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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9264.p', 'ambient_counter': 16, 'ambient_order': 9264, 'ambient_tex': 'C_{1544}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 579, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 579, 'label': '9264.p.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '579.1', 'subgroup_hash': 1, 'subgroup_order': 579, 'subgroup_tex': 'C_{193}:C_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '9264.p', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1158.a1.a1', 'complements': ['579.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'contains': ['48.a1.a1', '3088.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8619, 2367, 821, 7880, 1714, 2856, 1158, 1578], 'generators': [6950, 48], 'label': '9264.p.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '9264.p', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1158.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '3.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [192, 193], 'aut_gens': [[1, 3], [1, 114], [445, 3]], 'aut_group': '37056.a', 'aut_hash': 1432757702296672986, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 37056, 'aut_permdeg': 193, 'aut_perms': [39053339670721327572543569039395005031096653245802774324204298263788953285647090763476541643345676324473056783378543774660072842471514711015868302482279618194714261105949788702112347134548908091797187306612050281053946057960581089182560863568602379974419627409015496038525465690691519350455551181816446171767151758025418672254963521648341121096265656543605694, 27537046770698028029509447452483255633857520585283838421883440607221768231104384860166214394878916709368227289860720561987161029954363059081082583776521393368876604263321802053274125013685434525755757109968295753899028688290909515762484435944252483952769187280784953622110633939104871157686235761278347542756654691358393510201744955724775767189520816064076473], 'aut_phi_ratio': 96.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 193, 1, 2], [193, 3, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_{193}', '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': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [3, 193, 2], [193, 3, 64]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '579.1', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '193.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 193, 2, 1], [193, 3, 64, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8, 'exponent': 579, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [3, 193], 'faithful_reps': [[3, 0, 64]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '579.1', 'hash': 1, 'hyperelementary': 3, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 579, 'inner_gen_orders': [3, 193], 'inner_gens': [[1, 252], [331, 3]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 579, 'inner_split': True, 'inner_tex': 'C_{193}:C_3', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 192, 'irrQ_dim': 192, 'irrR_degree': 6, 'irrep_stats': [[1, 3], [3, 64]], 'label': '579.1', 'linC_count': 64, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 192, 'linQ_degree_count': 1, 'linQ_dim': 192, 'linQ_dim_count': 1, 'linR_count': 32, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C193:C3', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 67, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 196, 'old_label': None, 'order': 579, 'order_factorization_type': 11, 'order_stats': [[1, 1], [3, 386], [193, 192]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 64, 'outer_gen_orders': [64], 'outer_gen_pows': [2], 'outer_gens': [[1, 447]], 'outer_group': '64.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [2014594330940748694500315964401030837224914941382363373987443624058107002128920420940313], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{64}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 193, 'pgroup': 0, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [192, 1]], 'representations': {'PC': {'code': 12312959, 'gens': [1, 2], 'pres': [2, -3, -193, 1009]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 603880789]}, 'Perm': {'d': 193, 'gens': [155072081769025479153068005764655310398056985534484553249510570014180068596765767602220702796160851423904603713380353967374496827693048038873577863314427425322295450355127868085281304176469528282592426059218603719048013636231661630498986145587733965119292349387964516295495591000760117599793495606069314966880735163520645227705730930758607614125986326901066, 68159384284216415434244229769722897785298203470789342442007462716964519312047994015473537393503254737883254692840162175520283792238796194464802516244938515792342454228783658226402112128483243230028631870556954631033853483990335822197126471859553676149202878029250924171717175622127511797106029233701101543903723520000000000000000000000000000000000000000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{193}:C_3', 'transitive_degree': 193, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '48.23', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [2, 2, 2, 192, 193], 'aut_gens': [[1, 6], [4633, 2310], [1, 6942], [2317, 9258], [1, 5526], [6673, 6]], 'aut_group': None, 'aut_hash': 8680930637342299848, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 296448, 'aut_permdeg': 390, 'aut_perms': [427281579873169816594352209284502028822147093570856416432998835691733529803421358280808880981790585915768279768843332041399326244561793521463008146876771842827650461360799089421032936163299012444643097818282291750440716771988726137817566036810730952900675192163515122232540155899999451357360729436956567122154542804689560046941863417782950021955139589667172269824846968912478352095424603421603874999719084604927306811268526357228712590924684367127534045402683959736278463642661438333483504237934891047931621569887942109958041205993704036184084352146691753137253437098309894638622279439344783883159906524330336445220985300810733280991054391584764946117440747437468637360232935837052367164984204462464521958352722332372731745350060195519984343701585531823977472422890134931900861317869865404359244880372637854328009416326331836399056072382094599, 427281579873169816594352209284502028822147093570856416432998835691733529803421358280808880981790585915768279768843332041399326244561793521463008146876771842827650461360799089421032936163299012444643097818282653595838001779637693639078029148748698407515343762877133633857600386784786617408758405902947048517386178727507844858240636053841276977115192518590858338578860942079592859217452339666047751315189147201157598135005833852804222907131196008769478334493620650677013663719637825727448380308871012492191748382211958472971749423149660353542981952612970948136428855382756804943680224860338068246723933750430246443774279067576374548108895923064899981189002125371165848523187186339302427124699459094233354904501804479818777678700525899597425989439656565292524251201501737093564861317869865404359244880372637854328009416326331836399056072382094599, 466859042833283780912724613418197426567966575851244871531973490411843393811276232776613653756073296919495349722515158323368026327847653120763933209195651788726998372445913302110401253453603540589059364178792205233586289923877430392273731798454371317328591631314087673346843526756094379038629317901330922582186944726191639652946594754287727173018598460868395458688849490250711072664223711670648678057828067167773537704150204039810713523255229610137004748059304237951086055521673952414166296849785273565823917870405252310051411380271863281508235430359189380425786172375165521040314831413079060767821295410034013555367829724715316690437346589260747422846928670241917691884665586935181303614935271356590066937812448295886478238971830186344823159438430960019840050615246325042038273898348860176810009396607115237258617707265297698186777291339791805, 610008484387259170805041374860729361365810585673602430202466647898591484276668217360732164384392112660495476285988220293183315857453678617326599175675637608136242022240035520019392984130611297923794882987333126276873435140730070665410763968309215673771021228567313981484332134221649812298638151171383919562989524107640112359051598631076692217126130146033373121255754125692668156335138355273053209370180037526921506623463028917398086641341751123911492559898345883345046865866923032817834989619463053048728816111613915342077896020708787868557832127711566171162242470762946865657568148915100365778612996549159217856508971090772524370350155927813232670412757542676361658185412177249260813074128529413104668973027983140531107515672111429936358104027794719679284305183356472970707267344130028176140953717974526467809082458463982532532749802645352684, 578517379078003063717947232663325670884739214320153737019963511661092511405448456787072749656360695551172776248926212180680640573456034436080828107663603996181148272533863966394968613083586446048189384760956912702708233682586094553921961137308337514295460231869952410459961721965744587768523325796689303501913226509985556802741394442309402362823180676457147429832990650495191413130828110611179930587600717082078711367492337652782711292395285944964958039769447643557343898230068496808722609245653907342848735320548771846763916797594927077013035621427836029434973822040072365938333981567977783026360788075952555352172100162819819685544018311955004827447430107716218967981093520262986088260814397981428593673308612162005369935016186323752245745743582189501985900246659078872839340105505758801326210956698142233784808206254655439215715570067591686], 'aut_phi_ratio': 96.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 2, 1], [3, 193, 1, 2], [4, 1, 2, 1], [4, 193, 2, 1], [6, 193, 1, 2], [6, 193, 2, 2], [8, 1, 4, 1], [8, 193, 4, 1], [12, 193, 2, 4], [24, 193, 4, 4], [193, 6, 32, 1], [386, 6, 32, 1], [772, 6, 64, 1], [1544, 6, 128, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{193}.C_{96}.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 193, 2], [3, 193, 2], [4, 1, 2], [4, 193, 2], [6, 193, 6], [8, 1, 4], [8, 193, 4], [12, 193, 8], [24, 193, 16], [193, 6, 32], [386, 6, 32], [772, 6, 64], [1544, 6, 128]], 'center_label': '8.1', 'center_order': 8, 'central_product': True, 'central_quotient': '1158.1', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '193.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 16, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['1158.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 1, 2], [3, 193, 2, 1], [4, 1, 2, 1], [4, 193, 2, 1], [6, 193, 2, 3], [8, 1, 4, 1], [8, 193, 4, 1], [12, 193, 4, 2], [24, 193, 8, 2], [193, 6, 32, 1], [386, 6, 32, 1], [772, 6, 64, 1], [1544, 6, 128, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 96, 'exponent': 4632, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': [[6, 0, 128]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '2316.e', 'hash': 7925856653797502209, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 1158, 'inner_gen_orders': [6, 193], 'inner_gens': [[1, 5286], [3985, 6]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 1158, 'inner_split': False, 'inner_tex': 'C_{193}:C_6', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 768, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 48], [6, 256]], 'label': '9264.p', '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': True, 'monomial': True, 'name': 'C1544:C6', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 304, 'number_divisions': 20, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 44, 'number_subgroups': 3500, 'old_label': None, 'order': 9264, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 387], [3, 386], [4, 388], [6, 1158], [8, 776], [12, 1544], [24, 3088], [193, 192], [386, 192], [772, 384], [1544, 768]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 32, 'outer_gen_orders': [2, 2, 2, 32], 'outer_gen_pows': [0, 0, 0, 1], 'outer_gens': [[4633, 2310], [1, 6942], [2317, 9258], [1, 5526]], 'outer_group': '256.26959', 'outer_hash': 26959, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 38, 'outer_perms': [13763753091226345046315979581580902400000000, 10333147966386144929666651337523200000000, 8683317618811886495518194401280000000, 8497249472648064951935266660940313], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{32}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 201, 'pgroup': 0, 'primary_abelian_invariants': [2, 8, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 6], [4, 4], [8, 2], [192, 2], [384, 1], [768, 1]], 'representations': {'PC': {'code': '2246153011234655979630274269961340823442909270533455888862711367336127', 'gens': [1, 3], 'pres': [6, -2, -3, -2, -2, -2, -193, 12, 41695, 95150, 57950, 50, 31395, 43353, 69, 78484, 108370, 88, 188357, 93323]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 1272463275, 934577459]}, 'Perm': {'d': 201, 'gens': [3943691182271911012560688467754666641935312685255106502395048857424780063917805030088182979148314601321504533450634524374156741127855878791106005711193905489432452582662602100016366147202606039077001291038494238293485864041771000661267731548581570400160467301621816046753802647666912882295516994118375726110090399641338494828252060195587096729529401966441481119828020446461, 796545050593731377654169099292562387780736024747786074279670809346578040798583186648031878457015244296590118587322179953037184142979091858953277574093649291253544827311773885121273535019669459600422979068446589284766017738637652724022074327882145122533897772251547069721876903535015450321574646730160925328181083147236124098957966384875976450354788011084765370754533202436480, 11909833196621725278287090661090593903880226989488794635332771943366983459517778206341888809512223799124354986014010740061748957800675953854274883351642372370089116365789845004562835686614268262133258705155842518373018234652672361893538367563840575558985812835228313833634122481627653662658520367587246139469108980949688230336017121220324948963679168560790648678369940876676]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 24], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{1544}:C_6', 'transitive_degree': 1544, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '16.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2], 'aut_gens': [[1, 2], [1, 3], [9, 14], [1, 6], [1, 10]], 'aut_group': '16.11', 'aut_hash': 11, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 16, 'aut_permdeg': 6, 'aut_perms': [126, 55, 289, 288], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [4, 1, 2, 2], [8, 1, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.11', 'autcent_hash': 11, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times D_4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 3], [4, 1, 4], [8, 1, 8]], 'center_label': '16.5', 'center_order': 16, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 1, 2, 2], [8, 1, 4, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 6, 'exponent': 8, 'exponents_of_order': [4], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '4.2', 'hash': 5, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16]], 'label': '16.5', 'linC_count': 48, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 4, 'linQ_dim': 5, 'linQ_dim_count': 4, 'linR_count': 8, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C8', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 16, 'number_divisions': 8, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 9, 'number_subgroup_classes': 11, 'number_subgroups': 11, 'old_label': None, 'order': 16, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 3], [4, 4], [8, 8]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 3], [9, 14], [1, 6], [1, 10]], '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': 2, 'perfect': False, 'permutation_degree': 10, 'pgroup': 2, 'primary_abelian_invariants': [2, 8], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 2]], 'representations': {'PC': {'code': 9222, 'gens': [1, 2], 'pres': [4, -2, 2, -2, -2, 21, 34]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [141602720900, 706304316034]}, 'GLFp': {'d': 2, 'p': 17, 'gens': [19665, 44226]}, 'Perm': {'d': 10, 'gens': [40176, 362880, 16582, 5167]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 8], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_8', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
