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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3194400.c', 'ambient_counter': 3, 'ambient_order': 3194400, 'ambient_tex': 'C_{11}^2.C_{264}:C_{10}^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 968, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3194400.c.165._.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '165.D', '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': 165, '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': '19360.h', 'subgroup_hash': None, 'subgroup_order': 19360, 'subgroup_tex': 'C_{11}^2:(C_{10}\\times \\SD_{16})', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '3194400.c', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 33, 'diagramx': None, 'generators': [41892009063798686, 9148625241916853, 26655873145114582, 43985120431679230, 34951316363147629, 12855103595531635, 28747515053893751, 41772741070013040], 'label': '3194400.c.165._.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '165.D', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '165._.D', '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': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [20, 20, 20, 20, 10, 10], 'aut_gens': [[1, 10, 40, 440], [7441, 6970, 160, 16280], [8821, 11010, 5360, 13760], [4001, 14430, 10720, 12760], [14721, 11030, 2080, 1320], [1461, 3990, 120, 18440], [7361, 430, 16080, 2200]], 'aut_group': None, 'aut_hash': 6924539337684527549, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 154880, 'aut_permdeg': 297, 'aut_perms': [7981763939924546360764279891347510331416028051802311028847405748176021680524974958531783888904297415942642717507862049004320161971518192380606189829014126901419378151500691435705692825142189827977482899335345661026196356140681289702115466714016403813301679339142257995200908295976626190142752212711359289214332096802111076306118650912566705768746356007094827711799656106570118824436596745765730865798697708593311306919335153594543640844757055614989677436085366858493607917271772680313331884311406446131646366380326636633464951693243285444197902735317485948319399453823001895992766097361809504528490888641636, 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10877110785860949840434608649598775219658896940717142729782485870223152081055582046264052872596708373605319430391674083255157081466170536402533285578400813783468898912906500336001761538492257072165398243953820599547690274178760186501098972478680199500558288145982845740397827958230377417585639101286949519432616444661757330972099231571603995282361575686710120728815039916250191718869867780606942950570727264143650911476726403562846934488338838533240953925814283572498044727322758105836665283390354057947984227052575969652866212153969377573059601298748094043040678047507414880593774431889870189322850646985821, 4528487603208450142208928240749216875254352526615846622728539469391732956610921856863191929995510893736018080708174787260357438820087951294837650884171020647201396201989689341020569605391713888502451083826846031749174321205036116711210119471668157155920776469795612701621045531899689667973711732493306703468866248897677646835477184907015452131406051423467689628612754050421159248079677351492143914191653418257635681378756101437770536229159843793562701282230478680712604135297644680047754965206528357568592921686771910084471337320841592081598968746811124875662137491860540518840629936683234362646415211890435], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 44, 2, 1], [2, 121, 2, 1], [4, 2, 1, 1], [4, 44, 2, 1], [4, 242, 1, 1], [5, 121, 1, 4], [8, 242, 4, 1], [10, 121, 1, 4], [10, 121, 2, 4], [10, 484, 2, 4], [11, 20, 1, 2], [11, 40, 1, 2], [20, 242, 1, 8], [20, 484, 2, 4], [22, 20, 1, 2], [22, 40, 1, 2], [22, 440, 2, 1], [40, 242, 4, 4], [44, 40, 1, 2], [44, 40, 2, 2], [44, 440, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_2^3.C_5.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': None, 'autcentquo_hash': 5713448921273139074, 'autcentquo_nilpotent': False, 'autcentquo_order': 19360, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{11}^2.C_{10}.C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 44, 2], [2, 121, 2], [4, 2, 1], [4, 44, 2], [4, 242, 1], [5, 121, 4], [8, 242, 4], [10, 121, 12], [10, 484, 8], [11, 20, 2], [11, 40, 2], [20, 242, 8], [20, 484, 8], [22, 20, 2], [22, 40, 2], [22, 440, 2], [40, 242, 16], [44, 40, 6], [44, 440, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '9680.ba', 'commutator_count': 1, 'commutator_label': '484.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '11.1', '11.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 8, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 44, 1, 2], [2, 121, 1, 2], [4, 2, 1, 1], [4, 44, 1, 2], [4, 242, 1, 1], [5, 121, 4, 1], [8, 242, 2, 2], [10, 121, 4, 3], [10, 484, 4, 2], [11, 20, 1, 2], [11, 40, 1, 2], [20, 242, 4, 2], [20, 484, 4, 2], [22, 20, 1, 2], [22, 40, 1, 2], [22, 440, 1, 2], [40, 242, 8, 2], [44, 40, 1, 2], [44, 40, 2, 2], [44, 440, 1, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 15249024, 'exponent': 440, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[40, -1, 1], [40, 0, 4], [40, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '9680.ba', 'hash': 6161013968996120931, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 220, 'inner_gen_orders': [10, 4, 11, 22], 'inner_gens': [[1, 15870, 14440, 15400], [6181, 10, 12360, 9520], [5401, 7050, 40, 440], [4401, 10730, 40, 440]], 'inner_hash': 7887305892697447099, 'inner_nilpotent': False, 'inner_order': 9680, 'inner_split': True, 'inner_tex': 'C_2\\times D_{11}^2:C_{10}', 'inner_used': [1, 2, 4], 'irrC_degree': 40, 'irrQ_degree': 40, 'irrQ_dim': 40, 'irrR_degree': 40, 'irrep_stats': [[1, 40], [2, 30], [20, 8], [40, 10]], 'label': '19360.h', 'linC_count': 160, 'linC_degree': 22, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 24, 'linQ_degree_count': 16, 'linQ_dim': 24, 'linQ_dim_count': 16, 'linR_count': 80, 'linR_degree': 24, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C11^2:(C10*SD16)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 54, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 88, 'number_divisions': 40, 'number_normal_subgroups': 47, 'number_subgroup_autclasses': 182, 'number_subgroup_classes': 260, 'number_subgroups': 13840, 'old_label': None, 'order': 19360, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 331], [4, 332], [5, 484], [8, 968], [10, 5324], [11, 120], [20, 5808], [22, 1000], [40, 3872], [44, 1120]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 4840, 0], 'outer_gens': [[4841, 4850, 40, 10120], [1, 9690, 40, 10120], [14521, 10, 40, 440], [12401, 16730, 400, 9240]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [6, 415, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 10], [8, 2], [16, 2], [20, 8], [40, 6], [80, 2]], 'representations': {'PC': {'code': '237709070594190553847084917911028329208630051796201051475099379336692318935694701973809500934294955234405539276375703009009', 'gens': [1, 3, 5, 6], 'pres': [8, 2, 5, 2, 2, 11, 2, 2, 11, 16, 380882, 106210, 66, 86403, 203851, 15515, 577604, 3212, 49460, 828, 739205, 390733, 45717, 22205, 141, 640646, 369614, 104182, 51774, 166, 225287, 225295, 114199, 56351]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [10205032106821235, 10522401710269773, 3352440040187918, 28359274195767324, 16265167320216339, 39688262258321567, 40451685466516614, 41772741070013040]}, 'Perm': {'d': 30, 'gens': [10725617432828987907080673449809, 19932021658053053191376966091196, 29085808057853731426811931276437, 10192793457047840180283803040000, 36423478910311224388218174412800, 47009471610196414840525654366080, 56159299088347860887786997253751, 5329]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^2:(C_{10}\\times \\SD_{16})', 'transitive_degree': 88, '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': '200.52', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[19358111333213666, 2933956861135506, 19063078487671420, 27716778550151667, 17298483428108842, 5912944201328162, 10522401710269773, 12531822321003912, 33418192856010432, 20283505689400384, 4764541194236758], [7298497102823528, 15022613608546832, 7242339796576814, 36242457719323738, 4829038492381878, 17388429983692749, 5527207937934645, 20886370535006520, 25063644642007824, 15470168097752271, 22831675368159975], [11475431715444564, 9463804944590684, 35153917281539828, 16231497971563615, 29007247159556129, 3241877346734292, 13454907968984355, 37595466963011736, 8354548214002608, 27424426214498386, 8829161111884237], [33949356841112762, 1600747522704742, 14829307644139014, 37594418035369906, 17504246175570882, 30596473704876860, 17673550981269707, 20886370535006520, 25063644642007824, 4678100187979989, 23856575518392505], [35921811154852548, 40175704730766724, 28625040208723970, 44579785009069833, 18154597893076596, 17828180696307581, 15024737606805037, 16709096428005216, 29240918749009128, 2751127771311349, 44098189458608202], [22977100221757519, 25591127724366041, 23919007109583875, 16749137043952216, 4240384910491043, 23006341296640297, 17555292983921161, 12531822321003912, 33418192856010432, 31926465865539104, 23625412662210993], [41866220022414768, 29540793775862030, 20829116784550176, 39982666294645125, 42508625739814373, 44072372197060766, 11167754359050934, 20886370535006520, 25063644642007824, 3631573257885254, 22830656638291335], [45834906437098689, 29644003779418250, 9388547586614710, 9332044949058664, 26535722892229333, 1917056429144326, 6566261401987170, 37595466963011736, 8354548214002608, 7547274637166749, 45717050852203000], [7681465529686289, 9191408465957081, 41219239915019471, 9731583677608210, 15005466321478431, 6443688593188130, 17113476395752375, 16709096428005216, 29240918749009128, 20337437013021575, 19358818787108757]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 255552000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 330.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 132, 1, 1], [2, 1331, 2, 1], [2, 1452, 1, 1], [3, 242, 1, 1], [4, 22, 1, 1], [4, 132, 1, 1], [4, 242, 1, 1], [4, 1452, 1, 1], [5, 1, 4, 1], [5, 1331, 5, 4], [6, 242, 1, 1], [6, 2662, 2, 1], [8, 242, 2, 1], [8, 2662, 2, 1], [10, 1, 4, 1], [10, 132, 4, 1], [10, 1331, 5, 4], [10, 1331, 8, 1], [10, 1331, 10, 4], [10, 1452, 4, 1], [10, 15972, 5, 8], [11, 10, 1, 1], [11, 60, 1, 2], [11, 120, 5, 2], [12, 242, 1, 2], [12, 2662, 2, 1], [15, 242, 4, 1], [15, 2662, 5, 4], [20, 22, 4, 1], [20, 132, 4, 1], [20, 242, 4, 1], [20, 1452, 4, 1], [20, 2662, 5, 8], [20, 15972, 5, 8], [22, 10, 1, 1], [22, 60, 1, 2], [22, 120, 5, 2], [22, 1320, 1, 2], [22, 1320, 10, 1], [22, 14520, 1, 1], [24, 242, 2, 2], [24, 2662, 2, 2], [30, 242, 4, 1], [30, 2662, 5, 4], [30, 2662, 8, 1], [30, 2662, 10, 4], [33, 2420, 1, 1], [40, 242, 8, 1], [40, 2662, 8, 1], [40, 2662, 10, 8], [44, 1320, 1, 4], [44, 1320, 10, 1], [44, 2420, 1, 1], [44, 14520, 1, 1], [55, 10, 4, 1], [55, 60, 4, 2], [55, 120, 20, 2], [60, 242, 4, 2], [60, 2662, 5, 8], [60, 2662, 8, 1], [60, 2662, 10, 4], [66, 2420, 1, 1], [88, 2420, 2, 1], [110, 10, 4, 1], [110, 60, 4, 2], [110, 120, 20, 2], [110, 1320, 4, 2], [110, 1320, 40, 1], [110, 14520, 4, 1], [120, 242, 8, 2], [120, 2662, 8, 2], [120, 2662, 10, 16], [132, 2420, 1, 2], [165, 2420, 4, 1], [220, 1320, 4, 4], [220, 1320, 40, 1], [220, 2420, 4, 1], [220, 14520, 4, 1], [264, 2420, 2, 2], [330, 2420, 4, 1], [440, 2420, 8, 1], [660, 2420, 4, 2], [1320, 2420, 8, 2]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 132, 1], [2, 1331, 2], [2, 1452, 1], [3, 242, 1], [4, 22, 1], [4, 132, 1], [4, 242, 1], [4, 1452, 1], [5, 1, 4], [5, 1331, 20], [6, 242, 1], [6, 2662, 2], [8, 242, 2], [8, 2662, 2], [10, 1, 4], [10, 132, 4], [10, 1331, 68], [10, 1452, 4], [10, 15972, 40], [11, 10, 1], [11, 60, 2], [11, 120, 10], [12, 242, 2], [12, 2662, 2], [15, 242, 4], [15, 2662, 20], [20, 22, 4], [20, 132, 4], [20, 242, 4], [20, 1452, 4], [20, 2662, 40], [20, 15972, 40], [22, 10, 1], [22, 60, 2], [22, 120, 10], [22, 1320, 12], [22, 14520, 1], [24, 242, 4], [24, 2662, 4], [30, 242, 4], [30, 2662, 68], [33, 2420, 1], [40, 242, 8], [40, 2662, 88], [44, 1320, 14], [44, 2420, 1], [44, 14520, 1], [55, 10, 4], [55, 60, 8], [55, 120, 40], [60, 242, 8], [60, 2662, 88], [66, 2420, 1], [88, 2420, 2], [110, 10, 4], [110, 60, 8], [110, 120, 40], [110, 1320, 48], [110, 14520, 4], [120, 242, 16], [120, 2662, 176], [132, 2420, 2], [165, 2420, 4], [220, 1320, 56], [220, 2420, 4], [220, 14520, 4], [264, 2420, 4], [330, 2420, 4], [440, 2420, 8], [660, 2420, 8], [1320, 2420, 16]], 'center_label': '10.2', 'center_order': 10, 'central_product': None, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '15972.a', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1', '5.1', '11.1', '11.1', '11.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 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[17154781781066514, 12609920733236825, 20123654429140706, 37280277267900302, 27238780040815509, 5912944201328162, 13140307079051117, 12531822321003912, 33418192856010432, 34167653853121506, 14708290010338879], [25921905219956196, 17370708274012920, 42891146272563895, 6884513752281148, 45451992243043449, 43745275600511749, 10522401710269773, 12531822321003912, 33418192856010432, 26375648796824317, 26126965308031858], [19358111333213666, 2933956861135506, 19063078487671420, 27716778550151667, 17298483428108842, 5912944201328162, 10522401710269773, 12531822321003912, 33418192856010432, 20283505689400384, 4764541194236758], [19358111333213666, 2933956861135506, 19063078487671420, 27716778550151667, 17298483428108842, 5912944201328162, 10522401710269773, 12531822321003912, 33418192856010432, 20283505689400384, 4764541194236758], [15681347858950854, 24373688374438059, 1531656888644363, 10833840349768696, 8269385602214435, 6445834230877611, 37678271249731280, 12531822321003912, 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1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 3, 3, 0, 0, 1, 0, 1, 0, 1, 0, 3, 1, 0, 0, 6, 1, 3, 0, 0, 0, 3, 0, 0, 0, 18, 3, 3, 0, 0, 6, 1, 0, 0, 18, 1, 7, 1, 0, 18, 0, 0, 18, 0, 7, 3, 0, 18, 0, 1, 6, 1, 3, 0, 42, 3, 0, 3, 0, 42, 3, 1, 6, 7, 0, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 182, 'number_characteristic_subgroups': 119, 'number_conjugacy_classes': 1075, 'number_divisions': 250, 'number_normal_subgroups': 296, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 3194400, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 4247], [3, 242], [4, 1848], [5, 26624], [6, 5566], [8, 5808], [10, 735728], [11, 1330], [12, 5808], [15, 54208], [20, 752752], [22, 31690], [24, 11616], [30, 181984], [33, 2420], [40, 236192], [44, 35420], [55, 5320], [60, 236192], [66, 2420], [88, 4840], [110, 126760], [120, 472384], [132, 4840], [165, 9680], [220, 141680], [264, 9680], [330, 9680], [440, 19360], [660, 19360], [1320, 38720]], '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': '800.1204', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 800, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^2\\times C_{10}\\times F_5', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 90, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 6], [4, 52], [8, 38], [10, 4], [16, 24], [20, 3], [32, 12], [40, 6], [60, 8], [80, 4], [120, 32], [160, 2], [240, 13], [320, 1], [480, 32], [960, 5]], 'representations': {'PC': {'code': '2206227305133312568467607314889576942358831025160443074161667860466059441841037048772186097612301484198717730030259841292908460865923996358829961579224243091230946358621549863976576395377680107607027233037512718939205594994352300302724324924542583828775463914875146680067050135615690627421841099530377023703954046903030001999', 'gens': [1, 3, 5, 10, 11], 'pres': [11, -2, -5, -2, -5, -2, -2, -2, -3, -11, -11, 11, 22, 100188332, 40075378, 90, 62727283, 11035654, 51617504, 76694765, 15357676, 8646312, 158, 62898005, 94333816, 19260147, 2978618, 192, 175221206, 117455817, 17700788, 4612339, 226, 149600007, 57059218, 17459229, 14027240, 348, 475208, 475219, 118830, 35681, 5808009, 5808020, 1452031, 435642, 2642693, 1161664, 573615, 188846, 70276810, 70276821, 23958032, 5270803, 766710, 1741013, 782704, 91926]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [19358111333213666, 2933956861135506, 19063078487671420, 27716778550151667, 17298483428108842, 5912944201328162, 10522401710269773, 12531822321003912, 33418192856010432, 20283505689400384, 4764541194236758]}, 'Perm': {'d': 90, 'gens': [51, 17821258118396300243065891293117420311181090301799074835719993293737366440271760272597123621852772913719646450660779772805734193442816042, 486985731, 34527588153327830815457961199281997711826028795510822135016526822850410192575964972130925354493652989289143480586240805515370792304640089, 51222989746554863262554338507137368763009822216907376833727937347559888319598537324267774070498172287443598998141427771432141057574656089, 67918336419508559090826306487758538236521182901817495698506671709296735827627642045541975795805412171357592097467082508183970293353329891, 83129949827410727328708113667057519039846285436788629429746647165920311957610500839458326463629520678761244791638638420735242818031177731, 101101128366636876773600716025758444486983593664449582387342939320345927338694726807078150334989958228230359766126264249727726230113706080, 2255374688155429547714323035509441608185563619670155878051913467770964900789767813010621039964333537837866670407946389995839429532723316, 118003258654059241498325828926203283571642447352975279475959430137385007546570551015221377762854477597613447778972630726626326941510723120, 83319865743259231995609327110342354274334081688393545218647958832870809268554383141480209780594331174393527592479204174044930169609801796]}}, 'schur_multiplier': [2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10, 10], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 605, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^2.C_{264}:C_{10}^2', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
