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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6400000000.mw', 'ambient_counter': 335, 'ambient_order': 6400000000, 'ambient_tex': 'C_5^8.C_2^4.C_2^6.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 25000000, 'counter': 1650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6400000000.mw.256._.FV', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '256.FV', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '256.53354', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_2^2\\times D_8):C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': None, 'subgroup_order': 25000000, 'subgroup_tex': 'C_5^7.D_{10}.C_2^4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '6400000000.mw', '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': [256806671799686496, 33, 26584438305803936142808359002509131600, 256806323085312090, 1596967378493501284364236453280323159392892135, 62762715007740501701527364525216085668433984096, 1294848966823982304134433, 1938901383840457580544096, 79855142614401533834183, 26584437368957224469726684209803395879, 608358513305779152199601359080093062496, 9209579902861736034270696538592455024, 1046417237469607111132134103169978196481852124, 18315080354505307893301291910496], 'label': '6400000000.mw.256._.FV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '256.FV', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256._.FV', 'subgroup_fusion': None, 'weyl_group': None}
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label None does not appear in gps_groups
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[794471348962042407095380500156453014315275198004, 773536308812201377088251161734132759657894710236, 814318308622093017134636403935613125628922958773, 564695434616881310108185881074750238224811513586, 272113231603081628276299217674255041775884268724], [775105748362686939615213916885168684643783845116, 793934562886725610348108911473483807830215758804, 753152561878009929650025658674515746218201910210, 586138989939685165789128709263405133335516361669, 272113231915672839714872873734949700271920614316], [753661821046556294033053001423742749738951613989, 814318309221505037460484789961059694003594038233, 793934562287313590022261145947555524381195342783, 564695435207610039024327856300141849853809726056, 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16, 1], [40, 16000000, 8, 2], [40, 20000000, 8, 4], [40, 32000000, 8, 1], [40, 40000000, 8, 2]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 100, 3], [2, 1250, 7], [2, 5000, 3], [2, 40000, 4], [2, 62500, 3], [2, 390625, 1], [4, 200, 1], [4, 1000, 2], [4, 1250, 10], [4, 2500, 11], [4, 5000, 11], [4, 25000, 52], [4, 62500, 52], [4, 125000, 61], [4, 390625, 2], [4, 625000, 58], [4, 781250, 17], [4, 1000000, 16], [4, 1562500, 17], [4, 2000000, 12], [4, 3125000, 16], [4, 25000000, 4], [5, 32, 1], [5, 64, 7], [5, 256, 4], [5, 512, 12], [5, 2048, 11], [5, 4096, 8], [5, 8192, 24], [5, 16384, 8], [8, 1000000, 16], [8, 2000000, 8], [8, 5000000, 32], [8, 10000000, 16], [8, 25000000, 40], [8, 50000000, 20], [10, 800, 9], [10, 1600, 9], [10, 3200, 18], [10, 12800, 40], [10, 20000, 19], [10, 25600, 4], [10, 40000, 21], [10, 51200, 30], [10, 80000, 18], [10, 102400, 8], [10, 160000, 4], [10, 204800, 8], [10, 320000, 32], [10, 500000, 3], [10, 640000, 8], [10, 1000000, 3], [10, 1280000, 11], [10, 5120000, 16], [20, 800, 6], [20, 3200, 15], [20, 4000, 10], [20, 12800, 24], [20, 16000, 20], [20, 20000, 76], [20, 25600, 4], [20, 40000, 52], [20, 51200, 20], [20, 64000, 28], [20, 80000, 88], [20, 100000, 156], [20, 102400, 16], [20, 256000, 16], [20, 320000, 104], [20, 400000, 156], [20, 500000, 174], [20, 640000, 8], [20, 1000000, 52], [20, 1280000, 8], [20, 1600000, 52], [20, 2000000, 61], [20, 2500000, 58], 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4000, 2, 5], [20, 12800, 2, 12], [20, 16000, 2, 10], [20, 20000, 2, 38], [20, 25600, 1, 4], [20, 40000, 2, 26], [20, 51200, 2, 10], [20, 64000, 2, 14], [20, 80000, 1, 28], [20, 80000, 2, 30], [20, 100000, 2, 78], [20, 102400, 2, 8], [20, 256000, 2, 8], [20, 320000, 1, 8], [20, 320000, 2, 48], [20, 400000, 2, 78], [20, 500000, 2, 87], [20, 640000, 1, 8], [20, 1000000, 2, 26], [20, 1280000, 2, 4], [20, 1600000, 2, 26], [20, 2000000, 1, 29], [20, 2000000, 2, 16], [20, 2500000, 2, 29], [20, 8000000, 1, 40], [20, 16000000, 1, 16], [20, 32000000, 1, 12], [40, 4000000, 4, 8], [40, 8000000, 2, 8], [40, 16000000, 2, 8], [40, 20000000, 4, 8], [40, 32000000, 1, 8], [40, 40000000, 2, 8]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 40, 'exponents_of_order': [14, 8], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '6400000000.mw', 'hash': 6963347622072766499, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'C_5^8.C_2^4.C_2^6.C_2^4', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '6400000000.mw', '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': 'C5^8.C2^4.C2^6.C2^4', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 91, 0, 0, 0, 0, 115, 0, 0, 0, 163, 0, 0, 0, 203, 0, 0, 0, 215, 0, 0, 239, 0, 0, 283, 0, 227, 0, 155, 31, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 554, 'number_characteristic_subgroups': 86, 'number_conjugacy_classes': 2224, 'number_divisions': 1410, 'number_normal_subgroups': 1776, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 6400000000, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 762175], [4, 279147200], [5, 390624], [8, 2352000000], [10, 123847200], [20, 1595852800], [40, 2048000000]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '32.2', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 32, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2.C_4^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '39198989575173093240125539420380565981232372056568383423761983405158736765080636906466391222564712671239784275270033918097694222748226708679656272875343725448065185121168321120854296209408834895611469929450909795741383603081221488665436175901738825962537089150015500499430214363318171703967621992882384788385654246877125491478465585135046095501978642534116356416229723419840975011011869394166852175760138056655635977006505043007732758345850102773950124896199209018377874255727198669881865382187588825241073331566545086125231905713469820524118972760503678887003940746434936314797279291311912492576368625979127160520425810309348582995115900407051137603697282485688982068120525965026702962582527944825355810592736902158939563919418600118565765854562488045807407366474401178810432646343567293540327207435729651889389036727719780941188051477396160362079200902946567359937909789002602475960027403055511679219114117911097435326919700936790510829126238932535420987154629335764396890698531640971738458280835371688464103616310105815112569212792406578491358357601510758551444527521678174341251785198285402839678775379674608939388524669956477156482984802516494797008741236496763786799522721321775948138615308442275579595302999362447585694217501327289529901848052677666585404777928183279861872320667637147541359273325854422811963609959801247083249738093491644331233830416897467650888267606153527573516916884531543530224396696078027043348229702260706287433969217997035691839817334879739557672266464816669671341664417825926163747945525916386703096281836369146152850057565832403385733091810251262109002284662361132914540447413819135516189228624511186807241198513560604691624178204192318612745978391826122809267192319147808850985374672918165115719906554697691499452708671261905173498265395063169552419488372647648737060340205957971095267373414494261090561178268963047106282521811820192786923670798054338106485600869872066135299245930708122409002826688239311175357837108966817319160425635191353430759656164185833677407194257096703', 'gens': [1, 2, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 18, 19, 20, 21, 22], 'pres': [22, -2, -2, -2, -2, -2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -5, 5, 5, 5, 5, 5, 5, 5, 43919608832, 261550352713, 111, 75802115402, 4401923374, 270546865603, 277898111417, 136136074143, 64668043685, 4617791204, 304621138826, 3112018408, 8960174810, 312, 16357494917, 167828375643, 5746263121, 79751823959, 655218536902, 157757920348, 123474078162, 117384897240, 59907410118, 14904125352, 6458168778, 286342346759, 382294877213, 77498488371, 32785739081, 6645896671, 1757049653, 13462890987, 3297505889, 95672231432, 540445264158, 46225035700, 75782634122, 508910784, 64882342, 13390175444, 2206082502, 580, 27388753929, 384156523551, 60292165173, 136294414155, 1344360301, 511330323, 203520497674, 49182329888, 76881007158, 147630284108, 156134626, 312245944, 312776430, 9248185044, 78594, 714, 2963423243, 24395391009, 12876779575, 67799525453, 675873891, 84497017, 219318671, 381279525, 480417619980, 47487897634, 31555803192, 102061200462, 2031378020, 1922542458, 28275122448, 1283504102, 70218908, 120708226, 40535584, 5867258, 848, 1940167950349, 665930022947, 92294422585, 23256059983, 2376321125, 887276667, 14809349777, 644208039, 248558653, 49590675, 61932873, 37037871, 78386626574, 15368601636, 12673351738, 176079974480, 5069813862, 1901475964, 1111334546, 556934568, 171663550, 99042452, 66010794, 10816, 4954238, 2940, 129761280015, 1005419233317, 450560081, 5406823, 3604605, 12580085907, 6290043049, 450751, 112875, 14359, 14381, 440973885456, 421987467302, 3868057660, 56492789842, 758292584, 126382206, 33862163604, 16631786154, 32194112, 31296534, 7869196, 344338, 1945080, 75102, 1142392356881, 353868742695, 579059712061, 232015601747, 118952570985, 39185879167, 3276877973, 17762950827, 8954162113, 2339124695, 480110637, 40281379, 149260601, 396303, 9382461458, 12840960040, 3210240062, 12841044, 802560106, 535040128, 1605120150, 802560172, 66880194, 12540238, 8360260, 3135282, 2090304, 58803486739, 49561600041, 16896000063, 125809868885, 5913600107, 985600129, 492800151, 123200195, 66000239, 44000261, 15400283, 11000305, 33918517268, 1071544320042, 81607680064, 287273226326, 13601280108, 4139520130, 44795520152, 11198880174, 1182720196, 997920218, 512820240, 108570262, 100485284, 57750306, 1405154623509, 691384320043, 334540800065, 351245041751, 136604160109, 92308480131, 9912320153, 16301120175, 4994880197, 4985200219, 905080241, 326700263, 441650285, 302500307]}, 'Perm': {'d': 40, 'gens': [564695434616881310108185881074750238224811513586, 814318308622093017134636403935613125628922958773, 773536308812201377088251161734132759657894710236, 794471348962042407095380500156453014315275198004, 272113231603081628276299217674255041775884268724]}}, 'schur_multiplier': None, 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 5, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5^8.C_2^4.C_2^6.C_2^4', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 4, 4, 4, 4, 4, 2, 2, 4], 'aut_gens': [[1, 2, 4, 8, 16, 32], [201, 130, 140, 136, 24, 170], [11, 130, 20, 136, 24, 106], [129, 130, 132, 136, 24, 162], [193, 130, 132, 136, 24, 42], [129, 10, 222, 136, 144, 170], [193, 2, 222, 8, 144, 232], [11, 130, 20, 136, 16, 170], [1, 10, 12, 8, 24, 40], [11, 10, 78, 136, 24, 106]], 'aut_group': None, 'aut_hash': 1726825187373800649, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 32768, 'aut_permdeg': 48, 'aut_perms': [9265295149942680369732314036559871130070729431407255859817811, 9329746059478699129518467841043355739979571769203719532163627, 12271199796103102120952627971344644725842670064505636816913069, 11240771086725839656969319535342246468502691113138617479712304, 6643114062025235006429802728366578369902073499677633318001081, 2250348903639502892070828059313599348599557782279814290382417, 7002090216249116125026114263480789870510021597395609401663722, 101207713965257160002769327869321586871455157878814831937056, 11669971400377633629138536932077389783487659147157171713913364], 'aut_phi_ratio': 256.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 3], [2, 4, 4, 3], [2, 8, 2, 1], [4, 1, 4, 1], [4, 2, 1, 2], [4, 2, 2, 2], [4, 4, 4, 3], [4, 8, 2, 1], [4, 8, 4, 1], [8, 4, 4, 2], [8, 8, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^9.C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '1024.djt', 'autcent_hash': 1957374279625110839, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{10}', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '32.51', 'autcentquo_hash': 51, 'autcentquo_nilpotent': True, 'autcentquo_order': 32, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 6], [2, 4, 12], [2, 8, 2], [4, 1, 4], [4, 2, 6], [4, 4, 12], [4, 8, 6], [8, 4, 8], [8, 8, 4]], 'center_label': '8.2', 'center_order': 8, 'central_product': True, 'central_quotient': '32.46', 'commutator_count': 1, 'commutator_label': '8.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 53354, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 6], [2, 4, 1, 12], [2, 8, 1, 2], [4, 1, 2, 2], [4, 2, 1, 6], [4, 4, 1, 12], [4, 8, 1, 6], [8, 4, 2, 4], [8, 8, 1, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 9999360, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '32.51', 'hash': 53354, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 2, 1, 2, 4], 'inner_gens': [[1, 2, 4, 8, 144, 96], [1, 2, 132, 8, 16, 32], [1, 130, 4, 8, 16, 40], [1, 2, 4, 8, 16, 32], [129, 2, 4, 8, 16, 32], [193, 2, 12, 8, 16, 32]], 'inner_hash': 46, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': False, 'inner_tex': 'C_2^2\\times D_4', 'inner_used': [1, 2, 3, 5, 6], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 24], [4, 8]], 'label': '256.53354', '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': '(C2^2*D8):C2^2', 'ngens': 5, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 49, 'number_conjugacy_classes': 64, 'number_divisions': 58, 'number_normal_subgroups': 559, 'number_subgroup_autclasses': 500, 'number_subgroup_classes': 2391, 'number_subgroups': 4735, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 79], [4, 112], [8, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 2, 4, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 2, 0], 'outer_gens': [[75, 130, 78, 136, 24, 34], [75, 10, 206, 136, 24, 170], [75, 10, 206, 8, 16, 40], [1, 10, 214, 8, 152, 168], [195, 10, 156, 8, 144, 32], [9, 10, 222, 8, 152, 96], [9, 138, 4, 136, 152, 106]], 'outer_group': '6144.bkc', 'outer_hash': 2740595861738461669, 'outer_nilpotent': True, 'outer_order': 1024, 'outer_permdeg': 128, 'outer_perms': [147504021091619632733134330830358803366003274351320641445524498202182871223050798726051805590309251500828937112793146806964528864404702511759357190828063695360904751140663487617121886547168530045209457867563223913437, 341189161088141456720157436076190561604873512324166464832546966054597339717438960464221419576751710336206015752340685229270852557942540230050224463422533212509521530268113573840733750211617110396472813636804697158440, 208770194653316433099671464425203197193466348873278853841719677276583196361940237927244601650417431257132302085749842353650088966939427685073731491451969357914378698817655955849339787121189942101478682425221181830827, 77744487485952521117337143290043577691069099020173342787338903647133228135032766894329698394172634441942773914579239772078027933591523544310147551650273807173520938723732821881290270937527634509375502317706001635688, 50157963900187519666872992132629956906848987533337711087859362921217936429952036885055005075208392795888869687521989519163345233893083270292113849465277898317761487482452401373771407788400307934555229361395811603033, 88730659394864844307715242171578337509810654722571962848187765266056175202155805720063855996092164299772024485452765899812559428604787021598471966892695978778545665219103761856958296423600131588183166894602778901873, 308270309794025671659468965897655849874993625644565732124464577680339845670653096398654832409272000020975004226165623425944397585624842892278656577821325623637176906260520554833538924954569043587168235526123449745032], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': '(C_2^9\\times S_3).C_2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 36, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 24], [16, 2]], 'representations': {'PC': {'code': 154780432571670250437762144, 'gens': [1, 2, 3, 4, 5, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 1594, 5764, 4613, 501, 141, 10758, 166]}, 'Perm': {'d': 36, 'gens': [10414516732839566865936901639706764935605, 22440138968605967857067237361249809010600, 33153017124189258448691925241603423752487, 3429198206252537507928346589893622160, 43793695728853708620371109208036762768560, 54127066770150951194486592348650833882800, 64763645682164555027164755633584488310176, 64763645682164555027164755633584488310160]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2^2\\times D_8):C_2^2', 'transitive_degree': 64, 'wreath_data': None, 'wreath_product': False}
