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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2754990144.do', 'ambient_counter': 93, 'ambient_order': 2754990144, 'ambient_tex': 'C_3^8.C_3^8:(C_4^2:C_2^2)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 531441, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2754990144.do.5184._.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '5184.B', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5184.ff', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 5184, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^4:C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': None, 'subgroup_order': 531441, 'subgroup_tex': 'C_3^{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '2754990144.do', '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': [10628380783109273109697708045398805017840, 9146650338351416191655337984144, 51704033854380251097840, 174356582403, 711374856192144, 80883, 80640, 418802671169936714973312003, 43591104, 240, 526261673867387062888983132905517360, 4865804016353325360], 'label': '2754990144.do.5184._.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '5184.B', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5184._.B', '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': '32.45', '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': [[95737651150064593826060709321581682491278, 287201256751137266475269687081163740096785, 52579932907317825459588672623526378892771, 244341504308355481164048054882903778302595], [371989541073297986520350433772299420960453, 297829111172466262238038282569960236555525, 42542543910685004599715659805539593559651, 234014323579895093554419214715425225250495], [95737922503740181749217727366490814324554, 159851202405220101016804315995845997385434, 42246793256275023478314264878735295337438, 233718827558753100764474712475266841562759], [223383506393680782164071636652718551723517, 32206425185546005404652977002326983792599, 307867026230227236550075093518903206835597, 371694834343631894820462508661677789435914], 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52579932898781370613131854089321260326276, 244341775652884418697151934556966609953731], [116404218445658703144233830466988364202730, 297829111272572284417658530874931185220485, 42542289085109611061136965068947784965719, 233713394905142612392060222779259444347575], [116403947082836464934426875537869836795274, 287201256768820402682498007338910202842245, 52579932898780564030209600878131043596679, 233713123542930150871476938861344742488199], [106366558168627336659233030699694769972558, 307867552701593499151729580692064791578242, 42542289085109998841388048343690790277715, 244342030570029348551113255122944451663235], [244345026884666061366529534613283341512770, 287207520642472721393290635959728448902325, 180520749496189974492317009848860953061811, 106369825836290483712156327954257021896172], [244050057225305943958814410487393553645836, 287503016572654163136315781014621509003788, 170187609752338386520501828839717110813374, 96036143367403808202723805515562176073410], [244344763826764033521237034631549810227194, 287207520550576970089763362456596187871998, 180520749550831982955336142961823981838108, 106363587436392267046894461250672205015042], [212433571486368607219355786109023712907562, 287207775559622296596147205613185052921762, 180521275766406136467275156176131388692931, 339786638574267131493210068101373221821504]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 132239526912, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1458, 1, 1], [2, 1458, 2, 1], [2, 6561, 1, 1], [2, 13122, 4, 1], [2, 118098, 1, 1], [2, 118098, 2, 1], [2, 531441, 1, 2], [3, 8, 1, 2], [3, 8, 2, 2], [3, 24, 1, 1], [3, 24, 3, 1], [3, 32, 1, 1], [3, 36, 2, 1], [3, 48, 1, 1], [3, 48, 2, 1], [3, 48, 3, 1], [3, 48, 6, 1], [3, 72, 1, 1], [3, 72, 2, 1], [3, 72, 3, 1], [3, 72, 6, 1], [3, 96, 1, 1], [3, 96, 2, 1], [3, 96, 3, 1], [3, 96, 6, 2], [3, 144, 1, 1], [3, 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3], [18, 314928, 8, 5], [18, 629856, 3, 1], [18, 629856, 6, 1], [18, 629856, 12, 4], [18, 629856, 24, 1], [18, 944784, 2, 1], [18, 944784, 4, 2], [18, 1889568, 1, 1], [18, 1889568, 2, 3], [18, 1889568, 4, 8], [18, 1889568, 8, 2], [18, 2834352, 8, 1], [18, 5668704, 12, 1], [18, 17006112, 4, 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, 1458, 3], [2, 6561, 1], [2, 13122, 4], [2, 118098, 3], [2, 531441, 2], [3, 8, 6], [3, 24, 4], [3, 32, 1], [3, 36, 2], [3, 48, 12], [3, 72, 12], [3, 96, 18], [3, 144, 47], [3, 192, 1], [3, 216, 4], [3, 288, 68], [3, 324, 2], [3, 432, 34], [3, 576, 10], [3, 648, 10], [3, 864, 150], [3, 1296, 44], [3, 1728, 39], [3, 2592, 110], [3, 3888, 4], [3, 5184, 72], [3, 7776, 48], [3, 11664, 8], [3, 15552, 57], [3, 23328, 27], [3, 46656, 10], [3, 52488, 2], [3, 139968, 4], [4, 1062882, 8], [4, 9565938, 12], [6, 2916, 2], [6, 5832, 11], [6, 11664, 14], [6, 17496, 36], [6, 23328, 5], [6, 26244, 6], [6, 34992, 72], [6, 52488, 68], [6, 69984, 36], [6, 104976, 165], [6, 157464, 16], [6, 209952, 235], [6, 314928, 52], [6, 472392, 53], [6, 629856, 36], [6, 944784, 80], [6, 1889568, 109], [6, 2125764, 4], [6, 2834352, 16], [6, 4251528, 18], [6, 17006112, 1], [9, 144, 1], [9, 288, 3], [9, 432, 6], [9, 576, 5], [9, 864, 21], [9, 1296, 14], [9, 1728, 42], [9, 2592, 57], [9, 3888, 8], [9, 5184, 139], [9, 7776, 60], [9, 11664, 4], [9, 15552, 240], [9, 23328, 34], [9, 46656, 213], [9, 139968, 104], [9, 209952, 8], [9, 419904, 16], [12, 4251528, 64], [12, 8503056, 48], [12, 38263752, 24], [18, 104976, 27], [18, 209952, 27], [18, 314928, 54], [18, 629856, 81], [18, 944784, 10], [18, 1889568, 55], [18, 2834352, 8], [18, 5668704, 12], [18, 17006112, 8]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '2754990144.do', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 22, 'conjugacy_classes_known': False, 'counter': 93, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1458, 1, 3], [2, 6561, 1, 1], [2, 13122, 1, 4], [2, 118098, 1, 3], [2, 531441, 1, 2], [3, 8, 1, 6], [3, 24, 1, 4], [3, 32, 1, 1], [3, 36, 1, 2], [3, 48, 1, 12], [3, 72, 1, 12], [3, 96, 1, 18], [3, 144, 1, 47], [3, 192, 1, 1], [3, 216, 1, 4], [3, 288, 1, 68], [3, 324, 1, 2], [3, 432, 1, 34], [3, 576, 1, 10], [3, 648, 1, 10], [3, 864, 1, 150], [3, 1296, 1, 44], [3, 1728, 1, 39], [3, 2592, 1, 110], [3, 3888, 1, 4], [3, 5184, 1, 72], [3, 7776, 1, 48], [3, 11664, 1, 8], [3, 15552, 1, 57], [3, 23328, 1, 27], [3, 46656, 1, 10], [3, 52488, 1, 2], [3, 139968, 1, 4], [4, 1062882, 2, 4], [4, 9565938, 1, 4], [4, 9565938, 2, 4], [6, 2916, 1, 2], [6, 5832, 1, 11], [6, 11664, 1, 14], [6, 17496, 1, 36], [6, 23328, 1, 5], [6, 26244, 1, 6], [6, 34992, 1, 72], [6, 52488, 1, 68], [6, 69984, 1, 36], [6, 104976, 1, 165], [6, 157464, 1, 16], [6, 209952, 1, 235], [6, 314928, 1, 52], [6, 472392, 1, 53], [6, 629856, 1, 36], [6, 944784, 1, 80], [6, 1889568, 1, 109], [6, 2125764, 1, 4], [6, 2834352, 1, 16], [6, 4251528, 1, 18], [6, 17006112, 1, 1], [9, 144, 1, 1], [9, 288, 1, 3], [9, 432, 2, 3], [9, 576, 1, 5], [9, 864, 1, 9], [9, 864, 2, 6], [9, 1296, 1, 2], [9, 1296, 2, 6], [9, 1728, 1, 36], [9, 1728, 2, 3], [9, 2592, 1, 9], [9, 2592, 2, 24], [9, 3888, 2, 4], [9, 5184, 1, 103], [9, 5184, 2, 18], [9, 7776, 2, 30], [9, 11664, 2, 2], [9, 15552, 1, 162], [9, 15552, 2, 39], [9, 23328, 1, 14], [9, 23328, 2, 10], [9, 46656, 1, 141], [9, 46656, 2, 36], [9, 139968, 1, 78], [9, 139968, 2, 13], [9, 209952, 1, 8], [9, 419904, 1, 16], [12, 4251528, 2, 32], [12, 8503056, 2, 24], [12, 38263752, 1, 8], [12, 38263752, 2, 8], [18, 104976, 1, 3], [18, 104976, 2, 12], [18, 209952, 1, 3], [18, 209952, 2, 12], [18, 314928, 2, 27], [18, 629856, 1, 9], [18, 629856, 2, 36], [18, 944784, 1, 6], [18, 944784, 2, 2], [18, 1889568, 1, 11], [18, 1889568, 2, 22], [18, 2834352, 2, 4], [18, 5668704, 1, 12], [18, 17006112, 1, 8]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [16, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': None, 'familial': False, 'frattini_label': '6561.1396077', 'frattini_quotient': '419904.dw', 'hash': 800332183630066390, '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_3^8.C_3^8:(C_4^2:C_2^2)', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '2754990144.do', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^8.C3^8:(C4^2:C2^2)', 'ngens': 4, '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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 2, 0, 0, 0, 2, 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, 3, 0, 0, 0, 15, 0, 0, 43, 0, 43, 0, 15, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 600, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 3268, 'number_divisions': 2887, 'number_normal_subgroups': 130, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 2754990144, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1480599], [3, 4100624], [4, 123294312], [6, 571944240], [9, 38946096], [12, 1598574528], [18, 416649744]], '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': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 48, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '86018375938308377585667337779931660412182288382734088761174570935252063383079145550952987734463230806375878337547672092189491094436776353806707945190181042038695985801745447200255731795860823416411390827887285192307585402121796069851787156118817775911301198810119628883541710140801693226777635769547086453252988809806928529487825240374439462286071790689998616355034383763987416099341994838942693347125032058262307447803404150819216723305205186265150660728007566040373427993965358141866756607822431874167713134806940489753811170802494234593581263652463324123609466467030067881111383616597838761190220653019881680499383973143818154478965558959842672846064841388597807155591740011841482490882213685632154445657497326626554913196895205326226317215363801440856470242526134908331973483300145336739824985765658059619661079697951439220438195812072377330470872014678765067460216287372034370836004651994274180395721110838864831658182751904269335645249262162081484785018280165966127590400872851269479164999671535362868093657405699300286566275970397964863388559944928961721883838688001820006279492124879690257953794481356739807499870963169128389119808328823779535848564399165073348065782008442209596284032214247502865587578989691129568198352507834657802280839234653562072361211595503797374237886584466537145947263333939790067826550666909769179930722172022467220305846562065935730272920732719192824132516747591858536104963089410397991393683520590950578822794108220636947114998172996234159342457037235791907368844281649610857519923321504218573704054636195525781069242635507467965298685416393167455228228542558431888864744425753324695680949182745293401175510463290854195512666900220134942488499533811305660473069236329922325013660214636812887715282943', 'gens': [1, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 20, 21, 22], 'pres': [22, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 44, 54233342615, 1790850602, 28390355292, 8365278286, 157552317123, 49548108921, 12149698751, 245, 75226365284, 34855054986, 74504871368, 2026561772, 339373467845, 174640910427, 39038792017, 18460719095, 12646567125, 379, 16415207430, 211903995100, 104440555346, 35644890584, 9704723430, 6056301774, 269313082375, 57755208221, 118388633139, 18613220809, 6176045663, 7230958005, 6841811467, 237418473608, 114078, 123464401684, 2178692282, 8485591848, 11502043858, 30705424649, 237552543391, 53926266293, 2420906475, 13481590417, 9041606759, 610407125, 317552607, 247819368202, 196621430048, 68870381238, 43604872684, 41650329698, 14614195716, 9407509594, 108570806795, 334578385185, 25146101431, 56486557325, 36847369251, 22505486377, 10920980015, 3367809093, 449392075, 284003489, 34369863, 21369997, 356314578060, 176849614690, 178340763800, 88376436798, 44585191036, 713466590, 653026562, 217675668, 23151668, 640868698637, 299621365155, 18548459833, 41808738127, 52797352709, 15540072363, 6162056353, 4130041775, 366735789, 284881423, 97632845, 21310467, 16319965, 1223, 277136654, 202101894778, 969978320, 17321142, 12986449864, 647125157903, 198512410661, 110189128251, 38245577297, 58949016295, 2452678397, 7829110227, 4990769161, 247626911, 508340661, 184843531, 25965185, 18827703, 2398477, 6681, 980611005456, 430240695846, 188428799740, 122594079426, 4535738960, 30049446762, 8826369106, 294457850, 661166742, 285460576, 10906076, 10189140, 10572886, 1010102, 371728, 1490, 8979227153, 245806342909, 602772275, 561201801, 15994248463, 14568149394, 129138745886, 130345445028, 1777138810, 33025161044, 431429898259, 598615142441, 154642245183, 74203335445, 5300238347, 35230995489, 9275417071, 5975758973, 221324639, 8054945, 915109, 158771, 1225298067860, 144235764330, 180755445088, 93969336470, 46170964332, 5243944990, 13749441704, 3873850770, 1509528832, 503176430, 143476188, 55908730, 1272654, 125090, 46110, 117920613909, 375982041643, 82411198913, 130938851031, 28833758029, 32936535059, 16461916569, 1686203419, 1876734881, 625578447, 62452213, 69508955, 3371851, 379323, 122341]}, 'Perm': {'d': 36, 'gens': [244341504308355481164048054882903778302595, 52579932907317825459588672623526378892771, 95737651150064593826060709321581682491278, 287201256751137266475269687081163740096785]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_3^8.C_3^8:(C_4^2:C_2^2)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': None}
-
gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [24, 4, 4, 8, 4], 'aut_gens': [[2879290997287, 4035153024017, 1328391555240, 204387127], [9440766281640, 2966618069302, 15284078587567, 10862374523040], [2879290997287, 3314872930457, 9434463056040, 1322052041647], [8563293098760, 203747177, 1323968220840, 15689520], [37896364800, 878736510142, 15284078587560, 10917090254887], [14665160700840, 7206699993257, 1328391555240, 5699647312687]], 'aut_group': None, 'aut_hash': 6148241670926445892, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 331776, 'aut_permdeg': 144, 'aut_perms': [2956370211950635059086805705137391656757300763195586977198823272888985897601914967359841956494435108397700211590077637496610145435673829767681749413188426992746850395234884366771617721703128917382440716866780342842452019707591804385738919729239879326, 2172174657951613796249203941242676947745406030907635778317887403392707056235357213254336652841747817140898106494368283903103339987828079900650943243696445740077463693699891302461037450595510417930686727986265517720204046552776644940002226285849479475, 4064389229724298502835627306819678504223313255729803351187452133646174811703769007907899448055603710726263437258446159501424683729113444028984583006992031629643333280760523960817262273849347001132419757755503682128248354753738824563801368159335512058, 511336471060292743007116183652805229464609714840378578675611089072825331837320926286394441196471870183757162024296319920339728614020162123891585347046608960320900197552871773419899205176515218130217845568875169445721092731829978205509274822557043103, 2909934532499644610522591420421869937144971129713225927880707014702055129398802079256815324904388313540372223268888788203112837514783077016952968604218303366470283418681669966165148079992261472159852095839355475121395192822493179880176622583926849009], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 2, 1], [2, 18, 8, 1], [2, 81, 1, 2], [3, 8, 2, 1], [3, 8, 4, 1], [3, 32, 1, 1], [4, 18, 8, 1], [4, 162, 4, 1], [4, 162, 8, 1], [6, 8, 2, 1], [6, 8, 4, 1], [6, 32, 1, 1], [6, 72, 4, 1], [6, 72, 8, 2], [12, 72, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.C_2^3.C_2^5.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '20736.z', 'autcentquo_hash': 687264991867046508, 'autcentquo_nilpotent': False, 'autcentquo_order': 20736, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\wr D_4:C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 18, 10], [2, 81, 2], [3, 8, 6], [3, 32, 1], [4, 18, 8], [4, 162, 12], [6, 8, 6], [6, 32, 1], [6, 72, 20], [12, 72, 16]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '2592.ci', 'commutator_count': 1, 'commutator_label': '162.54', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 136, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 1, 10], [2, 81, 1, 2], [3, 8, 1, 6], [3, 32, 1, 1], [4, 18, 2, 4], [4, 162, 1, 4], [4, 162, 2, 4], [6, 8, 1, 6], [6, 32, 1, 1], [6, 72, 1, 20], [12, 72, 2, 8]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 669614400, 'exponent': 12, 'exponents_of_order': [6, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 0, 16], [8, 1, 8], [32, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2592.ci', 'hash': 1302982936702346125, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 2, 2], 'inner_gens': [[2879290997287, 13208557023377, 9967165096320, 881929854847], [10862374523047, 4035153024017, 9434463056040, 38048774407], [8301859912927, 529859594897, 1328391555240, 204387127], [3314985463567, 4047607468817, 1328391555240, 204387127]], 'inner_hash': 1359974926057248800, 'inner_nilpotent': False, 'inner_order': 2592, 'inner_split': True, 'inner_tex': 'C_3:S_3^3:C_2^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 32], [4, 2], [8, 48], [32, 2]], 'label': '5184.ff', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^4:C4^2:C2^2', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 19, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 84, 'number_divisions': 68, 'number_normal_subgroups': 123, 'number_subgroup_autclasses': 341, 'number_subgroup_classes': 1550, 'number_subgroups': 52150, 'old_label': None, 'order': 5184, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 343], [3, 80], [4, 2088], [6, 1520], [12, 1152]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 8, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 3412695607, 0, 1322056391160, 0, 0, 0], 'outer_gens': [[5412240980047, 13170711864977, 1328391555240, 37896364807], [1322052041640, 12332146997542, 9973500260400, 11950670970000], [2879290997280, 13208557023382, 1353873754927, 40682887], [5412240980047, 6722070138022, 9967165096320, 9992236116967], [2879290997280, 13208557023377, 1353873754920, 40682887], [2879290997280, 4035153024017, 1328391555240, 204387120], [2879290997287, 13208557023382, 1353873754920, 40682887]], 'outer_group': '128.928', 'outer_hash': 928, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 8, 'outer_perms': [11536, 34990, 5161, 40319, 7, 126, 5167], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\wr D_4', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 2], [8, 32], [16, 8], [32, 2]], 'representations': {'PC': {'code': '13237474955693019835211643851857837929357421579314179653775101737706341762235319316769731580295519999072303437110876489666589', 'gens': [1, 2, 3, 5, 7, 8, 9], 'pres': [10, 2, 2, 2, 2, 2, 3, 3, 3, 2, 3, 10921, 16442, 39072, 82, 79683, 63604, 2014, 52224, 13134, 144, 28805, 1935, 8665, 515, 286726, 26896, 71146, 1716, 3406, 322567, 667, 5797, 69868, 48638, 27588, 268, 18429, 43239, 23449]}, 'Perm': {'d': 16, 'gens': [2879290997287, 4035153024017, 1328391555240, 204387127]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:C_4^2:C_2^2', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
