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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '26244.hm', 'ambient_counter': 195, 'ambient_order': 26244, 'ambient_tex': 'C_3^6.D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 243, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '26244.hm.108._.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.B', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': None, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '26244.hm', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [143193, 23288, 2514057026007127267949533209, 2516539128733089649639648093, 1306795024823268197088891993], 'label': '26244.hm.108._.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '108.B', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108._.B', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '243.67', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1132560, 'aut_gen_orders': [2, 121], 'aut_gens': [[1, 3, 9, 27, 81], [1, 221, 227, 136, 81], [137, 212, 109, 124, 194]], 'aut_group': '475566474240.a', 'aut_hash': 5087610779101011723, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 475566474240, 'aut_permdeg': 123, 'aut_perms': [2173325930473163168494933070108538650107628394361232555359512641513093137189261028476067853604288948088894908796791799246170274485051140946019001589009351168874945574909129173023449810173348802079455880921, 2320296887375857246951940293789455241616121950690824187255474785887699828555527086044041761683101204617413121467847466058230205801857035117220644345002693782775359667357555797786146238572627101547573150230], 'aut_phi_ratio': 2935595520.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [3, 1, 242, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(5,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 1132560, 'autcent_group': '475566474240.a', 'autcent_hash': 5087610779101011723, 'autcent_nilpotent': False, 'autcent_order': 475566474240, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(5,3)', '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], [3, 1, 242]], 'center_label': '243.67', 'center_order': 243, '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': ['3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 67, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 5]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 121]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3, 5, 11, 13], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '243.67', 'hash': 67, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1, 1], 'inner_gens': [[1, 3, 9, 27, 81], [1, 3, 9, 27, 81], [1, 3, 9, 27, 81], [1, 3, 9, 27, 81], [1, 3, 9, 27, 81]], '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, 243]], 'label': '243.67', 'linC_count': None, 'linC_degree': 5, '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': 'C3^5', 'ngens': 5, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 243, 'number_divisions': 122, 'number_normal_subgroups': 2664, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 2664, 'number_subgroups': 2664, 'old_label': None, 'order': 243, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 242]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 1132560, 'outer_gen_orders': [2, 121], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 221, 227, 136, 81], [137, 212, 109, 124, 194]], 'outer_group': '475566474240.a', 'outer_hash': 5087610779101011723, 'outer_nilpotent': False, 'outer_order': 475566474240, 'outer_permdeg': 123, 'outer_perms': [2173325930473163168494933070108538650107628394361232555359512641513093137189261028476067853604288948088894908796791799246170274485051140946019001589009351168874945574909129173023449810173348802079455880921, 2320296887375857246951940293789455241616121950690824187255474785887699828555527086044041761683101204617413121467847466058230205801857035117220644345002693782775359667357555797786146238572627101547573150230], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\GL(5,3)', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 3, 'primary_abelian_invariants': [3, 3, 3, 3, 3], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 121]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3, 4, 5], 'pres': [5, -3, 3, 3, 3, 3]}, 'GLFq': {'d': 2, 'q': 243, 'gens': [1435351114, 2892333419, 2351581309, 576898846, 368382181]}, 'Perm': {'d': 15, 'gens': [174356582400, 79833600, 80640, 240, 4]}}, 'schur_multiplier': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3, 3, 3], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^5', 'transitive_degree': 243, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'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, 18, 18, 6], 'aut_gens': [[436278892515018047253209783, 16834366075051371869977862], [3805509313038068600424015220, 7035632049631159342731834756], [3863853891756618095122012575, 4236486230247777552872937418], [6938849098300006034486974886, 4458030914032907975522342767], [5017934005322286092766985191, 5895851624030837065163289363]], 'aut_group': '2880.dt', 'aut_hash': 367732542311087603, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 25509168, 'aut_permdeg': 486, 'aut_perms': [2216814390768518133826938055375375665785208898577635697292509761752406653396635071683551504545969169258644909989391366458123956965183710157526809942388078849908315328534914736740350866242568546016164309592167965791155539301422980513832085143262088285932252846375756104645790109616791617708068427464117093040594657529105126699280782813224569632172154915224117059700681171704040228325107483906142718805298487905498736942914187485969279140184309634662659987170326648383124996506208793382912257706461504751732069937962587312604312041081599174306516974174121088042157821007660757992509699214421428549561038950917472450364451937201831302291532472572690433683717469019659018984198342941838992964069834072350339225580832979492828324145339593364825203863663020679004413670897474814437086043205540423164281636235177813082525711713434580692830007026604311553044709375303251260340296345363402178688090559124428122231577202297592810675431707346679214268064953798744549861372244628092511560065593914861851370893684997860528069992675014855597162951621987388688340876193943658923351569244353699900985500115760966, 13981537647344209812144162595261973336265144900188308083706124393056806191503198183188699095756328191696738693565009102825022369960372697997693251832826599861293894689247943891992695770949046253989550561121708056853269156706843311723920406908203128004643601139677853142569814840000884396098945095832333679602674416092518637855260445137507051070735693492288748941320968566633624215589803952262839638308913994098763281718740588057443458249717232329095340328633258395553389759625761454615061077539971011384242564258117256838459324824875689451624548872252749385691252510052351047376208236662408798533184993398732711480124066479854526243012800143823475110805978033644880680486218418620306325692940017730704875547966345361735796444190360957119704409512039004243701051334771226196638487487868309779376761744622498666646431591785627881051217938771103059127365191916774437273793626262304753989923647614829627600873070429270516787425269147285349904899751741769318677207511921776665700309153521380976129541341929246685779116874573191656275115080309522683636005403007447914899057083635375891678362517682900004, 22065713072350507005788776874215412950613540825351289505369877753620168750458333289516871747865474085508907159257101536314535261989570192427059030266838351830117798667826756158377928486196392424064352434361544859127843728531283085350513154934627479307638795025783750483631824743990149236778864649214175140072090614978244986879185111341694666851145122381664957688643570514782689280275759857197869436907326727335834813540302403545572929102798400319924703625628806391725993078733099506687816618408787263314599930352355317639388977732911704602610058334860785485131370448569081564111447909371084721792383496834397347153610711125890783607116843381262262051035464055708892722845778280770311338667798233486133739328262866868322342697627481006174104217740894577244044403173707704795696814298144042509005041120039617915720816286532376350524410748512492022272549137452157307425264573681251879280237345518869433423631874506496219056865930911267254260467283688222722246724291568952047103294793476760118140217431762063395335942309932263208858789389686960949043406704431678543381547153879024920455983437039880066, 12758993395198120949746897507869816459150088800168147160597269991073560090693223284027779274661354756325542159412913941685707937947555475443879252400989705267084889346810944774007921781268379739528553554991434772462854743431088880478040461472375761059842515371278804679779184288251866821878381438457010811976038941654033657540084742696085835044694924657985185130559013547544570156132056610930498348933010091659956846126644760271065228561524632418154945950388415963469592279186061502733202139994896580049047670307990325412029582323063129052588367072867842641907214999408541750881746336411225637204501102663634396705903876016518741609824548780380248905796745864503595757019414194032413947928626476667608908704876778708199352784748412155038688914888404648068564838647128388078607448783932006581737877753743507366295934377817126970505676883787516146803700109616966956810225637421624001635565119905961654056256689907982325439548606015281232599815971695364852369208967553819732536723776092013642902752822537482353514861217417386177221945697553582873538340043061459993993392608033728971565566570476967006], 'aut_phi_ratio': 2916.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 243, 2, 1], [2, 729, 1, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 4, 2, 2], [3, 6, 6, 1], [3, 6, 18, 1], [3, 12, 3, 1], [3, 12, 6, 2], [3, 12, 18, 2], [3, 12, 27, 1], [3, 12, 36, 1], [3, 12, 54, 1], [6, 486, 2, 1], [6, 486, 6, 1], [6, 486, 18, 1], [6, 1458, 1, 1], [9, 162, 3, 1], [9, 324, 6, 2], [18, 1458, 3, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(2,4):C_2^4', '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': None, 'autcentquo_hash': 367732542311087603, 'autcentquo_nilpotent': False, 'autcentquo_order': 25509168, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^5.C_3^4.C_3.C_6.C_6^2.C_2', 'cc_stats': [[1, 1, 1], [2, 243, 2], [2, 729, 1], [3, 2, 3], [3, 4, 5], [3, 6, 24], [3, 12, 168], [6, 486, 26], [6, 1458, 1], [9, 162, 3], [9, 324, 12], [18, 1458, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '26244.hm', 'commutator_count': 1, 'commutator_label': '6561.86251', 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 195, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 243, 1, 2], [2, 729, 1, 1], [3, 2, 1, 3], [3, 4, 1, 3], [3, 4, 2, 1], [3, 6, 1, 24], [3, 12, 1, 72], [3, 12, 2, 48], [6, 486, 1, 26], [6, 1458, 1, 1], [9, 162, 3, 1], [9, 324, 3, 2], [9, 324, 6, 1], [18, 1458, 3, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 18, 'exponents_of_order': [8, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 54]], 'familial': False, 'frattini_label': '243.67', 'frattini_quotient': '108.40', 'hash': 2006197489004393808, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [6, 6], 'inner_gens': [[436278892515018047253209783, 4460512607897598351730194511], [1027004538665898431977465975, 16834366075051371869977862]], 'inner_hash': 2006197489004393808, 'inner_nilpotent': False, 'inner_order': 26244, 'inner_split': True, 'inner_tex': 'C_3^6.D_{18}', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 4], [2, 12], [4, 17], [6, 48], [12, 168]], 'label': '26244.hm', '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': True, 'name': 'C3^6.D18', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 0, 3, 0, 0, 9, 0, 0, 15, 0, 0, 15, 0, 0, 9, 0, 0, 4, 0, 1, 3, 0, 3, 1, 0, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 249, 'number_divisions': 187, 'number_normal_subgroups': 68, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 26244, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 1215], [3, 2186], [6, 14094], [9, 4374], [18, 4374]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [3, 6, 6, 3, 3], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[2921798408480607380549332073, 2563152611795460447631904181], [3883091217581296573895184610, 4238347677610337751047482375], [5880338475091958835383506179, 6942572659811682014084541446], [2876476551100464265993102733, 2530893586315054740222797231], [1619994360720748978804813673, 1319080564299162577531001781]], 'outer_group': '972.781', 'outer_hash': 781, 'outer_nilpotent': False, 'outer_order': 972, 'outer_permdeg': 15, 'outer_perms': [244, 6434310963, 482435175600, 120839040, 93525793200], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^4:D_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 3], [6, 50], [8, 1], [12, 74], [24, 49]], 'representations': {'PC': {'code': '215164389125029811880278669251022635585590035197102185425387222481461395164730652055730268993090398715751063274709851391', 'gens': [1, 2, 5, 6, 7, 8, 9, 10], 'pres': [10, -2, -2, -3, -3, -3, 3, 3, 3, 3, 3, 121680, 341241, 51, 196442, 112, 963, 30604, 15314, 3174, 25925, 16215, 6505, 45366, 22696, 155527, 272177, 123147, 495728, 72918, 160408, 997209, 1013419, 315029]}, 'Perm': {'d': 27, 'gens': [436278892515018047253209783, 16834366075051371869977862]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 36, 'supersolvable': True, 'sylow_subgroups_known': False, 'tex_name': 'C_3^6.D_{18}', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'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': 4, 'aut_exponent': 12, 'aut_gen_orders': [6, 3, 3, 3, 2, 12], 'aut_gens': [[7426, 11017, 14041, 8101, 13933], [8128, 10288, 14770, 8101, 18307], [7426, 11017, 14770, 8101, 14662], [8155, 11017, 13312, 8101, 16120], [7426, 11746, 13285, 8101, 13204], [9559, 7399, 15391, 7372, 14068], [12475, 7399, 13933, 8101, 14068]], 'aut_group': '216.87', 'aut_hash': 87, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 216, 'aut_permdeg': 18, 'aut_perms': [1213611130046965, 1255501060295824, 902303007950707, 3958862055362743, 3467157225073340, 6170692987614321], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 9, 2, 1], [3, 2, 1, 1], [3, 6, 2, 1], [3, 12, 1, 1], [6, 18, 1, 1], [6, 18, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '\\He_3: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': 12, 'autcentquo_group': '216.87', 'autcentquo_hash': 87, 'autcentquo_nilpotent': False, 'autcentquo_order': 216, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\He_3:D_4', 'cc_stats': [[1, 1, 1], [2, 9, 3], [3, 2, 1], [3, 6, 2], [3, 12, 1], [6, 18, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '108.17', 'commutator_count': 1, 'commutator_label': '27.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 17, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 3], [3, 2, 1, 1], [3, 6, 1, 2], [3, 12, 1, 1], [6, 18, 1, 3]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 9, 'exponent': 6, 'exponents_of_order': [3, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 1, 2]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '36.10', 'hash': 17, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [3, 3, 2, 3, 2], 'inner_gens': [[7426, 11746, 14743, 8101, 14662], [6697, 11017, 14770, 8101, 18307], [8128, 11746, 14041, 7372, 13933], [7426, 11017, 13312, 8101, 13204], [8155, 8830, 14041, 7372, 13933]], 'inner_hash': 17, 'inner_nilpotent': False, 'inner_order': 108, 'inner_split': True, 'inner_tex': 'C_3^2:D_6', 'inner_used': [1, 2, 3, 5], 'irrC_degree': 6, 'irrQ_degree': 6, 'irrQ_dim': 6, 'irrR_degree': 6, 'irrep_stats': [[1, 4], [2, 4], [4, 1], [6, 2]], 'label': '108.17', 'linC_count': 2, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 2, 'linQ_dim': 6, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^2:D6', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 11, 'number_divisions': 11, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 26, 'number_subgroup_classes': 39, 'number_subgroups': 193, 'old_label': None, 'order': 108, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 27], [3, 26], [6, 54]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [6643], 'outer_gens': [[12475, 6697, 16849, 7372, 14743]], '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': 4, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 1], [6, 2]], 'representations': {'PC': {'code': 1672019201374148167, 'gens': [1, 2, 4, 5], 'pres': [5, -2, -2, -3, -3, -3, 101, 26, 122, 968, 433, 1804, 909]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [78750847670572496, 74429456051931709]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [7426, 11017, 14041, 8101, 13933]}, 'Perm': {'d': 9, 'gens': [5515, 5065, 148, 276480, 80884]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:D_6', 'transitive_degree': 9, 'wreath_data': None, 'wreath_product': False}
