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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '158400.f', 'ambient_counter': 6, 'ambient_order': 158400, 'ambient_tex': 'C_{15}:Q_8\\times \\SL(2,11)', 'central': False, 'central_factor': False, 'centralizer_order': 220, 'characteristic': False, 'core_order': 20, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '158400.f.360.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.g1.a1', 'outer_equivalence': False, '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': 360, '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': '440.41', 'subgroup_hash': 41, 'subgroup_order': 440, 'subgroup_tex': 'Q_8\\times C_{55}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '158400.f', 'aut_centralizer_order': None, 'aut_label': '360.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '120.h1.a1', '180.a1.a1'], 'contains': ['720.d1.a1', '720.g1.a1', '720.g1.d1', '1800.c1.a1', '3960.p1.a1'], 'core': '7920.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39359773684668951, 19990544660987432, 2662909317218269, 10200559518208358, 37595466963011736], 'label': '158400.f.360.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '360.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.5'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '220.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [2, 4, 6, 2, 10], 'aut_gens': [[1, 2], [331, 222], [1, 354], [111, 153], [221, 222], [221, 162]], 'aut_group': '960.11068', 'aut_hash': 11068, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 960, 'aut_permdeg': 20, 'aut_perms': [1223231389784898480, 224, 1608107133907302054, 979941188764339200, 1042632754351222464], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 2, 3, 1], [5, 1, 4, 1], [10, 1, 4, 1], [11, 1, 10, 1], [20, 2, 12, 1], [22, 1, 10, 1], [44, 2, 30, 1], [55, 1, 40, 1], [110, 1, 40, 1], [220, 2, 120, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_{20}\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '160.228', 'autcent_hash': 228, 'autcent_nilpotent': True, 'autcent_order': 160, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_{20}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [4, 2, 3], [5, 1, 4], [10, 1, 4], [11, 1, 10], [20, 2, 12], [22, 1, 10], [44, 2, 30], [55, 1, 40], [110, 1, 40], [220, 2, 120]], 'center_label': '110.6', 'center_order': 110, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 41, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['5.1', 1], ['8.4', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 2, 1, 3], [5, 1, 4, 1], [10, 1, 4, 1], [11, 1, 10, 1], [20, 2, 4, 3], [22, 1, 10, 1], [44, 2, 10, 3], [55, 1, 40, 1], [110, 1, 40, 1], [220, 2, 40, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 72, 'exponent': 220, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[2, 0, 40]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '220.15', 'hash': 41, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2], 'inner_gens': [[1, 222], [221, 2]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 4, 'irrep_stats': [[1, 220], [2, 55]], 'label': '440.41', 'linC_count': 40, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 16, 'linQ_dim': 18, 'linQ_dim_count': 20, 'linR_count': 20, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'Q8*C55', 'ngens': 5, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 12, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 275, 'number_divisions': 20, 'number_normal_subgroups': 24, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 24, 'number_subgroups': 24, 'old_label': None, 'order': 440, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1], [4, 6], [5, 4], [10, 4], [11, 10], [20, 24], [22, 10], [44, 60], [55, 40], [110, 40], [220, 240]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 60, 'outer_gen_orders': [2, 2, 60], 'outer_gen_pows': [2, 0, 0], 'outer_gens': [[111, 2], [1, 42], [110, 75]], 'outer_group': '240.166', 'outer_hash': 166, 'outer_nilpotent': False, 'outer_order': 240, 'outer_permdeg': 14, 'outer_perms': [41046, 1, 13491969888], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6\\times C_{20}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 4], [8, 1], [10, 4], [20, 1], [40, 4], [80, 1]], 'representations': {'PC': {'code': 5035665093233871900039, 'gens': [1, 2], 'pres': [5, -2, -2, -2, -5, -11, 1100, 2221, 26, 42, 118]}, 'GLFp': {'d': 2, 'p': 331, 'gens': [9970944426, 36042590]}, 'Perm': {'d': 24, 'gens': [134021272924426567680000, 79804308122845802496000, 5230697472000, 36288000, 25903229681844523008000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 110], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'Q_8\\times C_{55}', 'transitive_degree': 440, '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': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [6, 20, 2, 4, 22, 12, 2], 'aut_gens': [[12531822321003912, 39359773684668951, 3330682782004535, 40324864276851944, 2079301094761262, 23289108651701890, 33418192856010432, 4120849228522789], [16709096428005216, 29976083422325622, 12120991314924448, 15089486603864456, 18751680690294991, 43048582318392398, 29240918749009128, 39465877030034882], [37595466963011736, 44666890714873202, 30859746305878974, 5284231846884112, 32480098460539581, 3753759348360852, 8354548214002608, 33938459828505165], [12531822321003912, 44666890714873202, 42376596697618876, 40324864276851944, 32367211677396136, 5282024756154213, 33418192856010432, 43129344135813229], [20886370535006520, 17023026959354956, 2912227572816974, 24891602932467958, 9632961313223658, 41275769067289568, 25063644642007824, 20639377355521144], [16709096428005216, 44666890714873202, 38423711320646036, 15089486603864456, 32271635345625870, 44248745097308543, 29240918749009128, 14454159267929393], [12531822321003912, 4412001206744059, 11857246767962687, 40324864276851944, 13447777875433732, 40721177611352055, 33418192856010432, 7500410218097488], [16709096428005216, 14231371820839879, 38423711320646036, 15089486603864456, 42150068459724526, 29908094543097532, 29240918749009128, 12965603497754810]], 'aut_group': None, 'aut_hash': 4754614136108486635, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1013760, 'aut_permdeg': 138, 'aut_perms': [504229921052071203477072004671254384185327408447650257757931344002848263172154682820050463233525636199613450319841726266944151151444782153007218609079483960751282949733700556810241733393492491926550352121075020592472428937066961720510654, 34357270877881322290270787404152594538550914462941137543442861782129861091411340200136181662804160099372623260826004648461108659967017400548004057770535507902801649341631680830484224186555761180623554468864145979263692911735438530763969, 432818960635306031660961118769967989106339039040359650803772009619568033382664265465010809971881538166039118247199262933299621045584437282241344248437921092590178788634996255427579532525129089116549046563614313444032913411928024754240639, 518115781372509404141367942680981044089292267894573590316782653788961910480847910952719920127119661403404304384175383707796078803919171702102739303403490417894910592643858639876988902463142167278457440269475526823862848041812222697296711, 460342273668657614427660458527338549104752166255402313666934514851105074891797586814419285360201805697545558057528886812427582802011126927693793867236689211110251353856677774107598745936226372948427907811306743636265740919758107636924643, 10097739208005658603262020878437300865428173635283369023946826462631544689605429911973250276992190620562249027453179465295108594086294496122393389148631431117422959960465072653857598781375881509193811055237469066399206104139701207989965, 163094122205025429067438216597390756919146365735687847637227152025830945270183010993470278992133454459174698852131323716403208059228699351563668963085911402282650071256370469572003255161903481845595836898622214845631892935352856649949346], 'aut_phi_ratio': 26.4, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [3, 110, 1, 1], [3, 220, 1, 1], [4, 2, 2, 1], [4, 6, 4, 1], [4, 110, 1, 2], [4, 220, 1, 1], [4, 660, 2, 1], [5, 1, 4, 1], [5, 132, 1, 2], [5, 132, 4, 2], [6, 2, 1, 3], [6, 110, 1, 3], [6, 220, 1, 3], [10, 1, 4, 3], [10, 132, 1, 6], [10, 132, 4, 6], [11, 60, 2, 1], [12, 2, 4, 1], [12, 110, 1, 4], [12, 220, 1, 6], [12, 220, 2, 3], [12, 220, 4, 2], [12, 660, 4, 2], [15, 2, 4, 1], [15, 110, 4, 1], [15, 220, 4, 1], [15, 264, 1, 2], [15, 264, 4, 2], [20, 2, 8, 1], [20, 6, 16, 1], [20, 110, 4, 2], [20, 220, 4, 1], [20, 264, 2, 2], [20, 264, 8, 2], [20, 660, 8, 1], [20, 792, 4, 2], [20, 792, 16, 2], [22, 60, 2, 3], [30, 2, 4, 3], [30, 110, 4, 3], [30, 220, 4, 3], [30, 264, 1, 6], [30, 264, 4, 6], [33, 120, 2, 1], [44, 120, 4, 1], [44, 360, 8, 1], [55, 60, 8, 1], [60, 2, 16, 1], [60, 110, 4, 4], [60, 220, 4, 6], [60, 220, 8, 3], [60, 220, 16, 2], [60, 264, 4, 2], [60, 264, 16, 2], [60, 660, 16, 2], [66, 120, 2, 3], [110, 60, 8, 3], [132, 120, 8, 1], [165, 120, 8, 1], [220, 120, 16, 1], [220, 360, 32, 1], [330, 120, 8, 3], [660, 120, 32, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_2^5\\times S_3).C_2^2.\\PSL(2,11).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.260', 'autcent_hash': 260, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 660, 'autcentquo_group': None, 'autcentquo_hash': 2842205202387851101, 'autcentquo_nilpotent': False, 'autcentquo_order': 15840, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times \\PSL(2,11).C_2\\times S_3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [3, 110, 1], [3, 220, 1], [4, 2, 2], [4, 6, 4], [4, 110, 2], [4, 220, 1], [4, 660, 2], [5, 1, 4], [5, 132, 10], [6, 2, 3], [6, 110, 3], [6, 220, 3], [10, 1, 12], [10, 132, 30], [11, 60, 2], [12, 2, 4], [12, 110, 4], [12, 220, 20], [12, 660, 8], [15, 2, 4], [15, 110, 4], [15, 220, 4], [15, 264, 10], [20, 2, 8], [20, 6, 16], [20, 110, 8], [20, 220, 4], [20, 264, 20], [20, 660, 8], [20, 792, 40], [22, 60, 6], [30, 2, 12], [30, 110, 12], [30, 220, 12], [30, 264, 30], [33, 120, 2], [44, 120, 4], [44, 360, 8], [55, 60, 8], [60, 2, 16], [60, 110, 16], [60, 220, 80], [60, 264, 40], [60, 660, 32], [66, 120, 6], [110, 60, 24], [132, 120, 8], [165, 120, 8], [220, 120, 16], [220, 360, 32], [330, 120, 24], [660, 120, 32]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '7920.n', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1', '660.13'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['1320.13', 1], ['24.4', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [3, 110, 1, 1], [3, 220, 1, 1], [4, 2, 1, 2], [4, 6, 1, 4], [4, 110, 1, 2], [4, 220, 1, 1], [4, 660, 1, 2], [5, 1, 4, 1], [5, 132, 2, 1], [5, 132, 4, 2], [6, 2, 1, 3], [6, 110, 1, 3], [6, 220, 1, 3], [10, 1, 4, 3], [10, 132, 2, 3], [10, 132, 4, 6], [11, 60, 2, 1], [12, 2, 2, 2], [12, 110, 2, 2], [12, 220, 1, 4], [12, 220, 2, 8], [12, 660, 1, 4], [12, 660, 2, 2], [15, 2, 4, 1], [15, 110, 4, 1], [15, 220, 4, 1], [15, 264, 2, 1], [15, 264, 4, 2], [20, 2, 4, 2], [20, 6, 4, 4], [20, 110, 4, 2], [20, 220, 4, 1], [20, 264, 2, 2], [20, 264, 4, 4], [20, 660, 4, 2], [20, 792, 2, 4], [20, 792, 4, 8], [22, 60, 2, 3], [30, 2, 4, 3], [30, 110, 4, 3], [30, 220, 4, 3], [30, 264, 2, 3], [30, 264, 4, 6], [33, 120, 2, 1], [44, 120, 2, 2], [44, 360, 2, 4], [55, 60, 8, 1], [60, 2, 8, 2], [60, 110, 8, 2], [60, 220, 4, 4], [60, 220, 8, 8], [60, 264, 4, 2], [60, 264, 8, 4], [60, 660, 4, 4], [60, 660, 8, 2], [66, 120, 2, 3], [110, 60, 8, 3], [132, 120, 4, 2], [165, 120, 8, 1], [220, 120, 8, 2], [220, 360, 8, 4], [330, 120, 8, 3], [660, 120, 16, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': None, 'exponent': 660, 'exponents_of_order': [6, 2, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': None, 'hash': 394379631837703570, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [1, 2, 6, 1, 5, 11, 1, 30], 'inner_gens': [[12531822321003912, 39359773684668951, 3330682782004535, 40324864276851944, 2079301094761262, 23289108651701890, 33418192856010432, 4120849228522789], [12531822321003912, 39359773684668951, 8168105937951608, 40324864276851944, 2079301094761262, 23289108651701890, 33418192856010432, 14452968361164730], [12531822321003912, 25059493691864754, 3330682782004535, 40324864276851944, 2079301094761262, 23289108651701890, 33418192856010432, 4120849228522789], [12531822321003912, 39359773684668951, 3330682782004535, 40324864276851944, 2079301094761262, 23289108651701890, 33418192856010432, 4120849228522789], [12531822321003912, 39359773684668951, 3330682782004535, 40324864276851944, 2079301094761262, 45051895940288427, 33418192856010432, 21956537702400630], [12531822321003912, 39359773684668951, 3330682782004535, 40324864276851944, 21438216643057680, 23289108651701890, 33418192856010432, 33209641511609791], [12531822321003912, 39359773684668951, 3330682782004535, 40324864276851944, 2079301094761262, 23289108651701890, 33418192856010432, 4120849228522789], [12531822321003912, 29976083422325622, 3330682782004535, 40324864276851944, 26016094509911641, 7342902615746842, 33418192856010432, 4120849228522789]], 'inner_hash': 3267698946426799616, 'inner_nilpotent': False, 'inner_order': 7920, 'inner_split': True, 'inner_tex': 'D_6.\\PSL(2,11)', 'inner_used': [2, 3, 5, 6], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 20], [2, 25], [5, 40], [6, 40], [10, 150], [11, 20], [12, 130], [20, 125], [22, 25], [24, 100]], 'label': '158400.f', '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': False, 'name': 'C15:Q8*SL(2,11)', '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, 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': 146, 'number_characteristic_subgroups': 40, 'number_conjugacy_classes': 675, 'number_divisions': 178, 'number_normal_subgroups': 72, 'number_subgroup_autclasses': 686, 'number_subgroup_classes': 1322, 'number_subgroups': 142492, 'old_label': None, 'order': 158400, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 3], [3, 332], [4, 1788], [5, 1324], [6, 996], [10, 3972], [11, 120], [12, 10128], [15, 3968], [20, 44112], [22, 360], [30, 11904], [33, 240], [44, 3360], [55, 480], [60, 51072], [66, 720], [110, 1440], [132, 960], [165, 960], [220, 13440], [330, 2880], [660, 3840]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4, 4], 'outer_gen_pows': [28458108757175193, 36220134612277089, 4177274107001304, 4177274107001304, 4177274107001304], 'outer_gens': [[16709096428005216, 11184928950901544, 2490893330742793, 15089486603864456, 12683150958880424, 24891169048037913, 29240918749009128, 11447908215492069], [16709096428005216, 7559090311288696, 2490893330742793, 15089486603864456, 12683150958880424, 24891169048037913, 29240918749009128, 11447908215492069], [16709096428005216, 11184928950901544, 25379762166371287, 15089486603864456, 3756207253727932, 15735264721909146, 29240918749009128, 38265990400617377], [37595466963011736, 39359773684668951, 4173351053404537, 5284231846884112, 1275084226059392, 19702061710776513, 8354548214002608, 4120849228522789], [12531822321003912, 7559090311288696, 1264290204351349, 40324864276851944, 2079301094761262, 23289108651701890, 33418192856010432, 470985329295323]], 'outer_group': '128.2154', 'outer_hash': 2154, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [11520, 87102736, 87096360, 119761920, 87107902], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4^2:C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 40, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 5], [8, 3], [10, 16], [11, 4], [12, 4], [16, 1], [20, 16], [22, 3], [24, 11], [40, 25], [44, 5], [48, 27], [80, 16], [88, 3], [96, 17], [160, 9], [176, 1], [192, 5]], 'representations': {'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 39359773684668951, 3330682782004535, 40324864276851944, 2079301094761262, 23289108651701890, 33418192856010432, 4120849228522789]}, 'Perm': {'d': 40, 'gens': [46, 1321086775743, 20440320319946374752605358938090917089062823120, 20440320319946374752605358938090915525115703726, 4297243472717, 42971266488743192171990332899688270899002196960, 63825147790970144394303423538512998457351991726, 84829082297194382151779799348753574365146935743]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}:Q_8\\times \\SL(2,11)', 'transitive_degree': 2880, 'wreath_data': None, 'wreath_product': False}
