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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6144.bbe', 'ambient_counter': 707, 'ambient_order': 6144, 'ambient_tex': 'C_4^3:C_2^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6144.bbe.4.H', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1536.408560389', 'subgroup_hash': 259221880236507025, 'subgroup_order': 1536, 'subgroup_tex': 'C_2^4.\\GL(2,\\mathbb{Z}/4)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '6144.bbe', 'aut_centralizer_order': None, 'aut_label': '4.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.G', '8.H', '8.I', '8.J', '8.K', '8.L', '8.M', '12.BZ', '16.J'], 'core': '24.B', 'coset_action_label': None, 'count': 4, 'diagramx': [1382, -1, 607, -1], 'generators': [122000787877207687, 25903229683158464676480, 5167, 40291342, 1313941673647, 51469037914089616686, 79804429415054842579207, 350258752815848003623552, 79804308124159703901382, 51212956962072729737], 'label': '6144.bbe.4.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '4.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.H', 'subgroup_fusion': None, 'weyl_group': '384.17949'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [6, 6, 2, 4, 12, 6], 'aut_gens': [[268257039121, 1589822448600, 2966657662207, 37888704736, 3066173470080, 355669619880, 4483749999000, 7, 4483546421760, 530066805960], [1334712561966, 6920311915560, 3053889298087, 561681268696, 11072377088760, 10985224281240, 4483749999000, 4483749999007, 4047851003160, 4483546421760], [12439495610761, 8202479454000, 3053889298080, 4016432045536, 442797834960, 2711396620920, 4483749999000, 7, 530066805960, 4047851003160], [704274414601, 8551638234840, 3053849379967, 561477692903, 10897856161920, 442797834960, 4483749999000, 7, 4483546421760, 530066805960], [5633060001841, 13098902641200, 11004318299647, 38132237663, 2979205328280, 3153482762400, 4483749999000, 4483749999007, 4483546421760, 4047851003160], [8496301808161, 9976378784520, 2966697580320, 4458590802016, 3153482762400, 2979205328280, 4483749999000, 4483749999007, 4047851003160, 4483546421760], [9447163857486, 2119631240880, 2966697580327, 38132237656, 2711396620920, 10897856161920, 4483749999000, 7, 4047851003160, 4483546421760]], 'aut_group': None, 'aut_hash': 8543985317884064529, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24576, 'aut_permdeg': 100, 'aut_perms': [63346267277726520348576192644630348333480665047406343884637776663356092221479807858781138443519933878388210530938969350992338964567602524636604235109673768918, 48173989779663009318707874429158318391931087551699441391953641404471701515550138144626700206520868036410607756179588229637808059871375229549683769490063896816, 8910404947129331747456334806646461184604820124983632404475675258867521080325063328208392717046391538907362015465787449068993718379363367938450189692453237323, 53460717431590680395750003481525113091994643923921565179626634483535868793172357094305925714009676995447614612704613115883792290774683506060883744197149689562, 24736960366149113852190033434079251212676042072621415785308208346180068252504056778994046774911908465230572604098129173968602171251062123073147671715568963601, 33053897548228864298633182870808573066831572913073002246388751298932637806010470578779357977543482219773842771496482564424277778309131298727558249436948093465], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 8, 2, 1], [2, 16, 1, 1], [2, 24, 2, 1], [2, 24, 4, 1], [2, 48, 1, 1], [3, 32, 1, 1], [4, 4, 1, 1], [4, 6, 2, 4], [4, 12, 1, 1], [4, 12, 4, 1], [4, 24, 4, 1], [4, 48, 2, 2], [6, 32, 1, 1], [6, 32, 2, 1], [6, 64, 2, 2], [8, 48, 4, 2], [12, 64, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4^2:C_3.C_2^6.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '384.5677', 'autcentquo_hash': 5677, 'autcentquo_nilpotent': False, 'autcentquo_order': 384, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [2, 8, 2], [2, 16, 1], [2, 24, 6], [2, 48, 1], [3, 32, 1], [4, 4, 1], [4, 6, 8], [4, 12, 5], [4, 24, 4], [4, 48, 4], [6, 32, 3], [6, 64, 4], [8, 48, 8], [12, 64, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '384.17949', 'commutator_count': 1, 'commutator_label': '192.992', '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', '2.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 408560389, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [2, 8, 1, 2], [2, 16, 1, 1], [2, 24, 1, 6], [2, 48, 1, 1], [3, 32, 1, 1], [4, 4, 1, 1], [4, 6, 1, 8], [4, 12, 1, 5], [4, 24, 1, 4], [4, 48, 1, 4], [6, 32, 1, 3], [6, 64, 1, 2], [6, 64, 2, 1], [8, 48, 1, 8], [12, 64, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 40320, 'exponent': 24, 'exponents_of_order': [9, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.14', 'frattini_quotient': '96.226', 'hash': 408560389, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 3, 2, 2, 4, 4, 1, 1, 2, 2], 'inner_gens': [[268257039121, 5278120097040, 2966657662207, 37888704743, 2711396620920, 442797834960, 4483749999000, 7, 4047851003160, 530066805960], [5365305000841, 1589822448600, 2966657662207, 37888704736, 355669619880, 10548780884640, 4483749999000, 7, 530066805960, 4047851003160], [268257039121, 1589822448600, 2966657662207, 4458834299656, 10897856161920, 442797834960, 4483749999000, 7, 4483546421760, 530066805960], [268257039126, 1589822448600, 11004358217767, 37888704736, 10897856161920, 442797834960, 4483749999000, 7, 4483546421760, 530066805960], [704274414601, 9889050619440, 11004318299647, 4458590802016, 3066173470080, 355669619880, 4483749999000, 7, 4483546421760, 530066805960], [878672245801, 7450015432320, 3053889298087, 561681268696, 3066173470080, 355669619880, 4483749999000, 7, 4483546421760, 530066805960], [268257039121, 1589822448600, 2966657662207, 37888704736, 3066173470080, 355669619880, 4483749999000, 7, 4483546421760, 530066805960], [268257039121, 1589822448600, 2966657662207, 37888704736, 3066173470080, 355669619880, 4483749999000, 7, 4483546421760, 530066805960], [878672245801, 2206863884280, 2966657662207, 37888704736, 3066173470080, 355669619880, 4483749999000, 7, 4483546421760, 530066805960], [268257039121, 9534143819640, 2966657662207, 37888704736, 3066173470080, 355669619880, 4483749999000, 7, 4483546421760, 530066805960]], 'inner_hash': 17949, 'inner_nilpotent': False, 'inner_order': 384, 'inner_split': False, 'inner_tex': 'C_2^4.S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 14], [3, 8], [4, 2], [6, 22], [12, 4]], 'label': '1536.408560389', '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': 'C2^4.GL(2,Z/4)', 'ngens': 10, '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': 29, 'number_characteristic_subgroups': 28, 'number_conjugacy_classes': 58, 'number_divisions': 56, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 1051, 'number_subgroup_classes': 2913, 'number_subgroups': 31362, 'old_label': None, 'order': 1536, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 239], [3, 32], [4, 400], [6, 352], [8, 384], [12, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [530066805960, 0, 530066805960, 0, 0], 'outer_gens': [[4221936230401, 5539871974440, 2966657662207, 37888704736, 2711396620920, 442797834960, 4483749999000, 7, 4047851003160, 530066805960], [268257039121, 1589822448600, 11004358217767, 37888704736, 3066173470080, 355669619880, 4483749999000, 7, 4483546421760, 530066805960], [4221936230401, 5539871974440, 11004358217760, 37888704736, 2711396620920, 442797834960, 4483749999000, 7, 4047851003160, 530066805960], [268257039121, 1589822448600, 2966657662207, 37888704736, 10897856161920, 442797834960, 4483749999000, 7, 4483546421760, 530066805960], [11265820958881, 1589822448600, 2966657662207, 37888704736, 10985224281240, 4396517355000, 4483749999000, 4483749999007, 4483546421760, 530066805960]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [16, 806407, 127, 7, 811446], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [3, 8], [4, 4], [6, 22], [12, 4]], 'representations': {'PC': {'code': '136266102602203934851756885009695414584187245274584286028959403773670019136', 'gens': [1, 2, 3, 5, 7, 9], 'pres': [10, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 662, 82, 643, 1304, 924, 144, 47046, 6746, 5916, 206, 76807, 15387, 9637, 15148, 3278, 268, 24029, 2439]}, 'Perm': {'d': 16, 'gens': [268257039121, 1589822448600, 2966657662207, 37888704736, 3066173470080, 355669619880, 4483749999000, 7, 4483546421760, 530066805960]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^4.\\GL(2,\\mathbb{Z}/4)', 'transitive_degree': 24, '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': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [8, 6, 8, 6, 4, 6, 8, 6], 'aut_gens': [[458377823445491894958712, 512330114843461387100758, 566496245137994806113217], [242140722027925822646262, 458326732515846868028758, 216237357894724624281622], [620448279711528939592198, 404210665741269806882512, 620448023980670266044743], [404210787394793291164776, 432525928718607576647638, 350207661526384719024001], [512279023891378264053119, 187973307870272231759982, 594544916296817560183086], [378307679713736645364463, 350207917601724234242512, 216237479892729109936560], [486478098094665037132792, 296092500499402600129896, 486477841638423231894967], [486427006787108599255806, 432525928718607576652793, 594544916296817560183086], [594596384627454126091567, 162121291491379510857617, 512329980028021039220976]], 'aut_group': None, 'aut_hash': 4880800731101327399, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49152, 'aut_permdeg': 176, 'aut_perms': [81139916180575964763438726123126103235084902025561336559787853436787530134587427391255383785053898921576077192195783342361866680064264006714384617296185896346342422042660741517550792895247615373775812240482328304274036310043965878000258260940797746748147722300681280324134292608042825510233140421120722485472489490190672, 166621796017545415840840151151759942875754850372464141427310139270299773492962295506022027043854324155240559747447923818476078412366578752187593945945047790181179217802216636688742254018814422074477475421195163923948274226049310697792542177108455287886676289874011387926307744901496873439565628445078080977773073116349354, 107622879336505147750350664727134860166710473061545748775451045214000035272546622715633411251371973373990899093903793155968685236356243946224879274625333971760325667326626590980915883407536521397325887126559558211266843488335613939630186107436961535840376702554945152206241985467807538510915574548941568927008503353436332, 19182955005356650003380091734611156238136429263846236580352499234364029269447601507697778714706925629727893161667059799154984110069016025097911830958629748961875567306499542328049300799873397972105779652611980311307380967549264916476233580140356887584406989210151491554293165247717193589015093334090096228531856515679929, 59465434023244174249918831502136025897953773392878026667745739004138078297921606273539602306517327246732895481977678030385022534381566693170822475644583975212900759375519973143925641159839768679553824904856358448932490349126898911239023433106645175435333797622719108053785778664998352461599137245107222075028663203497641, 150853786174102520575441632168493026356437642873960946409581577333064970797773484468432882259229417872001208623438244580577698744168144062454261499186176807956490128647787131422438322435727022626534342971962378534354529673320739915815792299526121266592098081219039131161350922908957581445873362815675588002385807495892821, 151181422736072991155852591246526394780517489806465511961980162601915216173524722163256511901462285225140353536027884486837127983908015045534715161294579065024255054392234234472371846475423944925819387724530865717461936349367650190824854343718648691489621421932680920215013676074370602688500963075006551246157782411510247, 185075210279242198235048582408942348854870735794721061574158647892273783566141707742748334915307817219031980236268778782618207864583421610562762599054077805259293185141419305395444571133290584635872556299048766911614898285297834565145515479327118744224315741931865649836916108981981805572666245854193897809057568605101887], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 4, 1, 2], [2, 24, 1, 4], [2, 32, 2, 1], [2, 48, 2, 2], [2, 64, 1, 1], [3, 128, 1, 1], [4, 6, 1, 4], [4, 12, 1, 2], [4, 16, 1, 1], [4, 24, 1, 4], [4, 24, 2, 1], [4, 48, 2, 4], [4, 192, 1, 2], [4, 192, 2, 2], [6, 128, 1, 3], [6, 256, 2, 2], [8, 48, 4, 1], [8, 96, 2, 5], [8, 192, 2, 2], [12, 256, 1, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_4^2:A_4.C_2^4.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': 24, 'autcentquo_group': None, 'autcentquo_hash': 2330610246365708940, 'autcentquo_nilpotent': False, 'autcentquo_order': 6144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_4^2.(D_4\\times S_4).C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 4, 2], [2, 24, 4], [2, 32, 2], [2, 48, 4], [2, 64, 1], [3, 128, 1], [4, 6, 4], [4, 12, 2], [4, 16, 1], [4, 24, 6], [4, 48, 8], [4, 192, 6], [6, 128, 3], [6, 256, 4], [8, 48, 4], [8, 96, 10], [8, 192, 4], [12, 256, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '768.1085082', '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', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 707, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 4, 1, 2], [2, 24, 1, 4], [2, 32, 1, 2], [2, 48, 1, 4], [2, 64, 1, 1], [3, 128, 1, 1], [4, 6, 1, 4], [4, 12, 1, 2], [4, 16, 1, 1], [4, 24, 1, 6], [4, 48, 1, 4], [4, 48, 2, 2], [4, 192, 1, 4], [4, 192, 2, 1], [6, 128, 1, 3], [6, 256, 1, 2], [6, 256, 2, 1], [8, 48, 1, 4], [8, 96, 1, 10], [8, 192, 1, 2], [8, 192, 2, 1], [12, 256, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 24, 'exponents_of_order': [11, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 8], [24, 1, 2]], 'familial': False, 'frattini_label': '64.192', 'frattini_quotient': '96.226', 'hash': 4379435077649205654, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [6, 8, 6], 'inner_gens': [[458377823445491894958712, 162070200189215585959657, 566445153845735636342406], [378307558424323624343623, 512330114843461387100758, 324406735728189507590536], [432525807057995746110736, 187922217290876303518200, 566496245137994806113217]], 'inner_hash': 937700766380363100, 'inner_nilpotent': False, 'inner_order': 3072, 'inner_split': None, 'inner_tex': 'C_4^2:A_4.D_4.C_2', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 14], [3, 8], [4, 2], [6, 22], [12, 12], [24, 6]], 'label': '6144.bbe', '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': 'C4^3:C2^2:S4', 'ngens': 3, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 50, 'number_characteristic_subgroups': 46, 'number_conjugacy_classes': 72, 'number_divisions': 66, 'number_normal_subgroups': 56, 'number_subgroup_autclasses': 4251, 'number_subgroup_classes': 6749, 'number_subgroups': 144648, 'old_label': None, 'order': 6144, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 431], [3, 128], [4, 1744], [6, 1408], [8, 1920], [12, 512]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [512278767433835012182457, 134021272925734282005112, 378307936172761975312681, 79855520719827889612673], 'outer_gens': [[620448279711528939592198, 404210665741269806882512, 620448023980670266044743], [404210787394793291164776, 432525928718607576647638, 350207661526384719024001], [512279023891378264053119, 187973307870272231759982, 594544916296817560183086], [378307679713736645364463, 350207917601724234242512, 216237479892729109936560]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 16, 'outer_perms': [1334672640450, 3054368323555, 4489977049102, 5894621917920], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [3, 8], [4, 4], [6, 14], [12, 16], [24, 6]], 'representations': {'PC': {'code': '30465297323577525206074325053104790093824223395550311012294351161441513208408888695924491749039577947346986787143409097477727762435923527341330485946828620570385418941052564731752306480439276032', 'gens': [1, 2, 4, 5, 6, 8, 11], 'pres': [12, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 52200, 4561, 61, 46082, 43203, 31983, 15867, 423, 47524, 34936, 7768, 4000, 38021, 15569, 22493, 905, 2789, 209, 72582, 36306, 16158, 327175, 34003, 16447, 2731, 5431, 1987, 283, 134792, 44084, 14288, 11276, 5240, 320, 5781, 25953, 355618, 126742, 90322, 26446, 3262, 394, 552971, 276503, 141731]}, 'Perm': {'d': 24, 'gens': [566496245137994806113217, 458377823445491894958712, 512330114843461387100758]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 48, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_4^3:C_2^2:S_4', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
