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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '373248.bm', 'ambient_counter': 39, 'ambient_order': 373248, 'ambient_tex': 'C_6^4.C_6^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 162, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '373248.bm.36.GI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.gi1', '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': 36, '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': '10368.di', 'subgroup_hash': 9217159457059374049, 'subgroup_order': 10368, 'subgroup_tex': 'C_6^3.(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '373248.bm', 'aut_centralizer_order': None, 'aut_label': '36.GI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': None, 'contains': None, 'core': '2304.B', 'coset_action_label': None, 'count': 72, 'diagramx': [8629, -1, 6541, -1], 'generators': [141996444024748243792480859526, 11373648727153736356325360208, 40326, 12169709221230957660455213689, 127869906584753033773208400, 3242489683987837839328859526, 7097101949657778708815334, 1134120, 7085808264142632139543848, 25132763538316337694393582120, 147255367395667153699453633320], 'label': '373248.bm.36.GI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.D', 'old_label': '36.gi1', 'projective_image': '373248.bm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.GI', '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [12, 12, 2, 4, 6, 4, 6, 4], 'aut_gens': [[1, 2, 4, 24, 288, 3456], [9361, 6277, 323, 4840, 10080, 3456], [3601, 4978, 2060, 9600, 4824, 2304], [145, 6267, 1677, 168, 8352, 6912], [7489, 3204, 3202, 7360, 8856, 2304], [8641, 2674, 10300, 1752, 3888, 6912], [1153, 5964, 8274, 2032, 5832, 2304], [4177, 7642, 5860, 9600, 4824, 1152], [5329, 5339, 7029, 7824, 7704, 1152]], 'aut_group': None, 'aut_hash': 8564989553364120192, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 331776, 'aut_permdeg': 168, 'aut_perms': [189478761539010596380544011110045428067770315082251738089819672369814191556673144359538169027922997587399655204906547143385174191568828811641979609564594028923110138369370664625251589073747961343224929579062106480544422398653706915129877117925966813641006018220762410822135967448640551970128191828404519, 98355937730980155587827165392327823032237667289908600254471935761403494180814082084626224743522622673563087239514645875912777319673885364561659785767128941462267631140310317803189975962718191529173897034585101851527838398447393157752770229240651101129441380874179461975086500287971048190784399989268750, 175263068836397292685377580902544982843394804068395165744553991796384365572520481623705414777259860609714093155729231987497908486187251093339033928396276506565583162887515159777510864642439832478605755405340136039644040055266061006169404523485490020142998915916313294914332685500379312928140653875544527, 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145465137290985905066837356143474688866719782857519849897703832001647013675776598818368808298358175676081859847316914805214802733288334905358482608140437050840270298624031005852070152052237737174880097034303612569644546059879314225599251748283976327196509451634411037174588727526579853950190451844951362, 143626355840880679104672378246448899347190720237916180347373425314316629041907945651172054079166722383912642827228705696907374219795285818809358047660770348824549328928103909410862511111182034013001154836355743242260820612271824825141918203127453492361354882597621812921317226892066099502063366714852707], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 24, 1, 1], [2, 36, 1, 2], [2, 36, 4, 1], [2, 81, 2, 1], [2, 162, 1, 1], [2, 216, 1, 1], [2, 324, 1, 1], [3, 2, 2, 1], [3, 4, 1, 3], [3, 8, 2, 3], [3, 16, 1, 1], [4, 12, 2, 1], [4, 18, 2, 2], [4, 36, 4, 1], [4, 108, 2, 1], [6, 2, 2, 1], [6, 4, 1, 5], [6, 4, 2, 2], [6, 8, 1, 1], [6, 8, 2, 9], [6, 8, 4, 1], [6, 16, 1, 3], [6, 16, 2, 3], [6, 16, 4, 3], [6, 48, 1, 1], [6, 48, 2, 2], [6, 48, 4, 2], [6, 72, 2, 2], [6, 72, 4, 2], [6, 144, 1, 2], [6, 144, 4, 1], [6, 432, 1, 1], [8, 216, 4, 1], [12, 24, 2, 1], [12, 24, 4, 2], [12, 36, 4, 1], [12, 48, 4, 2], [12, 72, 2, 3], [12, 72, 4, 2], [12, 144, 4, 1], [12, 216, 2, 1], [24, 432, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.C_2^6.C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': None, 'autcentquo_hash': 7113313633987731786, 'autcentquo_nilpotent': False, 'autcentquo_order': 20736, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4.C_2^6.C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 24, 1], [2, 36, 6], [2, 81, 2], [2, 162, 1], [2, 216, 1], [2, 324, 1], [3, 2, 2], [3, 4, 3], [3, 8, 6], [3, 16, 1], [4, 12, 2], [4, 18, 4], [4, 36, 4], [4, 108, 2], [6, 2, 2], [6, 4, 9], [6, 8, 23], [6, 16, 21], [6, 48, 13], [6, 72, 12], [6, 144, 6], [6, 432, 1], [8, 216, 4], [12, 24, 10], [12, 36, 4], [12, 48, 8], [12, 72, 14], [12, 144, 4], [12, 216, 2], [24, 432, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '648.687', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 87, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 24, 1, 1], [2, 36, 1, 6], [2, 81, 1, 2], [2, 162, 1, 1], [2, 216, 1, 1], [2, 324, 1, 1], [3, 2, 1, 2], [3, 4, 1, 3], [3, 8, 1, 6], [3, 16, 1, 1], [4, 12, 1, 2], [4, 18, 1, 4], [4, 36, 1, 4], [4, 108, 1, 2], [6, 2, 1, 2], [6, 4, 1, 9], [6, 8, 1, 23], [6, 16, 1, 21], [6, 48, 1, 13], [6, 72, 1, 12], [6, 144, 1, 6], [6, 432, 1, 1], [8, 216, 1, 4], [12, 24, 1, 10], [12, 36, 1, 4], [12, 48, 1, 8], [12, 72, 1, 14], [12, 144, 1, 4], [12, 216, 1, 2], [24, 432, 1, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 9921300480, 'exponent': 24, 'exponents_of_order': [7, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 8], [16, 1, 6]], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '2592.fh', 'hash': 9217159457059374049, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 6, 12, 12, 3], 'inner_gens': [[1, 2, 9220, 168, 10080, 6912], [1, 2, 20, 6144, 8280, 2304], [4609, 10, 4, 9696, 3672, 1152], [145, 4538, 7900, 24, 1440, 3456], [4033, 8426, 3820, 2328, 288, 6912], [6913, 4610, 5764, 24, 7200, 3456]], 'inner_hash': 5727878832586813877, 'inner_nilpotent': False, 'inner_order': 5184, 'inner_split': None, 'inner_tex': 'C_3^4.C_2^5.C_2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 28], [4, 48], [8, 64], [16, 21]], 'label': '10368.di', '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': 'C6^3.(S3*D4)', 'ngens': 11, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 81, 'number_characteristic_subgroups': 55, 'number_conjugacy_classes': 177, 'number_divisions': 177, 'number_normal_subgroups': 195, 'number_subgroup_autclasses': 3975, 'number_subgroup_classes': 10953, 'number_subgroups': 401184, 'old_label': None, 'order': 10368, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1111], [3, 80], [4, 456], [6, 3344], [8, 864], [12, 2784], [24, 1728]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [3257, 9224, 312, 7599, 0], 'outer_gens': [[7489, 9019, 4397, 1056, 7128, 2304], [7057, 1090, 8428, 1752, 3888, 6912], [3601, 4978, 2060, 9600, 4824, 2304], [7633, 7741, 6395, 9088, 6552, 1152], [7489, 3204, 3202, 7360, 8856, 2304]], 'outer_group': '64.261', 'outer_hash': 261, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 32, 'outer_perms': [43958692881100088213986114702981131, 251011381903811786101912456955750086, 8277786405963451254482467336750314, 139376863493070240569358298948386874, 26865700984845515980784346782063032], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times C_2^3', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 28], [4, 48], [8, 64], [16, 21]], 'representations': {'PC': {'code': '24023980865235236027441680711597826253913692758520416709835993704715205875625733717931422190717283081015172036646239609076355564520943577069902136975507', 'gens': [1, 2, 3, 5, 8, 11], 'pres': [11, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 304262, 343, 90, 203107, 366, 9244, 168975, 133346, 16042, 158, 63376, 30123, 192, 3724, 887047, 364338, 80813, 79240, 5331, 260, 285128, 178219, 174666, 11932, 294, 253449, 380180, 95071, 10613, 836362, 139413, 34880, 2991]}, 'Perm': {'d': 20, 'gens': [371694682967731201, 13160435322223464, 13161742514010720, 135516916810598403, 262539167514998400]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^3.(S_3\\times D_4)', 'transitive_degree': 24, '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': '16.14', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [8, 8, 6, 6, 6, 12], 'aut_gens': [[12147347173586427137412864385, 1710820164043610883405366726, 23892491726920618711608728406, 11776940190719642451726783654], [101866187587419918573400801560, 87536802701825548098059013870, 38829816889296927550883015785, 134801416277909890087178978094], [168720041582512674755635895448, 23561563367371131315025331287, 89129459918830741592276195311, 80007755448230146531109991049], [101725931782652546240051403246, 122245269655257528387585919464, 25148904886314358884000450025, 131956379571572400281047331208], [77184721100821758352721635008, 23443704023301133526258892264, 126015734690066978831626944889, 14739616191107947733730993240], [168672270135780077501505662280, 155453376860644199163257536831, 23939027330404002438524419728, 188358933750177233329807503048], [99412284034826770784427358974, 34332782134089489160600128385, 154620149197146764346569135761, 166672322098914120365976792841]], 'aut_group': None, 'aut_hash': 8823543877612885203, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2985984, 'aut_permdeg': 936, 'aut_perms': 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3227870960273308787, 'autcentquo_nilpotent': False, 'autcentquo_order': 373248, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^4.D_6\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 2], [2, 9, 2], [2, 36, 2], [2, 81, 2], [2, 108, 2], [2, 216, 4], [2, 324, 6], [2, 486, 2], [2, 729, 2], [2, 972, 2], [3, 4, 2], [3, 12, 1], [3, 18, 2], [3, 24, 1], [3, 48, 1], [3, 96, 2], [3, 192, 1], [3, 288, 3], [3, 576, 1], [3, 1152, 2], [3, 2304, 1], [4, 36, 2], [4, 108, 2], [4, 324, 6], [4, 648, 8], [4, 972, 2], [4, 3888, 4], [6, 4, 2], [6, 12, 7], [6, 18, 6], [6, 24, 7], [6, 36, 12], [6, 48, 3], [6, 72, 22], [6, 96, 2], [6, 144, 6], [6, 192, 1], [6, 216, 16], [6, 288, 13], [6, 432, 12], [6, 576, 9], [6, 648, 6], [6, 864, 2], [6, 1152, 2], [6, 1296, 12], [6, 1728, 8], [6, 1944, 2], [6, 2304, 1], [6, 2592, 2], [6, 3888, 2], [6, 5184, 8], [6, 10368, 4], [8, 3888, 4], [12, 72, 4], [12, 144, 2], [12, 216, 16], [12, 432, 8], [12, 648, 6], [12, 864, 2], [12, 1296, 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[3, 1152, 1, 2], [3, 2304, 1, 1], [4, 36, 1, 2], [4, 108, 1, 2], [4, 324, 1, 6], [4, 648, 1, 8], [4, 972, 1, 2], [4, 3888, 1, 4], [6, 4, 1, 2], [6, 12, 1, 7], [6, 18, 1, 6], [6, 24, 1, 7], [6, 36, 1, 12], [6, 48, 1, 3], [6, 72, 1, 22], [6, 96, 1, 2], [6, 144, 1, 6], [6, 192, 1, 1], [6, 216, 1, 16], [6, 288, 1, 13], [6, 432, 1, 12], [6, 576, 1, 9], [6, 648, 1, 6], [6, 864, 1, 2], [6, 1152, 1, 2], [6, 1296, 1, 12], [6, 1728, 1, 8], [6, 1944, 1, 2], [6, 2304, 1, 1], [6, 2592, 1, 2], [6, 3888, 1, 2], [6, 5184, 1, 8], [6, 10368, 1, 4], [8, 3888, 1, 4], [12, 72, 1, 4], [12, 144, 1, 2], [12, 216, 1, 16], [12, 432, 1, 8], [12, 648, 1, 6], [12, 864, 1, 2], [12, 1296, 1, 26], [12, 1728, 1, 8], [12, 1944, 1, 2], [12, 2592, 1, 8], [12, 5184, 1, 2], [12, 7776, 1, 4], [24, 7776, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 24, 'exponents_of_order': [9, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 4], [24, 1, 10], [36, 1, 12], [48, 1, 4], [72, 1, 16], [144, 1, 2]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '41472.et', 'hash': 1201881843971238203, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [8, 6, 12, 6], 'inner_gens': [[12147347173586427137412864385, 153033610963705928578168282104, 34423368938491541472841695366, 56220183238772776601438583270], [58609764695119002673348818055, 1710820164043610883405366726, 93222553687211767375965247254, 54652542864075418898704050384], [130746472789140502266041816785, 125462354187768947218733819910, 23892491726920618711608728406, 99693346037303449649096970528], [175453639899093476866354485649, 33070782688570641463508573430, 90104837631048763309603003206, 11776940190719642451726783654]], 'inner_hash': 6672558604723196619, 'inner_nilpotent': False, 'inner_order': 186624, 'inner_split': True, 'inner_tex': 'C_3^3.S_4^2:D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 16], [2, 20], [4, 28], [6, 16], [8, 24], [9, 16], [12, 56], [16, 2], [18, 20], [24, 44], [36, 44], [48, 10], [72, 32], [144, 4]], 'label': '373248.bm', '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': 'C6^4.C6^2:D4', 'ngens': 4, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 187, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 332, 'number_divisions': 332, 'number_normal_subgroups': 150, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 373248, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 7663], [3, 6560], [4, 24912], [6, 160736], [8, 15552], [12, 126720], [24, 31104]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[12210714865408754893791456385, 3339491790795034784171363526, 24295778541223570999805586006, 11759649981764200658595654054], [15793136514795230114340557184, 3339491790795034784171363527, 111885048158396244681298347606, 15019402453109659795941798054], [15793136514795230114340557184, 3339491790795034784171363526, 111885048158396244681298347607, 15019402453109659795941798054], [15793136514795230114340557184, 3339491790795034784171363526, 111885048158396244681298347606, 15019402453109659795941798055]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [289, 7, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 28, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': False, 'ratrep_stats': [[1, 16], [2, 20], [4, 28], [6, 16], [8, 24], [9, 16], [12, 56], [16, 2], [18, 20], [24, 44], [36, 44], [48, 10], [72, 32], [144, 4]], 'representations': {'PC': {'code': '2505245573632509054435682060261579312015856771052399473920409678548549263873840639406678415064796256368065244976171686190671520256895008804301516350278065433543134822519868752509453359197786740406058360836780410691818077065402556075306147088522231592594922622099982222673122601494981072666039784330213987989377519011152507049826736008282620662526190308527374451419140180060577534541455261142720941552954810116513073301622155972248257502264527443243060304116870872207043585664858298750292', 'gens': [1, 2, 4, 6, 8, 10, 12, 14, 15], 'pres': [15, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2464920, 1851061, 76, 13026782, 1545917, 4113363, 4930938, 3888213, 168, 6028204, 9106219, 4795684, 315964, 16183805, 12303920, 4809815, 255470, 330815, 260, 31207686, 6214341, 9329076, 1068531, 125436, 68136, 12182407, 15837142, 64837, 21652, 38242, 45817, 352, 2916023, 58358, 19493, 81083, 5076009, 20628024, 12992439, 1663254, 1447269, 318684, 253899, 444, 4752010, 10062385, 9230800, 4728295, 2435470, 665365, 326800, 47304011, 12778586, 15357641, 1684856, 1833911, 395366, 262541, 536, 16061772, 14503347, 9645522, 5166777, 2330712, 856527, 421302, 9797773, 5715388, 14696683, 22828, 7723, 3958, 1453, 1749614, 874829, 5248859, 874889, 8249, 12314, 1529, 2219]}, 'Perm': {'d': 28, 'gens': [12147347173586427137412864385, 1710820164043610883405366726, 23892491726920618711608728406, 11776940190719642451726783654]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^4.C_6^2:D_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
