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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '186624.ej', 'ambient_counter': 114, 'ambient_order': 186624, 'ambient_tex': 'C_3^4.C_4^2:D_6^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 72, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '186624.ej.18._.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.J', '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': 18, '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': None, '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': '186624.ej', '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': 9, 'diagramx': None, 'generators': [163297, 124440, 64584, 5184, 65664, 6, 147744, 72912, 432, 62208, 36], 'label': '186624.ej.18._.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '18.J', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18._.J', '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': 72, 'aut_gen_orders': [4, 6, 12, 18, 12, 6, 18, 12], 'aut_gens': [[1, 2, 12, 72, 864, 10368, 31104], [104477, 61258, 160500, 186336, 48600, 3456, 31104], [135129, 124450, 177996, 62160, 63072, 62208, 114048], [90025, 54794, 38460, 62280, 4320, 10368, 155520], [78537, 6146, 39108, 165552, 42120, 124416, 96768], [12913, 146786, 9132, 14184, 146016, 10368, 155520], [139349, 80282, 23172, 32568, 141048, 6912, 114048], [69485, 75794, 74532, 104880, 130680, 6912, 103680], [21965, 68242, 40884, 172224, 52056, 6912, 31104]], 'aut_group': None, 'aut_hash': 5270842697441228155, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1492992, 'aut_permdeg': 360, 'aut_perms': 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1, 1], [3, 12, 1, 3], [3, 16, 1, 1], [3, 24, 1, 3], [3, 48, 1, 2], [3, 864, 1, 1], [3, 1728, 1, 1], [4, 54, 1, 4], [4, 108, 2, 2], [4, 162, 2, 2], [4, 324, 2, 2], [6, 2, 1, 1], [6, 6, 1, 8], [6, 8, 1, 1], [6, 12, 1, 13], [6, 16, 1, 1], [6, 24, 1, 21], [6, 48, 1, 16], [6, 72, 2, 5], [6, 72, 4, 2], [6, 96, 1, 2], [6, 144, 2, 4], [6, 144, 4, 6], [6, 216, 2, 11], [6, 432, 2, 6], [6, 648, 2, 5], [6, 864, 1, 1], [6, 864, 2, 2], [6, 1296, 2, 2], [6, 1728, 1, 1], [6, 1944, 2, 1], [6, 2592, 2, 2], [6, 5184, 2, 1], [6, 7776, 2, 1], [8, 648, 2, 2], [8, 1944, 2, 2], [9, 1728, 1, 1], [9, 3456, 1, 1], [12, 108, 1, 12], [12, 216, 1, 12], [12, 216, 2, 6], [12, 432, 1, 4], [12, 432, 2, 6], [12, 648, 2, 8], [12, 864, 2, 2], [12, 1296, 2, 2], [18, 1728, 1, 1], [18, 3456, 1, 1], [18, 5184, 2, 1], [24, 1296, 2, 4], [24, 1296, 4, 2], [24, 3888, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.C_{12}^2.C_6.C_2^6', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': None, 'autcentquo_hash': 2201406838260405918, 'autcentquo_nilpotent': False, 'autcentquo_order': 186624, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4.C_4^2.D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 36, 4], [2, 108, 6], [2, 243, 2], [2, 324, 4], [2, 729, 2], [2, 972, 2], [3, 2, 1], [3, 6, 2], [3, 8, 1], [3, 12, 3], [3, 16, 1], [3, 24, 3], [3, 48, 2], [3, 864, 1], [3, 1728, 1], [4, 54, 4], [4, 108, 4], [4, 162, 4], [4, 324, 4], [6, 2, 1], [6, 6, 8], [6, 8, 1], [6, 12, 13], [6, 16, 1], [6, 24, 21], [6, 48, 16], [6, 72, 18], [6, 96, 2], [6, 144, 32], [6, 216, 22], [6, 432, 12], [6, 648, 10], [6, 864, 5], [6, 1296, 4], [6, 1728, 1], [6, 1944, 2], [6, 2592, 4], [6, 5184, 2], [6, 7776, 2], [8, 648, 4], [8, 1944, 4], [9, 1728, 1], [9, 3456, 1], [12, 108, 12], [12, 216, 24], [12, 432, 16], [12, 648, 16], [12, 864, 4], [12, 1296, 4], [18, 1728, 1], [18, 3456, 1], [18, 5184, 2], [24, 1296, 16], [24, 3888, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': None, 'central_quotient': '93312.iq', 'commutator_count': 1, 'commutator_label': '11664.fv', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 14, 'conjugacy_classes_known': True, 'counter': 114, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 36, 1, 4], [2, 108, 1, 6], [2, 243, 1, 2], [2, 324, 1, 4], [2, 729, 1, 2], [2, 972, 1, 2], [3, 2, 1, 1], [3, 6, 1, 2], [3, 8, 1, 1], [3, 12, 1, 3], [3, 16, 1, 1], [3, 24, 1, 3], [3, 48, 1, 2], [3, 864, 1, 1], [3, 1728, 1, 1], [4, 54, 1, 4], [4, 108, 1, 4], [4, 162, 1, 4], [4, 324, 1, 4], [6, 2, 1, 1], [6, 6, 1, 8], [6, 8, 1, 1], [6, 12, 1, 13], [6, 16, 1, 1], [6, 24, 1, 21], [6, 48, 1, 16], [6, 72, 1, 18], [6, 96, 1, 2], [6, 144, 1, 32], [6, 216, 1, 22], [6, 432, 1, 12], [6, 648, 1, 10], [6, 864, 1, 5], [6, 1296, 1, 4], [6, 1728, 1, 1], [6, 1944, 1, 2], [6, 2592, 1, 4], [6, 5184, 1, 2], [6, 7776, 1, 2], [8, 648, 1, 4], [8, 1944, 1, 4], [9, 1728, 1, 1], [9, 3456, 1, 1], [12, 108, 1, 12], [12, 216, 1, 24], [12, 432, 1, 16], [12, 648, 1, 16], [12, 864, 1, 4], [12, 1296, 1, 4], [18, 1728, 1, 1], [18, 3456, 1, 1], [18, 5184, 1, 2], [24, 1296, 1, 16], [24, 3888, 1, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [8, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 4], [24, 1, 9], [48, 1, 13], [96, 1, 1]], 'familial': False, 'frattini_label': '12.5', 'frattini_quotient': '15552.jf', 'hash': 1212579475730342375, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 72, 'inner_gen_orders': [8, 6, 6, 12, 12, 3, 3], 'inner_gens': [[1, 79906, 62868, 124824, 130680, 20736, 96768], [104669, 2, 84948, 103416, 143208, 3456, 114048], [62425, 12770, 12, 66168, 71712, 10368, 31104], [125017, 180986, 131772, 72, 139104, 10368, 155520], [2377, 24410, 126156, 89928, 864, 20736, 155520], [20737, 17282, 12, 72, 21600, 10368, 31104], [131329, 134786, 12, 62280, 63072, 10368, 31104]], 'inner_hash': 9073412677889748987, 'inner_nilpotent': False, 'inner_order': 93312, 'inner_split': None, 'inner_tex': 'C_6^2.S_3^3:D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 16], [2, 16], [3, 16], [4, 4], [6, 56], [8, 8], [12, 96], [16, 8], [24, 72], [32, 2], [48, 46], [96, 2]], 'label': '186624.ej', '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': 'C3^4.C4^2:D6^2', 'ngens': 14, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 3, 1, 0, 1, 0, 1, 1, 0, 3, 1, 0, 0, 1, 0, 2, 3, 0, 3, 0, 0, 3, 2, 0, 2, 0, 1, 7, 0, 3, 0, 0, 9, 1, 0, 0, 15, 0, 1, 14, 0, 15, 2, 35, 0, 15, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 221, 'number_characteristic_subgroups': 67, 'number_conjugacy_classes': 342, 'number_divisions': 342, 'number_normal_subgroups': 159, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 186624, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 5983], [3, 2834], [4, 2592], [6, 75422], [8, 10368], [9, 5184], [12, 32400], [18, 15552], [24, 36288]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [5616, 89880, 158888, 141940], 'outer_gens': [[104477, 61258, 160500, 186336, 48600, 3456, 31104], [135129, 124450, 177996, 62160, 63072, 62208, 114048], [78537, 6146, 39108, 165552, 42120, 124416, 96768], [139349, 80282, 23172, 32568, 141048, 6912, 114048]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 16, 'outer_perms': [1327912203241, 2966658509284, 4396538203938, 5800737348096], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': False, 'ratrep_stats': [[1, 16], [2, 16], [3, 16], [4, 4], [6, 56], [8, 8], [12, 96], [16, 8], [24, 72], [32, 2], [48, 46], [96, 2]], 'representations': {'PC': {'code': '172845776961604419206746023664460921840096195213461578911959056824226479312213300044238792178823725927873478147048065977659348664577680951794595303615384615853124030643381652095842974514081176574611411261899780937731234609122003243118791363901350090967309633819211059793954632970860283445525032186759387928995313721252198295803000510735895117', 'gens': [1, 2, 4, 6, 9, 12, 13], 'pres': [14, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 3, 2, 3, 9072, 2237369, 71, 1797602, 3520611, 2378561, 747127, 157, 9194644, 2541858, 2238212, 10485221, 4343491, 1299345, 463223, 435769, 243, 12265686, 3996068, 3687970, 286, 7037191, 8549205, 2040899, 16465688, 9022126, 5354784, 753026, 657784, 243510, 18992, 5020, 372, 18204489, 9102263, 740917, 100851, 16879, 415, 9580042, 4790040, 399206, 88756, 14864, 3483659, 290329, 2612775, 4155, 17611788, 10378394, 4560232, 393202, 32884, 544, 1354765, 1016091, 169385, 338771, 28349]}, 'Perm': {'d': 30, 'gens': [632021031330091425166959854159, 9779492920819391314041087412319, 17717821138833586958901190621807, 9474529402019617745711932852295]}}, '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': 18, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_3^4.C_4^2:D_6^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
