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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '314928.ce', 'ambient_counter': 57, 'ambient_order': 314928, 'ambient_tex': 'C_3^8.(S_3\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 243, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.ce.1296.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1296.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1296.3576', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3576, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1296, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times C_3^4:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '314928.ce', 'aut_centralizer_order': None, 'aut_label': '1296.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 935, -1, 9050], 'generators': [275962361222754980676170136525526424760384, 9146650338351416191655337984144, 17684330570401657831826661504243, 271353676394454377792702048198864643, 20666567295595334703766545046519969962387], 'label': '314928.ce.1296.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1296.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1296.a1.N', 'projective_image': '314928.ce', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.A', 'subgroup_fusion': None, 'weyl_group': '1296.3576'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '243.67', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1132560, 'aut_gen_orders': [2, 121], 'aut_gens': [[1, 3, 9, 27, 81], [1, 221, 227, 136, 81], [137, 212, 109, 124, 194]], 'aut_group': '475566474240.a', 'aut_hash': 5087610779101011723, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 475566474240, 'aut_permdeg': 123, 'aut_perms': [2173325930473163168494933070108538650107628394361232555359512641513093137189261028476067853604288948088894908796791799246170274485051140946019001589009351168874945574909129173023449810173348802079455880921, 2320296887375857246951940293789455241616121950690824187255474785887699828555527086044041761683101204617413121467847466058230205801857035117220644345002693782775359667357555797786146238572627101547573150230], 'aut_phi_ratio': 2935595520.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [3, 1, 242, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(5,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 1132560, 'autcent_group': '475566474240.a', 'autcent_hash': 5087610779101011723, 'autcent_nilpotent': False, 'autcent_order': 475566474240, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(5,3)', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [3, 1, 242]], 'center_label': '243.67', 'center_order': 243, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 67, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 5]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 121]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3, 5, 11, 13], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '243.67', 'hash': 67, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1, 1], 'inner_gens': [[1, 3, 9, 27, 81], [1, 3, 9, 27, 81], [1, 3, 9, 27, 81], [1, 3, 9, 27, 81], [1, 3, 9, 27, 81]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 243]], 'label': '243.67', 'linC_count': None, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^5', 'ngens': 5, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 243, 'number_divisions': 122, 'number_normal_subgroups': 2664, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 2664, 'number_subgroups': 2664, 'old_label': None, 'order': 243, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 242]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 1132560, 'outer_gen_orders': [2, 121], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 221, 227, 136, 81], [137, 212, 109, 124, 194]], 'outer_group': '475566474240.a', 'outer_hash': 5087610779101011723, 'outer_nilpotent': False, 'outer_order': 475566474240, 'outer_permdeg': 123, 'outer_perms': [2173325930473163168494933070108538650107628394361232555359512641513093137189261028476067853604288948088894908796791799246170274485051140946019001589009351168874945574909129173023449810173348802079455880921, 2320296887375857246951940293789455241616121950690824187255474785887699828555527086044041761683101204617413121467847466058230205801857035117220644345002693782775359667357555797786146238572627101547573150230], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\GL(5,3)', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 3, 'primary_abelian_invariants': [3, 3, 3, 3, 3], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 121]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3, 4, 5], 'pres': [5, -3, 3, 3, 3, 3]}, 'GLFq': {'d': 2, 'q': 243, 'gens': [1435351114, 2892333419, 2351581309, 576898846, 368382181]}, 'Perm': {'d': 15, 'gens': [174356582400, 79833600, 80640, 240, 4]}}, 'schur_multiplier': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3, 3, 3], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^5', 'transitive_degree': 243, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [4, 8, 8, 8, 8], 'aut_gens': [[116702702448996862478153539133966584620744, 191475828451913004234288436969304030851798, 159556224531858510516865615316287682980080], [95740910577506257228910240049428120919605, 191475573526230394175257759456596049527093, 42250570529950447068259005232599695571815], [116702447523315865533256157463435605446344, 340075895986120028774228007270597238619785, 52878425042239590205815162654196136016695], [191767538730539240898167106668574120677305, 371697822636880330527040876421275515146874, 52583200474880417721988211606085845621517], [116702447523315865506285005465931367209867, 329743011159412176241491666681363871633347, 42545285307533876960147507978561092270798], [202100423574929810835460598666730602496148, 106364113524691038505694427484866299942279, 52583455365194754499149020395831720481998]], 'aut_group': None, 'aut_hash': 7446123280704170672, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 15116544, 'aut_permdeg': 567, 'aut_perms': 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'aut_phi_ratio': 144.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 162, 2, 1], [2, 243, 1, 2], [2, 486, 2, 1], [2, 6561, 1, 1], [3, 4, 8, 1], [3, 8, 6, 1], [3, 12, 8, 1], [3, 24, 6, 1], [3, 24, 8, 2], [3, 24, 24, 1], [3, 48, 6, 1], [3, 48, 8, 1], [3, 48, 12, 2], [3, 48, 24, 3], [3, 162, 1, 1], [3, 648, 8, 1], [3, 1296, 6, 1], [4, 13122, 1, 1], [4, 39366, 1, 1], [6, 324, 8, 1], [6, 972, 8, 5], [6, 1944, 6, 2], [6, 1944, 8, 2], [6, 1944, 24, 1], [6, 2916, 2, 1], [6, 5832, 8, 1], [6, 13122, 1, 1], [12, 26244, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^8.Q_8.D_6^2.C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': None, 'autcentquo_hash': 7446123280704170672, 'autcentquo_nilpotent': False, 'autcentquo_order': 15116544, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^8.Q_8.D_6^2.C_2', 'cc_stats': [[1, 1, 1], [2, 162, 2], [2, 243, 2], [2, 486, 2], [2, 6561, 1], [3, 4, 8], [3, 8, 6], [3, 12, 8], [3, 24, 46], [3, 48, 110], [3, 162, 1], [3, 648, 8], [3, 1296, 6], [4, 13122, 1], [4, 39366, 1], [6, 324, 8], [6, 972, 40], [6, 1944, 52], [6, 2916, 2], [6, 5832, 8], [6, 13122, 1], [12, 26244, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '314928.ce', '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', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 57, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 162, 1, 2], [2, 243, 1, 2], [2, 486, 1, 2], [2, 6561, 1, 1], [3, 4, 1, 8], [3, 8, 1, 6], [3, 12, 1, 8], [3, 24, 1, 46], [3, 48, 1, 110], [3, 162, 1, 1], [3, 648, 1, 8], [3, 1296, 1, 6], [4, 13122, 1, 1], [4, 39366, 1, 1], [6, 324, 1, 8], [6, 972, 1, 40], [6, 1944, 1, 52], [6, 2916, 1, 2], [6, 5832, 1, 8], [6, 13122, 1, 1], [12, 26244, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 12, 'exponents_of_order': [9, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 12], [48, 1, 78]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '3888.dx', 'hash': 5880241862171865822, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 6, 12], 'inner_gens': [[116702702448996862478153539133966584620744, 191770798102736247968147556990044461067275, 169889380703094493948074684132584870409145], [95741181931182651734989511305608341045282, 191475828451913004234288436969304030851798, 42250570538487320717382127522532049060211], [116407732780490094707356429346109627198145, 319409871407022520178699974863855927131789, 159556224531858510516865615316287682980080]], 'inner_hash': 5880241862171865822, 'inner_nilpotent': False, 'inner_order': 314928, 'inner_split': False, 'inner_tex': 'C_3^8.(S_3\\times D_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 8], [2, 6], [4, 33], [8, 28], [12, 32], [16, 6], [24, 92], [48, 110]], 'label': '314928.ce', '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.(S3*D4)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 40, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 315, 'number_divisions': 315, 'number_normal_subgroups': 49, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 314928, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 8343], [3, 19682], [4, 52488], [6, 208170], [12, 26244]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2], 'outer_gen_pows': [0, 295495930181441691325976670032409359545, 0, 295495930181441691325976670032409359545, 295495930181441691325976670032409359545], 'outer_gens': [[116702973802672838129857607352365581157784, 202104209208801491902397099178707937401973, 180222520455484149986143468321908748170240], [191767538748222764833944789068080697954042, 116402028682890510153490874795669609855735, 180517761486204573615966628666598218146601], [106074066775573640450226157229372427216120, 191475573543914724770385121665825247251813, 170184350371602068277070896213166288846228], [96036406507078310009013315893820482486520, 202104209208801491875421081000496176595810, 180222791800623283035867651495780874740484], [106074593028100050940738283768395635564843, 191475573526230813002656945404405901469493, 180222265538948996873117030017203742644720]], 'outer_group': '48.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 6, 'outer_perms': [391, 659, 181, 657, 26], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times S_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 6], [4, 33], [8, 28], [12, 32], [16, 6], [24, 92], [48, 110]], 'representations': {'PC': {'code': '825386663154835096507722705984954159389080286949282002451727334415348542396919844973976534198583536107608412760698362273672543541762650602505201018037920822549620340324566924732800181966772049015441493888194556254849929691889218832916863371280254963429728526761311513571779670991330632724400054573532800255', 'gens': [1, 2, 4, 6, 7, 8, 9, 10, 11, 12, 13], 'pres': [13, -2, -2, -3, -2, -2, -3, 3, 3, 3, 3, 3, 3, 3, 2963376, 6338853, 66, 5852186, 371283, 2236120, 62585, 146, 2837644, 5596517, 2751480, 17739077, 12147426, 3993007, 619364, 369, 6827190, 406243, 1490612, 1402901, 1150, 17716615, 13445972, 3369633, 226350, 3803, 26518760, 474573, 4779250, 2409779, 12696, 11481609, 9166582, 6514595, 2184048, 42181, 37408810, 15924503, 192228, 2900089, 139058, 48529739, 2875416, 11642005, 2014322, 454959, 18373692, 10715977, 8588618, 668615, 1478476]}, 'Perm': {'d': 36, 'gens': [159556224531858510516865615316287682980080, 116702702448996862478153539133966584620744, 191475828451913004234288436969304030851798]}}, 'schur_multiplier': [2, 2, 6], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 27, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^8.(S_3\\times D_4)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
-
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': 5, 'aut_exponent': 24, 'aut_gen_orders': [12, 24, 8, 6, 8], 'aut_gens': [[23554882, 26114888, 14520385, 29354483, 28816400, 31414312, 41653360, 23548240], [26212087, 26646329, 26099902, 39898415, 28816400, 14839930, 33817826, 15051826], [26099902, 22912958, 26212087, 39976661, 28816400, 14839930, 17949845, 14901976], [14507101, 22926242, 25530796, 28751438, 28816400, 30994571, 31562623, 23418316], [22342150, 14914046, 22379815, 37294346, 28816400, 28944785, 21670417, 15433417], [23442697, 15479426, 23411674, 37319456, 28816400, 14748400, 25454981, 15045184]], 'aut_group': None, 'aut_hash': 1694224934503634087, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 124416, 'aut_permdeg': 72, 'aut_perms': [28659295078281946444529139699091847017172596426473699400125642540231325875925204935226768296839390337477, 60273965071827812402490320218421567218450587494445529217765399132949638498855917870315561428126374539284, 48439263394808489840265086691562655451468540983497728638249083105677853837697948770334700258345048406124, 22666433000574381088724985481144385992226506860082399258260909112177745191877480913378362730806758916087, 34874502590650981732764719707292361046614235881683808800857561984301861189253509976157577366701494395721], 'aut_phi_ratio': 288.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 4, 1], [2, 81, 1, 2], [3, 4, 8, 1], [3, 8, 6, 1], [4, 162, 2, 1], [6, 4, 8, 1], [6, 8, 6, 1], [6, 36, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.Q_8.C_6.C_2^4.C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '31104.mg', 'autcentquo_hash': 7361170441374917732, 'autcentquo_nilpotent': False, 'autcentquo_order': 31104, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:\\GL(2,3):D_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 18, 4], [2, 81, 2], [3, 4, 8], [3, 8, 6], [4, 162, 2], [6, 4, 8], [6, 8, 6], [6, 36, 16]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '648.725', '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', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3576, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['648.725', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 1, 4], [2, 81, 1, 2], [3, 4, 1, 8], [3, 8, 1, 6], [4, 162, 1, 2], [6, 4, 1, 8], [6, 8, 1, 6], [6, 36, 1, 16]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 5460, 'exponent': 12, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1296.3576', 'hash': 3576, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [3, 2, 3, 3, 1, 2, 4, 3], 'inner_gens': [[23554882, 23403818, 14520385, 29354483, 28816400, 41511691, 34264135, 23548240], [26068879, 26114888, 14377177, 29892566, 28816400, 34071517, 41697667, 26075521], [23554882, 26061023, 14520385, 29354483, 28816400, 34071517, 31555981, 23548240], [23554882, 26633045, 14520385, 29354483, 28816400, 30351430, 42198085, 23548240], [23554882, 26114888, 14520385, 29354483, 28816400, 31414312, 41653360, 23548240], [14520385, 14423186, 23554882, 28823042, 28816400, 31414312, 17950330, 15576625], [14520385, 15569498, 26068879, 28823042, 28816400, 21836548, 41653360, 15038542], [23554882, 23410460, 14520385, 29354483, 28816400, 42574573, 33732694, 23548240]], 'inner_hash': 725, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': False, 'inner_tex': 'C_3^4:D_4', 'inner_used': [1, 2, 3, 4, 6, 7], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 2], [4, 32], [8, 12]], 'label': '1296.3576', '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': 'C2*C3^4:D4', 'ngens': 8, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 11, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 54, 'number_divisions': 54, 'number_normal_subgroups': 29, 'number_subgroup_autclasses': 120, 'number_subgroup_classes': 841, 'number_subgroups': 15310, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 235], [3, 80], [4, 324], [6, 656]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 3, 2, 2], 'outer_gen_pows': [14408200, 14408200, 31699189, 14408200, 14408200, 14408200, 14408200], 'outer_gens': [[26606962, 26211602, 14383819, 29354483, 28816400, 31414312, 33719410, 26600320], [23554882, 26114888, 14520385, 29354483, 28816400, 31414312, 21125207, 23548240], [23442697, 15576140, 23411674, 29347841, 28816400, 14826646, 34213186, 22917898], [26068879, 25680161, 14377177, 29892566, 28816400, 18187580, 34264135, 26075521], [26606962, 14954627, 14383819, 40476350, 28816400, 31414312, 33719410, 26637985], [14507101, 25680161, 25530796, 28744796, 28816400, 21836548, 34887835, 22880233], [14421484, 15432203, 14946283, 28751438, 28816400, 21836548, 31167748, 23548240]], 'outer_group': '192.1472', 'outer_hash': 1472, 'outer_nilpotent': False, 'outer_order': 192, 'outer_permdeg': 8, 'outer_perms': [720, 1, 16, 7, 840, 5160, 11520], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'D_4\\times S_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 32], [8, 12]], 'representations': {'PC': {'code': 430562379058743544259422727463640389724784016093475928982045, 'gens': [1, 2, 4, 5, 6, 7], 'pres': [8, 2, 2, 2, 3, 3, 3, 2, 3, 97, 41, 3587, 1803, 147, 9292, 500, 22477, 1749, 64518, 32270, 15142, 166, 64519, 32271, 13847]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [23554882, 26114888, 14520385, 29354483, 28816400, 31414312, 41653360, 23548240]}, 'Perm': {'d': 14, 'gens': [6314112002, 123747247, 5040, 127370903, 56, 285, 13539415758, 1001549111]}}, 'schur_multiplier': [2, 2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_3^4:D_4', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
