 162, 4], [6, 18, 6], [6, 36, 20], [6, 72, 8], [6, 162, 1], [12, 324, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '3888.dk', 'commutator_count': 1, 'commutator_label': '486.259', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 89, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 18, 1, 2], [2, 81, 1, 1], [3, 2, 1, 1], [3, 4, 1, 4], [3, 4, 2, 2], [3, 8, 1, 4], [3, 8, 2, 2], [3, 16, 1, 3], [3, 16, 2, 3], [4, 162, 2, 2], [6, 18, 1, 2], [6, 18, 2, 2], [6, 36, 1, 8], [6, 36, 2, 6], [6, 72, 1, 4], [6, 72, 2, 2], [6, 162, 1, 1], [12, 324, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 48, 'exponent': 12, 'exponents_of_order': [5, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 0, 8], [16, 0, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '3888.dk', 'hash': 5387043051655160496, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 12], 'inner_gens': [[100115008562, 361729756237], [13415754873, 193121112394]], 'inner_hash': 5387043051655160496, 'inner_nilpotent': False, 'inner_order': 3888, 'inner_split': True, 'inner_tex': 'C_3^3:S_3^2:C_4', 'inner_used': [1, 2], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 10], [4, 32], [8, 16], [16, 9]], 'label': '3888.dk', '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': 'C3^3:S3^2:C4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 28, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 75, 'number_divisions': 54, 'number_normal_subgroups': 29, 'number_subgroup_autclasses': 378, 'number_subgroup_classes': 894, 'number_subgroups': 19656, 'old_label': None, 'order': 3888, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 135], [3, 242], [4, 648], [6, 1566], [12, 1296]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 12936672713, 0, 0], 'outer_gens': [[100115043861, 193121112615], [268240977329, 361250674070], [262017549414, 193121112737], [100115043842, 193121112781]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [126, 55, 289, 288], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 14], [8, 18], [16, 7], [32, 3]], 'representations': {'PC': {'code': '21836155762007731365262521521083754232986598708595860964407876720108632757517292242214866487', 'gens': [1, 3, 5, 6, 8, 9], 'pres': [9, 2, 2, 2, 3, 3, 2, 3, 3, 3, 18, 4330, 44930, 35705, 74, 57603, 23484, 38884, 562, 143213, 21398, 22379, 18014, 158, 81654, 9087, 4560, 3463, 916, 23336, 104993, 2969]}, 'Perm': {'d': 15, 'gens': [100115008562, 193121112394]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3:S_3^2:C_4', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 2, 6], 'aut_gens': [[56, 2059, 1718], [336, 2059, 1718], [56, 349, 1034], [126, 349, 1718]], 'aut_group': '24.14', 'aut_hash': 14, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24, 'aut_permdeg': 7, 'aut_perms': [7, 136, 856], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 6, 1, 1], [3, 2, 1, 1], [4, 6, 1, 1], [6, 2, 1, 1], [6, 2, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 6, 1], [3, 2, 1], [4, 6, 1], [6, 2, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 8, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 6, 1, 1], [3, 2, 1, 1], [4, 6, 1, 1], [6, 2, 1, 1], [6, 2, 2, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 6, 'exponent': 12, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '12.4', 'hash': 8, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 3], 'inner_gens': [[56, 349, 1034], [336, 2059, 1718], [126, 2059, 1718]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': True, 'inner_tex': 'D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 2, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 5]], 'label': '24.8', 'linC_count': 2, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 3, 'linQ_dim': 4, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3:D4', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 9, 'number_divisions': 8, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 16, 'number_subgroups': 30, 'old_label': None, 'order': 24, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 9], [3, 2], [4, 6], [6, 6]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [344], 'outer_gens': [[56, 2059, 1034]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 1]], 'representations': {'PC': {'code': 6300481, 'gens': [1, 2, 3], 'pres': [4, -2, -2, 2, -3, 266, 34, 259]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16563489, 7233423]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [56, 2059, 1718]}, 'Perm': {'d': 7, 'gens': [745, 264, 1680, 3]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3:D_4', 'transitive_degree': 12, 'wreath_data': None, 'wreath_product': False}
