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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '22674816.mj', 'ambient_counter': 322, 'ambient_order': 22674816, 'ambient_tex': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 11337408, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '22674816.mj.2.C', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11337408.lw', 'subgroup_hash': 1932737650862991384, 'subgroup_order': 11337408, 'subgroup_tex': 'C_3^7.S_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '22674816.mj', 'aut_centralizer_order': None, 'aut_label': '2.C', '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': '2.C', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [148311879831258572617263545887398359486134, 271353676394454377792702129150099764, 10872818880982496732313752133, 109900955613340922550081068540160, 8222838669689168581034339899808375, 8223143542522570255320234346169784, 10628380765426167900161457350544321177603, 418802671169936714973312003, 191469869419146555635461657520918225014892, 6790244583891749623177323607624408918, 51704034189144853017744, 17683942790150574557177061504243, 8223143542522567700438361122524824, 8222838654177955983155394012802560, 96029344131055825226289645747504485985841, 10333156189529703288896251288337297841869, 2554547282942135043], 'label': '22674816.mj.2.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.C', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.9', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 72, 'aut_gen_orders': None, 'aut_gens': [[1, 12, 72, 1296, 23328, 139968, 1259712], [2867479, 6815436, 397260, 10518192, 4798224, 699840, 5038848], [3823699, 348228, 8491524, 9788928, 4568268, 1353744, 3836160], [1493497, 4072356, 1950168, 6212388, 10819644, 7664544, 10125360]], 'aut_group': None, 'aut_hash': 8826279076269810851, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 22674816, 'aut_permdeg': 105048, 'aut_perms': None, 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': None, 'aut_supersolvable': False, 'aut_tex': 'C_9^4.C_6^2.C_2.C_6.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': None, 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': 22674816, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 36, 1], [2, 162, 1], [2, 324, 1], [2, 2916, 2], [2, 6561, 1], [3, 8, 2], [3, 16, 2], [3, 32, 1], [3, 36, 3], [3, 72, 6], [3, 81, 2], [3, 108, 2], [3, 144, 3], [3, 216, 2], [3, 324, 1], [4, 52488, 3], [4, 236196, 1], [6, 72, 3], [6, 108, 6], [6, 144, 3], [6, 216, 12], [6, 288, 1], [6, 324, 15], [6, 432, 6], [6, 648, 22], [6, 972, 26], [6, 1296, 4], [6, 1458, 2], [6, 1944, 18], [6, 2916, 25], [6, 5832, 9], [6, 6561, 2], [6, 8748, 18], [6, 11664, 2], [6, 26244, 8], [8, 472392, 2], [9, 24, 1], [9, 48, 3], [9, 72, 7], [9, 96, 3], [9, 144, 16], [9, 192, 1], [9, 216, 12], [9, 288, 16], [9, 432, 31], [9, 576, 4], [9, 648, 10], [9, 864, 28], [9, 1296, 19], [9, 1728, 9], [9, 2592, 18], [9, 5184, 6], [12, 104976, 3], [12, 157464, 6], [12, 236196, 2], [18, 216, 9], [18, 432, 18], [18, 648, 36], [18, 864, 9], [18, 1296, 63], [18, 1944, 63], [18, 2592, 27], [18, 3888, 81], [18, 5832, 57], [18, 7776, 27], [18, 11664, 39], [18, 17496, 27], [18, 34992, 2], [18, 69984, 2], [18, 104976, 4], [24, 472392, 4], [36, 314928, 9]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '11337408.lw', 'commutator_count': 1, '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'], 'composition_length': 17, 'conjugacy_classes_known': True, 'counter': 309, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 162, 1, 1], [2, 324, 1, 1], [2, 2916, 1, 2], [2, 6561, 1, 1], [3, 8, 1, 2], [3, 16, 1, 2], [3, 32, 1, 1], [3, 36, 1, 1], [3, 36, 2, 1], [3, 72, 2, 3], [3, 81, 2, 1], [3, 108, 2, 1], [3, 144, 1, 1], [3, 144, 2, 1], [3, 216, 2, 1], [3, 324, 1, 1], [4, 52488, 1, 1], [4, 52488, 2, 1], [4, 236196, 1, 1], [6, 72, 1, 3], [6, 108, 2, 3], [6, 144, 1, 3], [6, 216, 2, 6], [6, 288, 1, 1], [6, 324, 1, 1], [6, 324, 2, 7], [6, 432, 2, 3], [6, 648, 1, 4], [6, 648, 2, 9], [6, 972, 2, 13], [6, 1296, 1, 2], [6, 1296, 2, 1], [6, 1458, 2, 1], [6, 1944, 2, 9], [6, 2916, 1, 3], [6, 2916, 2, 11], [6, 5832, 1, 1], [6, 5832, 2, 4], [6, 6561, 2, 1], [6, 8748, 2, 9], [6, 11664, 1, 2], [6, 26244, 1, 2], [6, 26244, 2, 3], [8, 472392, 2, 1], [9, 24, 1, 1], [9, 48, 1, 3], [9, 72, 1, 1], [9, 72, 2, 3], [9, 96, 1, 3], [9, 144, 1, 2], [9, 144, 2, 7], [9, 192, 1, 1], [9, 216, 2, 6], [9, 288, 1, 4], [9, 288, 2, 6], [9, 432, 1, 1], [9, 432, 2, 15], [9, 576, 1, 2], [9, 576, 2, 1], [9, 648, 2, 5], [9, 864, 1, 2], [9, 864, 2, 13], [9, 1296, 1, 3], [9, 1296, 2, 8], [9, 1728, 1, 1], [9, 1728, 2, 4], [9, 2592, 2, 9], [9, 5184, 1, 2], [9, 5184, 2, 2], [12, 104976, 1, 1], [12, 104976, 2, 1], [12, 157464, 2, 1], [12, 157464, 4, 1], [12, 236196, 2, 1], [18, 216, 1, 3], [18, 216, 2, 3], [18, 432, 1, 6], [18, 432, 2, 6], [18, 648, 2, 18], [18, 864, 1, 3], [18, 864, 2, 3], [18, 1296, 1, 3], [18, 1296, 2, 30], [18, 1944, 1, 3], [18, 1944, 2, 30], [18, 2592, 1, 3], [18, 2592, 2, 12], [18, 3888, 1, 3], [18, 3888, 2, 39], [18, 5832, 1, 1], [18, 5832, 2, 28], [18, 7776, 1, 1], [18, 7776, 2, 13], [18, 11664, 1, 5], [18, 11664, 2, 17], [18, 17496, 1, 1], [18, 17496, 2, 13], [18, 34992, 1, 2], [18, 69984, 1, 2], [18, 104976, 2, 2], [24, 472392, 4, 1], [36, 314928, 1, 1], [36, 314928, 2, 2], [36, 314928, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [11, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 64], [24, 1, 8], [48, 0, 96], [48, 1, 12], [72, 1, 4], [96, 0, 48], [96, 1, 6], [144, 0, 10], [144, 1, 7], [192, 0, 8], [192, 1, 1], [288, 0, 12], [288, 1, 8], [432, 0, 2], [432, 1, 2], [576, 0, 2], [576, 1, 2], [864, 1, 4], [1728, 1, 1]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': None, 'hash': 1932737650862991384, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 72, 'inner_gen_orders': [24, 6, 18, 18, 6, 9, 9], 'inner_gens': [[1, 55332, 10809636, 10398048, 4189404, 1353744, 3843936], [109345, 12, 3972168, 5558976, 11081664, 1119744, 10077696], [11130205, 1231356, 72, 8933328, 1283040, 699840, 8817984], [10244713, 3424908, 2568744, 1296, 8841312, 559872, 2519424], [4360093, 5319228, 10077768, 2520720, 23328, 279936, 6298560], [2706625, 279948, 699912, 841104, 1143072, 139968, 1259712], [8916481, 2519436, 3779208, 10078992, 6321888, 139968, 1259712]], 'inner_hash': 1932737650862991384, 'inner_nilpotent': False, 'inner_order': 11337408, 'inner_split': None, 'inner_tex': 'C_3^7.S_3\\wr C_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 24], [2, 6], [4, 105], [8, 228], [16, 171], [24, 72], [32, 54], [48, 108], [64, 6], [72, 4], [96, 54], [144, 17], [192, 9], [288, 20], [432, 4], [576, 4], [864, 4], [1728, 1]], 'label': '11337408.lw', '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': 'C3^7.S3wrC4', 'ngens': 17, '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, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 3, 0, 1, 3, 0, 3, 3, 3, 1, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 41, 'number_conjugacy_classes': 891, 'number_divisions': 494, 'number_normal_subgroups': 41, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 11337408, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 12915], [3, 2186], [4, 393660], [6, 623502], [8, 944784], [9, 174960], [12, 1732104], [18, 2729376], [24, 1889568], [36, 2834352]], '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': 2, '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, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 8], [4, 15], [8, 59], [16, 123], [24, 8], [32, 78], [48, 44], [64, 29], [72, 4], [96, 54], [128, 2], [144, 7], [192, 25], [288, 13], [384, 4], [432, 2], [576, 8], [864, 5], [1152, 1], [1728, 1]], 'representations': {'PC': {'code': '2903592711438399819495190925465560236359292534133066143905216287959291775881159903488745512682190751478075787636355998891862707106191326645460998091815049890069020615578384645795310639274825049550259467527228369569056888880683287982957717998505200700420092038048520759172455767092944425225661576210878139731468673409684449520998502798654205385277256692469020566427702005951626468336037756486080803207557382716202047098624826176952434358633709581760880280195909852891580533751645316983503734725542655700180930622281919808533144879327142429156192374720535473135504243776805517890002891753698701082670654006968787633560662057966537090894466849255897453122753731702369880764246662639139689873347326444218670305188447443981932459080533563103', 'gens': [1, 4, 6, 9, 12, 14, 16], 'pres': [17, 2, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 34, 86, 5365287, 3762579, 157339916, 14284321, 190, 43660084, 2061, 1102582877, 479106058, 15618891, 33763484, 16098427, 294, 1055257734, 464265671, 138810208, 8802249, 37479362, 465, 515020039, 29082264, 29417, 9850, 1590901352, 713583457, 212630874, 70877003, 57910, 18983415, 10709039, 2677474, 450, 739034889, 429721946, 38262283, 12754140, 128597, 18005134, 8926131, 672, 78522058, 353430027, 727100, 242413, 40487, 854638427, 27848476, 329598765, 188388350, 3635376, 14309897, 3580330, 1391835, 299432, 606, 1672292868, 939205829, 25801354, 8600499, 23343001, 5871642, 1296976, 322191085, 749528670, 41640527, 22208320, 2313458, 1619467, 102965, 90130, 3056, 3073, 948, 963900014, 963679711, 53537808, 17845985, 2974419, 9381, 1045550607, 19035680, 428302129, 228427842, 33312484, 9517941, 528919, 528936, 73642, 51627, 1086, 2247280, 60676161, 546085202, 182028451, 1685600, 93839]}, 'Perm': {'d': 36, 'gens': [116402843603465367009499615239146169907320, 52876795402540268831878148585326792988187]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_3^7.S_3\\wr C_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 72, 'aut_gen_orders': [18, 18, 36], 'aut_gens': [[10341559710233054493134541928070270514932, 116402028737842036772929287354544384054773, 297539038794244101560037845226962645183757], [10341559710237248103881856892595945932535, 42247319343021719307074191646154195549813, 244048435616148696543643428893473878692668], [191468494787246195873979803215743350179345, 95735732914962282284234659076128213673970, 95733848183496167046094071919977363471504], [339786086637375768470520602767931290460163, 159556232855746276054893328282476031099587, 159557591096606382292863491650499145519507]], 'aut_group': '22674816.mj', 'aut_hash': 8826279076269810851, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 22674816, 'aut_permdeg': 2124, 'aut_perms': 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[18, 216, 1, 1], [18, 216, 2, 1], [18, 432, 1, 1], [18, 432, 2, 1], [18, 648, 1, 1], [18, 864, 1, 4], [18, 864, 2, 4], [18, 1296, 1, 2], [18, 1296, 2, 10], [18, 1728, 1, 1], [18, 1728, 2, 1], [18, 1944, 1, 1], [18, 1944, 2, 4], [18, 2592, 1, 7], [18, 2592, 2, 15], [18, 3888, 1, 5], [18, 3888, 2, 19], [18, 5184, 1, 3], [18, 5184, 2, 5], [18, 5832, 1, 1], [18, 5832, 2, 5], [18, 7776, 1, 9], [18, 7776, 2, 25], [18, 11664, 1, 6], [18, 11664, 2, 23], [18, 15552, 1, 3], [18, 15552, 2, 5], [18, 17496, 1, 1], [18, 17496, 2, 4], [18, 23328, 1, 5], [18, 23328, 2, 13], [18, 34992, 1, 3], [18, 34992, 2, 10], [18, 46656, 1, 2], [18, 46656, 2, 2], [18, 52488, 1, 1], [18, 52488, 2, 1], [18, 69984, 1, 4], [18, 69984, 2, 8], [18, 104976, 1, 1], [18, 104976, 2, 3], [18, 139968, 1, 1], [18, 139968, 2, 1], [24, 944784, 2, 1], [36, 11664, 1, 1], [36, 11664, 2, 1], [36, 23328, 1, 1], [36, 23328, 2, 1], [36, 34992, 1, 1], [36, 34992, 2, 4], [36, 69984, 1, 1], [36, 69984, 2, 1], [36, 104976, 1, 1], [36, 104976, 2, 4], [36, 209952, 1, 1], [36, 209952, 2, 4], [36, 314928, 1, 1], [36, 314928, 2, 1], [36, 629856, 1, 1], [36, 629856, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [11, 7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 16], [24, 1, 8], [48, 0, 32], [48, 1, 10], [72, 1, 8], [96, 0, 52], [96, 1, 11], [144, 0, 12], [144, 1, 10], [192, 0, 24], [192, 1, 6], [288, 0, 10], [288, 1, 9], [384, 0, 2], [384, 1, 1], [432, 1, 4], [576, 0, 8], [576, 1, 6], [864, 1, 9], [1728, 1, 2]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '279936.u', 'hash': 8826279076269810851, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 72, 'inner_gen_orders': [18, 18, 36], 'inner_gens': [[10341559710233054493134541928070270514932, 42542017731129522868572191379389885566655, 96031254153417223945134656449944120505411], [201801116326817428051637866875376806869615, 116402028737842036772929287354544384054773, 116402851945042948313084818602476764612295], [329449408073640901719775972431899375328028, 297534141504575641997075264153031179734796, 297539038794244101560037845226962645183757]], 'inner_hash': 8826279076269810851, 'inner_nilpotent': False, 'inner_order': 22674816, 'inner_split': True, 'inner_tex': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 24], [2, 18], [4, 90], [8, 126], [16, 180], [24, 24], [32, 99], [48, 42], [64, 30], [72, 8], [96, 63], [144, 22], [192, 30], [288, 19], [384, 3], [432, 4], [576, 14], [864, 9], [1728, 2]], 'label': '22674816.mj', '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': 'C3^6.(C3*S3wrD4)', '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, 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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 807, 'number_characteristic_subgroups': 71, 'number_conjugacy_classes': 807, 'number_divisions': 492, 'number_normal_subgroups': 71, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 22674816, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 25659], [3, 2186], [4, 683316], [6, 1188126], [8, 944784], [9, 174960], [12, 5064120], [18, 6403536], [24, 1889568], [36, 6298560]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 14], [4, 24], [8, 56], [16, 77], [24, 8], [32, 89], [48, 18], [64, 50], [72, 8], [96, 27], [128, 12], [144, 10], [192, 32], [288, 15], [384, 13], [432, 4], [576, 11], [768, 1], [864, 9], [1152, 4], [1728, 2]], 'representations': {'PC': {'code': '204753924464296186969946519059962375052652655475942633568214243427490136073407930074016560457401090758537159028231590404130482766329098938130388729837530391094828875584511118200227703157844612941215182329908480334752322883765913875948411016494417544765931299291642024743845676310532080892374929434764549838331695343823269578187068826408567792155284713829628961499749037323627366548038341873190493293365599438982450894799256332546048845508911613530946071784879863941886876707819948508685463361930474072589461315775216445223007363038598937475536066547926401390585134985878227548532034793956994513598410894989156133140369601191232459037995320970281916461416661527939855296155230678890617507301750322135724738672420720413495878018377795647746822981001316894306571013552751651583865453982375687948007991113346077794474868874988118590632861002409256968891022415042539068708390634273870401527472460447232081372665331661649351332922367', 'gens': [1, 3, 5, 7, 8, 10, 12, 13, 15, 16, 17, 18], 'pres': [18, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 36, 1679635, 555220334, 292450358, 146, 814548963, 552531909, 109755705, 540771124, 140746702, 291605440, 78564118, 256, 1427264069, 992655671, 31362377, 137729003, 28942367, 1298977350, 968460216, 421241226, 80104812, 52837926, 34423548, 1351842, 2239411975, 228690457, 178789291, 177591229, 5941519, 1824289, 1584403, 421, 3346168328, 445969178, 205213868, 357758, 37332656, 18478466, 13082588, 1338596, 3280988169, 725787, 613993005, 307008063, 153530001, 34659, 9990117, 8775, 711, 1053119242, 3079342, 87760000, 43880050, 28612, 14374, 7264, 2302193675, 2208135197, 82991, 192596033, 559955, 886565, 46236215, 23013209, 221825, 2518304268, 25474206, 798490416, 211476162, 104828340, 99773958, 26535720, 13002582, 930, 223388977, 429141955, 214571029, 490009, 2218026254, 1360488992, 394865330, 5326646, 75096824, 7105442, 11547500, 7086038, 9932, 87710, 5455392783, 3063619617, 340402227, 515082309, 271019607, 114794601, 2820219, 29958477, 15959103, 979953, 28725, 197223, 2512705552, 2013019810, 947199796, 7314694, 5948728, 65479210, 914452, 16656334, 10484638, 77326, 129670, 6622166033, 1103881013, 5132231, 2612825, 86920235, 51018461, 30705623]}, 'Perm': {'d': 36, 'gens': [10341559710233054493134541928070270514932, 297539038794244101560037845226962645183757, 116402028737842036772929287354544384054773]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], '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, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
