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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '324000.bp', 'ambient_counter': 42, 'ambient_order': 324000, 'ambient_tex': 'C_{15}^3.(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324000.bp.180.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.a1', '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': 180, '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': '1800.704', 'subgroup_hash': 704, 'subgroup_order': 1800, 'subgroup_tex': 'C_6\\times C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '324000.bp', 'aut_centralizer_order': None, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18000.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '60.a1', '90.b1'], 'contains': ['360.a1', '360.ct1', '360.df1', '540.a1', '540.b1', '540.d1', '900.a1', '900.b1', '900.c1', '900.d1'], 'core': '324000.a1', 'coset_action_label': None, 'count': 90, 'diagramx': None, 'generators': [15025, 138528, 216000, 15360, 18, 64800, 116172], 'label': '324000.bp.180.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '90.b1', 'old_label': '180.a1', 'projective_image': '324000.bp', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '72.36', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 120, 'aut_gen_orders': [40, 20, 24, 24], 'aut_gens': [[1, 4, 60], [1489, 516, 1052], [409, 128, 60], [913, 528, 784], [1285, 1000, 592]], 'aut_group': None, 'aut_hash': 3401745568645604803, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1152000, 'aut_permdeg': 58, 'aut_perms': [899488600826653558709416665506240553115537661040596530198019815455811705657777, 1622339450439635486222078306590183953646177615966380803316761693567189114541873, 234928708564699181620862789498442034335706154646404735219968698929466361807410, 1084100406615023476507404855624553598154537084075918693917789840942101433184431], 'aut_phi_ratio': 2400.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 25, 1, 2], [3, 1, 8, 1], [4, 25, 2, 2], [5, 4, 6, 1], [6, 1, 8, 1], [6, 25, 8, 2], [10, 4, 6, 1], [12, 25, 16, 2], [15, 4, 48, 1], [30, 4, 48, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times \\GL(2,3)\\times C_5^2:C_4.S_5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '96.189', 'autcent_hash': 189, 'autcent_nilpotent': False, 'autcent_order': 96, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2\\times \\GL(2,3)', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '12000.a', 'autcentquo_hash': 5912173750379521722, 'autcentquo_nilpotent': False, 'autcentquo_order': 12000, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_5^2.\\GL(2,5)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 25, 2], [3, 1, 8], [4, 25, 4], [5, 4, 6], [6, 1, 8], [6, 25, 16], [10, 4, 6], [12, 25, 32], [15, 4, 48], [30, 4, 48]], 'center_label': '18.5', 'center_order': 18, 'central_product': True, 'central_quotient': '100.11', 'commutator_count': 1, 'commutator_label': '25.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '5.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 704, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['100.11', 1], ['2.1', 1], ['3.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 25, 1, 2], [3, 1, 2, 4], [4, 25, 2, 2], [5, 4, 1, 6], [6, 1, 2, 4], [6, 25, 2, 8], [10, 4, 1, 6], [12, 25, 4, 8], [15, 4, 2, 24], [30, 4, 2, 24]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2184, 'exponent': 60, 'exponents_of_order': [3, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1800.704', 'hash': 704, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [4, 5, 5], 'inner_gens': [[1, 52, 780], [13, 4, 60], [1081, 4, 60]], 'inner_hash': 11, 'inner_nilpotent': False, 'inner_order': 100, 'inner_split': False, 'inner_tex': 'C_5:F_5', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 72], [4, 108]], 'label': '1800.704', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6*C15:F5', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 180, 'number_divisions': 90, 'number_normal_subgroups': 132, 'number_subgroup_autclasses': 63, 'number_subgroup_classes': 384, 'number_subgroups': 2112, 'old_label': None, 'order': 1800, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 51], [3, 8], [4, 100], [5, 24], [6, 408], [10, 24], [12, 800], [15, 192], [30, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 120, 'outer_gen_orders': [2, 2, 6, 4, 4, 2, 2, 24], 'outer_gen_pows': [1, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[901, 736, 84], [1, 44, 60], [901, 604, 60], [901, 1224, 1300], [1, 644, 100], [901, 4, 60], [1, 44, 660], [901, 1368, 1504]], 'outer_group': '11520.gn', 'outer_hash': 3840190186149365950, 'outer_nilpotent': False, 'outer_order': 11520, 'outer_permdeg': 15, 'outer_perms': [355459104000, 90727, 2310751, 1574911, 1191774, 1, 2039280, 186852241831], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times S_5\\times \\GL(2,3)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 18], [4, 20], [8, 48]], 'representations': {'PC': {'code': 13739603406365247787550394990058656185715278561617461703, 'gens': [1, 3, 5], 'pres': [7, -2, -2, -3, -5, -2, -3, -5, 14, 1094, 177, 79, 1011, 682, 27304, 19961, 102, 65525, 10092, 166, 52926, 35293]}, 'Perm': {'d': 18, 'gens': [44548150711680, 24, 5760, 3, 21010055270400, 397620712339200, 713990731104000]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6, 12], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6\\times C_{15}:F_5', 'transitive_degree': 450, '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 180, 'aut_gen_orders': [30, 12, 2, 30, 30, 15], 'aut_gens': [[1, 2, 24, 48, 1440, 21600], [123961, 274906, 20376, 161256, 1248, 21600], [146217, 19034, 173256, 28056, 1056, 15840], [3169, 19178, 18168, 4272, 20160, 21600], [201889, 254954, 232632, 145488, 1440, 302400], [10201, 110930, 20184, 286608, 20160, 21600], [2209, 303842, 2904, 2928, 1440, 21600]], 'aut_group': '648000.v', 'aut_hash': 2811864275658790406, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 648000, 'aut_permdeg': 215, 'aut_perms': [32995629315523956193609127484885509181229242167529868966020107537723933531376823736441028475493810093701163310587814590669560863633296445841228769195929473158244047997450849251785384525457592620121955238271511840169584098722247246523435024672043029886883374806417883460809147889532189592650420872128588817901302172960442694697075654646884654676180185043717088081919865347915977158748437113022664917395496268810, 36343553597388359075654899974187145664069689079710442646225195558986267012922420497813817745808225974953382827306929352123406078932427321805983300506921148734302258344568865577501388400981187081969043867775310720893823639817641131805596031507681929832251545312081135472942351112380880798638094215336937823790441775390984573032351592441431220581505585809314400402697155281514701360874793932082485358864607097465, 11700852545342192459546327085479180405692507468151656993645823268797873579994023934600163292695169058463492480031456808948037561145291650768817690377081097259514470751956877855580222504193022685041333151043354533099816899338713472601923826160471684041404127631304956064376528807396652973508758655225533681942989337167569939475180784012979399748060552411179274803951486395118427860939702180464098219809996368462, 9113154545296417930646914216316248247490248725467280199956295297899834791896851296911604353151575700733091501671493152489910690964209599834970050028005812134771102233864919444685329491345580884158085262517095584396076825132286931642061259490162044793823781402976798081236857442085797028937123177806454636830259405336917528623474218771076997470414918168768158677053778231889794898432218080023682399139313764729, 7016781850008337111096785110740107093986691292852732845405057017771404359328222334559044718862089558398470109644720759334723930103872211148740992986212628487587529258321344538283422475966986658260341336962825383717535121454906295429679669771855578286159511499748288498050270712385093292881052782145153294376502630089854267369527473085928985929390513263212144162771139272930315482552518859533048364701789020432, 42961684309568102565019083322785650492565266204560767664770239543970446731557211475821141187147359082248281470663875482792602360276772444875257581110664522319863567640988691252659428948024763645081298152014543455199658001535724417046946090928515290300329984208501351418867004496388523974440260274552768278765847740878062075864027257953571247108771195828712444177546851597073895275214911865869641575841101742524], 'aut_phi_ratio': 7.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 90, 1, 1], [2, 125, 1, 1], [2, 135, 1, 1], [2, 450, 1, 1], [2, 675, 1, 1], [3, 4, 2, 1], [3, 6, 1, 1], [3, 12, 1, 1], [3, 1800, 1, 1], [4, 125, 1, 2], [4, 2250, 1, 2], [4, 3375, 1, 2], [4, 4050, 1, 3], [4, 20250, 1, 1], [5, 12, 1, 1], [5, 16, 1, 1], [5, 24, 1, 2], [5, 48, 1, 1], [6, 90, 2, 1], [6, 180, 1, 1], [6, 180, 2, 1], [6, 270, 1, 1], [6, 450, 2, 1], [6, 500, 2, 1], [6, 750, 1, 1], [6, 900, 1, 1], [6, 900, 2, 1], [6, 1350, 1, 1], [6, 1500, 1, 1], [6, 9000, 1, 1], [9, 1800, 2, 1], [10, 360, 1, 2], [10, 720, 1, 2], [10, 1080, 1, 3], [10, 1800, 1, 1], [10, 2700, 1, 1], [12, 500, 2, 2], [12, 750, 1, 2], [12, 1500, 1, 2], [12, 2250, 2, 2], [12, 4500, 1, 2], [12, 4500, 2, 2], [12, 6750, 1, 2], [12, 9000, 1, 2], [15, 16, 2, 1], [15, 24, 1, 1], [15, 24, 2, 1], [15, 48, 1, 5], [15, 48, 2, 10], [15, 96, 1, 6], [15, 96, 2, 7], [15, 7200, 1, 1], [18, 9000, 2, 1], [20, 16200, 1, 3], [30, 360, 2, 2], [30, 720, 1, 2], [30, 720, 2, 10], [30, 1080, 2, 1], [30, 1800, 2, 1], [30, 2160, 1, 2], [30, 3600, 1, 1], [30, 3600, 2, 1], [30, 5400, 1, 1], [36, 9000, 2, 2], [45, 7200, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_{15}\\wr S_3.C_4', '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': 180, 'autcentquo_group': '648000.v', 'autcentquo_hash': 2811864275658790406, 'autcentquo_nilpotent': False, 'autcentquo_order': 648000, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_{15}\\wr S_3.C_4', 'cc_stats': [[1, 1, 1], [2, 90, 1], [2, 125, 1], [2, 135, 1], [2, 450, 1], [2, 675, 1], [3, 4, 2], [3, 6, 1], [3, 12, 1], [3, 1800, 1], [4, 125, 2], [4, 2250, 2], [4, 3375, 2], [4, 4050, 3], [4, 20250, 1], [5, 12, 1], [5, 16, 1], [5, 24, 2], [5, 48, 1], [6, 90, 2], [6, 180, 3], [6, 270, 1], [6, 450, 2], [6, 500, 2], [6, 750, 1], [6, 900, 3], [6, 1350, 1], [6, 1500, 1], [6, 9000, 1], [9, 1800, 2], [10, 360, 2], [10, 720, 2], [10, 1080, 3], [10, 1800, 1], [10, 2700, 1], [12, 500, 4], [12, 750, 2], [12, 1500, 2], [12, 2250, 4], [12, 4500, 6], [12, 6750, 2], [12, 9000, 2], [15, 16, 2], [15, 24, 3], [15, 48, 25], [15, 96, 20], [15, 7200, 1], [18, 9000, 2], [20, 16200, 3], [30, 360, 4], [30, 720, 22], [30, 1080, 2], [30, 1800, 2], [30, 2160, 2], [30, 3600, 3], [30, 5400, 1], [36, 9000, 4], [45, 7200, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '324000.bp', 'commutator_count': 1, 'commutator_label': '40500.j', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '5.1', '5.1', '5.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 42, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 90, 1, 1], [2, 125, 1, 1], [2, 135, 1, 1], [2, 450, 1, 1], [2, 675, 1, 1], [3, 4, 2, 1], [3, 6, 1, 1], [3, 12, 1, 1], [3, 1800, 1, 1], [4, 125, 2, 1], [4, 2250, 2, 1], [4, 3375, 2, 1], [4, 4050, 1, 1], [4, 4050, 2, 1], [4, 20250, 1, 1], [5, 12, 1, 1], [5, 16, 1, 1], [5, 24, 1, 2], [5, 48, 1, 1], [6, 90, 2, 1], [6, 180, 1, 1], [6, 180, 2, 1], [6, 270, 1, 1], [6, 450, 2, 1], [6, 500, 2, 1], [6, 750, 1, 1], [6, 900, 1, 1], [6, 900, 2, 1], [6, 1350, 1, 1], [6, 1500, 1, 1], [6, 9000, 1, 1], [9, 1800, 2, 1], [10, 360, 1, 2], [10, 720, 1, 2], [10, 1080, 1, 3], [10, 1800, 1, 1], [10, 2700, 1, 1], [12, 500, 4, 1], [12, 750, 2, 1], [12, 1500, 2, 1], [12, 2250, 4, 1], [12, 4500, 2, 1], [12, 4500, 4, 1], [12, 6750, 2, 1], [12, 9000, 2, 1], [15, 16, 2, 1], [15, 24, 1, 1], [15, 24, 2, 1], [15, 48, 1, 5], [15, 48, 2, 10], [15, 96, 1, 6], [15, 96, 2, 7], [15, 7200, 1, 1], [18, 9000, 2, 1], [20, 16200, 1, 1], [20, 16200, 2, 1], [30, 360, 2, 2], [30, 720, 1, 2], [30, 720, 2, 10], [30, 1080, 2, 1], [30, 1800, 2, 1], [30, 2160, 1, 2], [30, 3600, 1, 1], [30, 3600, 2, 1], [30, 5400, 1, 1], [36, 9000, 4, 1], [45, 7200, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 29016, 'exponent': 180, 'exponents_of_order': [5, 4, 3], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[16, 0, 4], [24, 0, 10], [24, 1, 2], [32, 0, 2], [48, -1, 1], [48, 0, 40], [48, 1, 9], [96, 0, 14], [96, 1, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '324000.bp', 'hash': 7964935506185039152, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 180, 'inner_gen_orders': [20, 36, 6, 30, 15, 15], 'inner_gens': [[1, 31138, 231576, 38376, 672, 237600], [276857, 2, 318000, 305544, 21600, 768], [115489, 102026, 24, 116592, 20160, 21600], [312025, 39194, 230520, 48, 20160, 302400], [2209, 303842, 2904, 2928, 1440, 21600], [108001, 22274, 24, 43248, 1440, 21600]], 'inner_hash': 7964935506185039152, 'inner_nilpotent': False, 'inner_order': 324000, 'inner_split': True, 'inner_tex': 'C_{15}^3.(C_4\\times S_4)', 'inner_used': [1, 2], 'irrC_degree': 16, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 4], [3, 8], [4, 16], [6, 16], [8, 8], [12, 12], [16, 6], [24, 21], [32, 3], [48, 52], [96, 20]], 'label': '324000.bp', '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': 'C15^3.(C4*S4)', 'ngens': 12, '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, 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': 123, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 174, 'number_divisions': 109, 'number_normal_subgroups': 19, 'number_subgroup_autclasses': 2508, 'number_subgroup_classes': 2508, 'number_subgroups': 1025152, 'old_label': None, 'order': 324000, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1475], [3, 1826], [4, 43900], [5, 124], [6, 18190], [9, 3600], [10, 9900], [12, 74000], [15, 10424], [18, 18000], [20, 48600], [30, 43560], [36, 36000], [45, 14400]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[115201, 108002, 216024, 115728, 15840, 237600]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [3, 4], [4, 1], [6, 6], [8, 4], [12, 12], [16, 6], [24, 12], [32, 4], [48, 18], [64, 1], [96, 26], [192, 7]], 'representations': {'PC': {'code': '829755918063173543615172156008532097129689704085891325294816884153235174239617495237113969569005796162028256761589635866145225410487383691921223936832456738998164272130221725853325485089090906326933790374184096418253396448539186402974574030095093175284742663042217252289374689689937500930934150222914132392347511', 'gens': [1, 2, 5, 6, 9, 11], 'pres': [12, 2, 2, 2, 3, 2, 2, 3, 5, 3, 5, 3, 5, 2898720, 747313, 61, 4025234, 98, 10259331, 696999, 13894564, 9540016, 3038068, 2039440, 270052, 2763077, 10999601, 4816397, 2518385, 349829, 209, 241926, 846738, 6350430, 121002, 4758, 330, 829447, 829459, 6220831, 155563, 4663, 72584, 1166420, 20768, 2041244, 90776, 45428, 428, 69129, 3888021, 25953, 1944045, 86457, 43269, 31363210, 50710, 332674, 17470, 831670, 526, 62231, 311075, 5231, 777671]}, 'Perm': {'d': 24, 'gens': [55281047937248389139296, 28263542648118695004529]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}^3.(C_4\\times S_4)', 'transitive_degree': 45, 'wreath_data': None, 'wreath_product': False}
