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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12706092.s', 'ambient_counter': 19, 'ambient_order': 12706092, 'ambient_tex': 'C_7^6.C_3^2.D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 343, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12706092.s.37044._.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '37044.B', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '37044.y', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 37044, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_7^3:C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '343.5', 'subgroup_hash': None, 'subgroup_order': 343, 'subgroup_tex': 'C_7^3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '12706092.s', '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': 1, 'diagramx': None, 'generators': [11928924, 7038360, 1561140], 'label': '12706092.s.37044._.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '37044.B', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '37044._.B', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '343.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 19152, 'aut_gen_orders': [6, 48], 'aut_gens': [[1, 7, 49], [5, 13, 51], [307, 206, 3]], 'aut_group': '33784128.a', 'aut_hash': 2114063431006713936, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 33784128, 'aut_permdeg': 342, 'aut_perms': [12191216650448738501877432755228267970228496595214947454759085749974580569992329180601952253898380950542411220235770191404048981081314805831151803605019370777844409394486640119511499038326774515146125555587034080239175693097548096319520141214936856306595945501792541385889103186406280144166665509016440452364250949294758937173770554254436333511402491326061481526702698397597573161282826059617442758102788014372489751372529750436544036995125361211777827292379504899533967209080345371828098648679229593625335852535218359400106160814580036793765150269554849972637101348829311824498437276462518280783227092903867990909551342834551681638107532662778797277323071233853326849435302690121074779324309666231317660925018778101240, 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2114063431006713936, 'autcent_nilpotent': False, 'autcent_order': 33784128, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(3,7)', '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], [7, 1, 342]], 'center_label': '343.5', 'center_order': 343, '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': ['7.1', '7.1', '7.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['7.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [7, 1, 6, 57]], 'element_repr_type': 'PC', 'elementary': 7, 'eulerian_function': 1, 'exponent': 7, 'exponents_of_order': [3], 'factors_of_aut_order': [2, 3, 7, 19], 'factors_of_order': [7], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '343.5', 'hash': 5, 'hyperelementary': 7, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 7, 49], [1, 7, 49], [1, 7, 49]], '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, 343]], 'label': '343.5', 'linC_count': 5630688, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 26068, 'linQ_dim': 18, 'linQ_dim_count': 26068, 'linR_count': 703836, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C7^3', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 343, 'number_divisions': 58, 'number_normal_subgroups': 116, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 116, 'number_subgroups': 116, 'old_label': None, 'order': 343, 'order_factorization_type': 3, 'order_stats': [[1, 1], [7, 342]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 19152, 'outer_gen_orders': [6, 48], 'outer_gen_pows': [0, 0], 'outer_gens': [[5, 13, 51], [307, 206, 3]], 'outer_group': '33784128.a', 'outer_hash': 2114063431006713936, 'outer_nilpotent': False, 'outer_order': 33784128, 'outer_permdeg': 342, 'outer_perms': [12191216650448738501877432755228267970228496595214947454759085749974580569992329180601952253898380950542411220235770191404048981081314805831151803605019370777844409394486640119511499038326774515146125555587034080239175693097548096319520141214936856306595945501792541385889103186406280144166665509016440452364250949294758937173770554254436333511402491326061481526702698397597573161282826059617442758102788014372489751372529750436544036995125361211777827292379504899533967209080345371828098648679229593625335852535218359400106160814580036793765150269554849972637101348829311824498437276462518280783227092903867990909551342834551681638107532662778797277323071233853326849435302690121074779324309666231317660925018778101240, 25546439107436771115143287883693399476275785322768611942682659863464992073672883050295892208340393709114795164101921278548648235159975895198584167945840843195067983475495436352420919353358822066506985275629641595462504237373662402573171299342824120060723649853554676889537588137285206673242673778487328919286981059128674141820492145623020057259026360218586550598923149634960008604966945304363141472977814242578400836018684844965043269771439773686310052072582485939990581294488571913716856502208840049981911249547628211278106182852062955849175026550220194783100554280251939852188277229984632859725887106516812446482520452427234113112319295094561670906674900725914200378977568006661091892917513361130930240097034304041363], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\GL(3,7)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 21, 'pgroup': 7, 'primary_abelian_invariants': [7, 7, 7], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [6, 57]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3], 'pres': [3, -7, 7, 7]}, 'GLFq': {'d': 2, 'q': 343, 'gens': [12129966271, 7730888522, 7679405938]}, 'GLZq': {'d': 2, 'q': 49, 'gens': [1010178, 117993, 2657222]}, 'Perm': {'d': 21, 'gens': [14597412049059840000, 37362124800, 4320]}}, 'schur_multiplier': [7, 7, 7], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [7, 7, 7], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_7^3', 'transitive_degree': 343, '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': '4.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 6, 'aut_exponent': 252, 'aut_gen_orders': [42, 84, 6], 'aut_gens': [[1, 2, 12, 36, 756, 5292, 37044, 259308, 1815156], [10316061, 428770, 2272224, 8419568, 5525064, 5221692, 2457864, 539784, 6557004], [8547121, 11487582, 100236, 11403640, 6368436, 3489372, 6405696, 11477268, 6404940], [11458269, 6471586, 12598104, 4639428, 3134376, 10373832, 4279716, 5480244, 10397268]], 'aut_group': None, 'aut_hash': 3499738716716678470, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 914838624, 'aut_permdeg': 784, 'aut_perms': 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'aut_phi_ratio': 252.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 343, 1, 1], [2, 441, 1, 1], [2, 3087, 1, 1], [3, 14406, 4, 1], [3, 117649, 1, 2], [6, 100842, 4, 1], [6, 117649, 1, 2], [6, 1058841, 1, 4], [7, 9, 8, 1], [7, 18, 4, 1], [7, 18, 24, 1], [7, 27, 8, 1], [7, 54, 1, 2], [7, 54, 4, 1], [7, 54, 24, 5], [7, 54, 72, 4], [7, 108, 3, 1], [7, 108, 8, 1], [7, 108, 12, 2], [7, 108, 24, 8], [7, 108, 72, 9], [14, 1323, 8, 2], [14, 2646, 4, 2], [14, 2646, 24, 4], [14, 2646, 72, 4], [14, 3087, 8, 1], [14, 9261, 8, 3], [14, 18522, 1, 2], [14, 18522, 24, 2], [21, 43218, 8, 1], [21, 86436, 4, 1], [21, 86436, 24, 1], [42, 302526, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_7^6.\\He_3.Q_8.C_6^2', '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': 252, 'autcentquo_group': None, 'autcentquo_hash': 3499738716716678470, 'autcentquo_nilpotent': False, 'autcentquo_order': 914838624, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_7^6.\\He_3.Q_8.C_6^2', 'cc_stats': [[1, 1, 1], [2, 343, 1], [2, 441, 1], [2, 3087, 1], [3, 14406, 4], [3, 117649, 2], [6, 100842, 4], [6, 117649, 2], [6, 1058841, 4], [7, 9, 8], [7, 18, 28], [7, 27, 8], [7, 54, 414], [7, 108, 875], [14, 1323, 16], [14, 2646, 392], [14, 3087, 8], [14, 9261, 24], [14, 18522, 50], [21, 43218, 8], [21, 86436, 28], [42, 302526, 8]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '12706092.s', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '7.1', '7.1', '7.1', '7.1', '7.1', '7.1'], 'composition_length': 11, 'conjugacy_classes_known': False, 'counter': 19, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 343, 1, 1], [2, 441, 1, 1], [2, 3087, 1, 1], [3, 14406, 1, 4], [3, 117649, 2, 1], [6, 100842, 1, 4], [6, 117649, 2, 1], [6, 1058841, 2, 2], [7, 9, 2, 4], [7, 18, 1, 4], [7, 18, 2, 12], [7, 27, 2, 4], [7, 54, 1, 6], [7, 54, 2, 204], [7, 108, 1, 27], [7, 108, 2, 424], [14, 1323, 2, 8], [14, 2646, 1, 8], [14, 2646, 2, 192], [14, 3087, 2, 4], [14, 9261, 2, 12], [14, 18522, 1, 2], [14, 18522, 2, 24], [21, 43218, 2, 4], [21, 86436, 1, 4], [21, 86436, 2, 12], [42, 302526, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 42, 'exponents_of_order': [6, 3, 2], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[18, 0, 48], [36, 0, 24], [54, 0, 816], [108, 0, 848], [108, 1, 27]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '12706092.s', 'hash': 3413613090818454634, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [6, 42, 3, 21, 7, 7, 7, 7, 7], 'inner_gens': [[1, 505126, 9238224, 8418252, 12126672, 95364, 540, 7814124, 12501324], [3518537, 2, 9364152, 1493592, 10512720, 3147012, 9970884, 10496088, 8055612], [3770281, 5200202, 12, 5598756, 1512, 10584, 74088, 518616, 3630312], [110473, 8318390, 7372740, 36, 4416552, 7017948, 74088, 10156860, 359856], [2697733, 4311686, 4548, 10147824, 756, 5292, 37044, 259308, 1815156], [207037, 11422622, 31764, 7550964, 756, 5292, 37044, 259308, 1815156], [37261, 4889054, 222276, 222300, 756, 5292, 37044, 259308, 1815156], [7009525, 4586870, 1555860, 4925376, 756, 5292, 37044, 259308, 1815156], [4137481, 8323886, 10890948, 3566844, 756, 5292, 37044, 259308, 1815156]], 'inner_hash': 3413613090818454634, 'inner_nilpotent': False, 'inner_order': 12706092, 'inner_split': True, 'inner_tex': 'C_7^6.C_3^2.D_6', 'inner_used': [1, 2, 4], 'irrC_degree': 18, 'irrQ_degree': 36, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 4], [2, 8], [3, 8], [9, 32], [18, 72], [27, 32], [36, 28], [54, 828], [108, 875]], 'label': '12706092.s', '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': 'C7^6.C3^2.D6', 'ngens': 11, '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 4, 0, 0, 4, 1, 0, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 75, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 1887, 'number_divisions': 975, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 12706092, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 3871], [3, 292922], [6, 4874030], [7, 117648], [14, 2231460], [21, 2765952], [42, 2420208]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [4, 6, 3], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[5823753, 824986, 11315064, 3433588, 4728456, 3222072, 11599524, 10704960, 4726188], [8761721, 10685306, 8496804, 2394852, 12532428, 4013064, 1144584, 7557948, 3466584], [5892805, 818750, 11593488, 1894052, 2093688, 7781508, 8630280, 5988276, 3374352]], 'outer_group': '72.25', 'outer_hash': 25, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 11, 'outer_perms': [19817280, 3669867, 27580587], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_3\\times \\SL(2,3)', 'pc_rank': None, 'perfect': False, 'permutation_degree': 42, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 8], [6, 4], [18, 24], [36, 36], [54, 28], [72, 12], [108, 435], [216, 424]], 'representations': {'PC': {'code': '44937215869050905024562031388590899263223318442085353639346418573098428581783897344209892257373726651366490841395108696808591590820575518807512717195255952534752986477313996236277991203240243414712712129617332564028157620726009761975447805772755097275343328829933045828369377390062578707230033039243902719980985060238801663', 'gens': [1, 2, 4, 5, 7, 8, 9, 10, 11], 'pres': [11, -2, -2, -3, -3, 3, -7, 7, 7, 7, 7, 7, 88964700, 11112773, 56, 209388830, 35135718, 406481859, 206011358, 446845, 463003864, 41073795, 167541356, 25661002, 213, 14669429, 146868892, 37796247, 1226, 933753750, 404739737, 241916626, 9741, 9446564, 8392039, 138468546, 95089925, 77656, 17155035, 53468, 493558777, 8049, 611267, 203794, 859553649, 577284860, 250546261, 4754022, 31034903, 1512660214, 487364547, 300893999, 36605689, 1209570]}, 'Perm': {'d': 42, 'gens': [374712854015786771398801848439884843565588329868601, 514361588868991877746139461683972811734357820011274, 583694499324279856548902081908129392465691181644474]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 196, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_7^6.C_3^2.D_6', 'transitive_degree': 42, 'wreath_data': None, 'wreath_product': False}
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 6, 'aut_exponent': 252, 'aut_gen_orders': [18, 9, 42], 'aut_gens': [[1, 2, 6, 18, 756, 5292], [747, 26252, 19770, 31988, 25920, 18036], [36367, 13622, 22254, 17624, 30132, 7776], [24021, 2854, 1734, 522, 26460, 4536]], 'aut_group': None, 'aut_hash': 3107281057440367973, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 889056, 'aut_permdeg': 126, 'aut_perms': [10620727347822408217680329584642408478508403475414945808574307939426668035478146208971694784874336725206141909633449951706321237915282891484647631086374592448399319449619477329915388945106194794043736999805177330, 10094104563558345635993622032807825920877400659036642668916669165452372584526003944486254777592413162612876077460079746764215223032652323445570082493985529338489803050152641036081777271005740896704700982906915783, 18196470431018616444808768559396253995978644259124732521461397531028084686632175371437807413509713173757661817831229291574330335260815176036984600032900918050093985253250623869061984304808023531764016633004675571], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 63, 2, 1], [3, 294, 4, 1], [3, 343, 1, 2], [6, 294, 4, 1], [6, 343, 1, 2], [6, 3087, 2, 2], [7, 9, 8, 1], [7, 27, 8, 1], [7, 54, 1, 1], [14, 9, 8, 1], [14, 27, 8, 1], [14, 54, 1, 1], [14, 189, 16, 2], [21, 882, 8, 1], [42, 882, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_7^3.\\He_3.Q_8.C_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 252, 'autcentquo_group': None, 'autcentquo_hash': 4061174464532135472, 'autcentquo_nilpotent': False, 'autcentquo_order': 444528, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_7^3.\\He_3.Q_8.C_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 63, 2], [3, 294, 4], [3, 343, 2], [6, 294, 4], [6, 343, 2], [6, 3087, 4], [7, 9, 8], [7, 27, 8], [7, 54, 1], [14, 9, 8], [14, 27, 8], [14, 54, 1], [14, 189, 32], [21, 882, 8], [42, 882, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '18522.q', 'commutator_count': 1, 'commutator_label': '9261.e', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '7.1', '7.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 25, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['18522.q', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 63, 1, 2], [3, 294, 1, 4], [3, 343, 2, 1], [6, 294, 1, 4], [6, 343, 2, 1], [6, 3087, 2, 2], [7, 9, 2, 4], [7, 27, 2, 4], [7, 54, 1, 1], [14, 9, 2, 4], [14, 27, 2, 4], [14, 54, 1, 1], [14, 189, 2, 16], [21, 882, 2, 4], [42, 882, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 22235472, 'exponent': 42, 'exponents_of_order': [3, 3, 2], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[9, 0, 16], [18, 0, 8], [27, 0, 16], [54, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '37044.y', 'hash': 2377675945736179954, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [14, 3, 3, 21, 7, 7], 'inner_gens': [[1, 4, 9834, 27204, 756, 216], [5, 2, 21930, 36318, 648, 3780], [32509, 20414, 6, 22590, 1512, 10584], [4261, 27332, 20526, 18, 3024, 10584], [1, 866, 4542, 3042, 756, 5292], [5833, 6806, 31758, 31770, 756, 5292]], 'inner_hash': 4981235326282517820, 'inner_nilpotent': False, 'inner_order': 18522, 'inner_split': True, 'inner_tex': 'C_7^3:C_3^2:S_3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 9, 'irrQ_degree': 18, 'irrQ_dim': 18, 'irrR_degree': 18, 'irrep_stats': [[1, 4], [2, 8], [3, 8], [9, 32], [18, 16], [27, 32], [54, 2]], 'label': '37044.y', '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': 'C7^3:C3^2:D6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 21, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 102, 'number_divisions': 58, 'number_normal_subgroups': 19, 'number_subgroup_autclasses': 108, 'number_subgroup_classes': 386, 'number_subgroups': 59248, 'old_label': None, 'order': 37044, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 127], [3, 1862], [6, 14210], [7, 342], [14, 6390], [21, 7056], [42, 7056]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 4, 4], 'outer_gen_pows': [0, 26472, 26472], 'outer_gens': [[35695, 1768, 11886, 14648, 29808, 25380], [25057, 33528, 1842, 13676, 33804, 7668], [18793, 20930, 1086, 19748, 28296, 9180]], 'outer_group': '48.32', 'outer_hash': 32, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 10, 'outer_perms': [11809, 2442654, 1169688], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times \\SL(2,3)', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [6, 4], [18, 16], [36, 8], [54, 18]], 'representations': {'PC': {'code': '208410501127347573839785152705260198664258147606117210618420796113656290368478900130026150055751887355146943987262767042383', 'gens': [1, 2, 3, 4, 7, 8], 'pres': [8, 2, 3, 3, 2, 3, 7, 7, 7, 270432, 65, 236018, 263170, 870531, 581099, 120499, 91, 517444, 145572, 205460, 156, 1016069, 508045, 1749, 18158, 14134, 9438, 2390, 13831, 120975, 112919, 37663, 37671]}, 'Perm': {'d': 23, 'gens': [3584442402004827868854, 2413569518227183983361, 1185471876850837396086]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_7^3:C_3^2:D_6', 'transitive_degree': 42, 'wreath_data': None, 'wreath_product': False}
