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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '466560.s', 'ambient_counter': 19, 'ambient_order': 466560, 'ambient_tex': 'C_3^3:S_4\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '466560.s.180.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.bf1', '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': 180, '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': '2592.od', 'subgroup_hash': 8913694849733206168, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '466560.s', 'aut_centralizer_order': None, 'aut_label': '180.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.D', '60.H'], 'contains': ['360.BB', '360.BL', '360.BT', '360.CD', '360.CG', '360.DH', '360.FA', '540.DC', '540.DP', '540.DQ'], 'core': '466560.a1', 'coset_action_label': None, 'count': 120, 'diagramx': None, 'generators': [178680, 199308211347, 180623565603, 322105, 45364, 461278586164, 199348209356, 244, 375138086875], 'label': '466560.s.180.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '60.H', 'old_label': '180.bf1', 'projective_image': '466560.s', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.BH', 'subgroup_fusion': None, 'weyl_group': '1296.2919'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [8, 6, 12, 12, 6], 'aut_gens': [[1, 2, 12, 72, 432], [2529, 154, 156, 1140, 2160], [793, 1226, 1740, 384, 2160], [657, 1954, 324, 996, 432], [2405, 2014, 2088, 300, 432], [569, 1402, 2088, 1164, 432]], 'aut_group': None, 'aut_hash': 3863387222522641359, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 41472, 'aut_permdeg': 30, 'aut_perms': [64696080023119189730685085544107, 64765640639221841944102385362618, 203716867922817029624095962902839, 87443201562726212895504874204252, 24699727264670479722414868979762], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 2, 1], [2, 9, 2, 1], [2, 27, 2, 1], [2, 54, 2, 1], [3, 1, 2, 1], [3, 6, 4, 1], [3, 8, 1, 1], [3, 8, 2, 1], [3, 48, 4, 1], [4, 6, 2, 1], [4, 54, 2, 1], [6, 1, 2, 1], [6, 3, 2, 2], [6, 6, 4, 2], [6, 8, 1, 1], [6, 8, 2, 1], [6, 9, 4, 1], [6, 18, 4, 2], [6, 27, 4, 1], [6, 36, 8, 1], [6, 48, 4, 1], [6, 54, 4, 1], [6, 72, 2, 1], [6, 72, 4, 1], [12, 6, 4, 1], [12, 36, 8, 1], [12, 54, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4\\times \\AGL(2,3).C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '10368.qn', 'autcentquo_hash': 3718250448986069408, 'autcentquo_nilpotent': False, 'autcentquo_order': 10368, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4\\times C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 6, 2], [2, 9, 2], [2, 27, 2], [2, 54, 2], [3, 1, 2], [3, 6, 4], [3, 8, 3], [3, 48, 4], [4, 6, 2], [4, 54, 2], [6, 1, 2], [6, 3, 4], [6, 6, 8], [6, 8, 3], [6, 9, 4], [6, 18, 8], [6, 27, 4], [6, 36, 8], [6, 48, 4], [6, 54, 4], [6, 72, 6], [12, 6, 4], [12, 36, 8], [12, 54, 4]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '432.746', 'commutator_count': 1, 'commutator_label': '324.130', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 368, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['24.12', 1], ['54.8', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 1, 2], [2, 9, 1, 2], [2, 27, 1, 2], [2, 54, 1, 2], [3, 1, 2, 1], [3, 6, 1, 4], [3, 8, 1, 1], [3, 8, 2, 1], [3, 48, 1, 4], [4, 6, 1, 2], [4, 54, 1, 2], [6, 1, 2, 1], [6, 3, 2, 2], [6, 6, 1, 4], [6, 6, 2, 2], [6, 8, 1, 1], [6, 8, 2, 1], [6, 9, 2, 2], [6, 18, 1, 8], [6, 27, 2, 2], [6, 36, 1, 8], [6, 48, 1, 4], [6, 54, 2, 2], [6, 72, 1, 2], [6, 72, 2, 2], [12, 6, 2, 2], [12, 36, 1, 8], [12, 54, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 68040, 'exponent': 12, 'exponents_of_order': [5, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[9, 0, 8]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '864.4691', 'hash': 8913694849733206168, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 6, 6, 1], 'inner_gens': [[1, 1774, 276, 360, 432], [1085, 2, 276, 180, 432], [241, 242, 12, 936, 432], [145, 398, 1740, 72, 432], [1, 2, 12, 72, 432]], 'inner_hash': 746, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': False, 'inner_tex': 'C_6^2:D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 9, 'irrQ_degree': 18, 'irrQ_dim': 18, 'irrR_degree': 18, 'irrep_stats': [[1, 8], [2, 20], [3, 24], [4, 8], [6, 24], [9, 16]], 'label': '2592.od', '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': True, 'name': 'C3^2:D6*S4', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 34, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 100, 'number_divisions': 80, 'number_normal_subgroups': 80, 'number_subgroup_autclasses': 425, 'number_subgroup_classes': 1611, 'number_subgroups': 19518, 'old_label': None, 'order': 2592, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 199], [3, 242], [4, 120], [6, 1502], [12, 528]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 6, 2, 2], 'outer_gen_pows': [0, 0, 0, 6, 6], 'outer_gens': [[1, 1298, 12, 72, 432], [1729, 866, 60, 72, 2160], [1297, 1298, 1212, 360, 432], [1, 2, 1020, 2112, 432], [1, 2, 324, 240, 432]], 'outer_group': '96.226', 'outer_hash': 226, 'outer_nilpotent': False, 'outer_order': 96, 'outer_permdeg': 8, 'outer_perms': [7, 5047, 10096, 16680, 5160], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^2\\times S_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 20], [3, 8], [4, 8], [6, 24], [12, 4], [18, 8]], 'representations': {'PC': {'code': '1688981209501920702345952786198433367794088439773212474301133195773955228696710174293', 'gens': [1, 2, 4, 6, 8], 'pres': [9, 2, 2, 3, 2, 3, 2, 3, 2, 3, 7776, 31933, 46, 30350, 9939, 4980, 2397, 102, 2164, 1093, 19445, 4874, 1481, 4244, 4091, 158, 18150, 9087, 9861, 2688, 214]}, 'Perm': {'d': 15, 'gens': [3674876, 316802, 147, 80784, 1520650803, 479318852, 460803449762, 87178475516, 138240]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:D_6\\times S_4', 'transitive_degree': 54, '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': 4, 'aut_exponent': 360, 'aut_gen_orders': [60, 12, 18, 6, 72], 'aut_gens': [[147, 93924276210, 178565, 316920, 80784, 269, 40584, 3674610, 240], [45504, 436450429444, 40894, 138838, 147, 40440, 125, 479139844, 240], [80643, 24988198915, 86154, 281521, 243, 85682, 26, 268241178115, 4], [80880, 13931101443, 317373, 357123, 80644, 40440, 40321, 180583741443, 45360], [147, 175833585238, 276956, 219474, 45363, 29, 40325, 479082838, 4], [80643, 24908446055, 40916, 362284, 147, 40321, 25, 287883953255, 4]], 'aut_group': None, 'aut_hash': 4003788620574699767, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1866240, 'aut_permdeg': 48, 'aut_perms': [3076738730291466655884770164447453963998793012717622612209753, 182245449675936102608481383277925380529819829747550277449062, 10948114306644822250340256671825114780973621612096647592618072, 11111286963839472721160418418324457584150622299387861434385911, 8570405517023778681022640085896857869355212728751129839466918], 'aut_phi_ratio': 15.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 15, 2, 1], [2, 18, 1, 1], [2, 27, 1, 1], [2, 45, 1, 1], [2, 270, 2, 1], [2, 405, 2, 1], [2, 810, 1, 1], [2, 1215, 1, 1], [3, 4, 2, 1], [3, 6, 1, 1], [3, 12, 1, 1], [3, 40, 2, 1], [3, 72, 1, 1], [3, 160, 4, 1], [3, 240, 2, 1], [3, 480, 2, 1], [3, 2880, 2, 1], [4, 90, 1, 2], [4, 162, 1, 1], [4, 1620, 1, 2], [4, 2430, 1, 2], [4, 2430, 2, 1], [4, 7290, 1, 1], [4, 14580, 1, 2], [5, 144, 1, 1], [6, 18, 2, 1], [6, 36, 1, 1], [6, 36, 2, 1], [6, 54, 1, 1], [6, 60, 4, 1], [6, 90, 2, 1], [6, 120, 2, 1], [6, 180, 2, 2], [6, 270, 1, 1], [6, 270, 4, 1], [6, 480, 4, 1], [6, 540, 1, 1], [6, 540, 2, 1], [6, 540, 4, 1], [6, 720, 2, 2], [6, 720, 4, 1], [6, 810, 2, 2], [6, 1080, 2, 2], [6, 1440, 2, 2], [6, 1440, 4, 1], [6, 1620, 1, 1], [6, 1620, 2, 1], [6, 2160, 2, 2], [6, 2160, 4, 1], [6, 2430, 1, 1], [6, 3240, 1, 1], [6, 3240, 2, 1], [6, 4320, 2, 1], [6, 4320, 4, 1], [6, 6480, 2, 1], [6, 8640, 2, 1], [9, 72, 2, 1], [9, 2880, 4, 1], [10, 2592, 1, 1], [10, 3888, 1, 1], [12, 360, 2, 2], [12, 540, 1, 2], [12, 1080, 1, 2], [12, 1620, 2, 2], [12, 3240, 1, 2], [12, 3240, 2, 2], [12, 4860, 1, 2], [12, 6480, 1, 2], [12, 6480, 2, 1], [12, 19440, 2, 1], [15, 576, 2, 1], [15, 864, 1, 1], [15, 1728, 1, 1], [15, 10368, 1, 1], [18, 1080, 4, 1], [18, 3240, 2, 1], [18, 8640, 4, 1], [20, 23328, 1, 1], [30, 2592, 2, 1], [30, 5184, 1, 1], [30, 5184, 2, 1], [30, 7776, 1, 1], [36, 6480, 2, 2], [45, 10368, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3:C_2^2.D_6.A_6.C_2^2', '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': 360, 'autcentquo_group': None, 'autcentquo_hash': 4003788620574699767, 'autcentquo_nilpotent': False, 'autcentquo_order': 1866240, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3:C_2^2.D_6.A_6.C_2^2', 'cc_stats': [[1, 1, 1], [2, 15, 2], [2, 18, 1], [2, 27, 1], [2, 45, 1], [2, 270, 2], [2, 405, 2], [2, 810, 1], [2, 1215, 1], [3, 4, 2], [3, 6, 1], [3, 12, 1], [3, 40, 2], [3, 72, 1], [3, 160, 4], [3, 240, 2], [3, 480, 2], [3, 2880, 2], [4, 90, 2], [4, 162, 1], [4, 1620, 2], [4, 2430, 4], [4, 7290, 1], [4, 14580, 2], [5, 144, 1], [6, 18, 2], [6, 36, 3], [6, 54, 1], [6, 60, 4], [6, 90, 2], [6, 120, 2], [6, 180, 4], [6, 270, 5], [6, 480, 4], [6, 540, 7], [6, 720, 8], [6, 810, 4], [6, 1080, 4], [6, 1440, 8], [6, 1620, 3], [6, 2160, 8], [6, 2430, 1], [6, 3240, 3], [6, 4320, 6], [6, 6480, 2], [6, 8640, 2], [9, 72, 2], [9, 2880, 4], [10, 2592, 1], [10, 3888, 1], [12, 360, 4], [12, 540, 2], [12, 1080, 2], [12, 1620, 4], [12, 3240, 6], [12, 4860, 2], [12, 6480, 4], [12, 19440, 2], [15, 576, 2], [15, 864, 1], [15, 1728, 1], [15, 10368, 1], [18, 1080, 4], [18, 3240, 2], [18, 8640, 4], [20, 23328, 1], [30, 2592, 2], [30, 5184, 3], [30, 7776, 1], [36, 6480, 4], [45, 10368, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '466560.s', 'commutator_count': 1, 'commutator_label': '116640.x', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '360.118'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 19, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['648.704', 1], ['720.763', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 15, 1, 2], [2, 18, 1, 1], [2, 27, 1, 1], [2, 45, 1, 1], [2, 270, 1, 2], [2, 405, 1, 2], [2, 810, 1, 1], [2, 1215, 1, 1], [3, 4, 2, 1], [3, 6, 1, 1], [3, 12, 1, 1], [3, 40, 1, 2], [3, 72, 1, 1], [3, 160, 2, 2], [3, 240, 1, 2], [3, 480, 1, 2], [3, 2880, 1, 2], [4, 90, 1, 2], [4, 162, 1, 1], [4, 1620, 1, 2], [4, 2430, 1, 4], [4, 7290, 1, 1], [4, 14580, 1, 2], [5, 144, 1, 1], [6, 18, 2, 1], [6, 36, 1, 1], [6, 36, 2, 1], [6, 54, 1, 1], [6, 60, 2, 2], [6, 90, 1, 2], [6, 120, 1, 2], [6, 180, 1, 2], [6, 180, 2, 1], [6, 270, 1, 1], [6, 270, 2, 2], [6, 480, 2, 2], [6, 540, 1, 3], [6, 540, 2, 2], [6, 720, 1, 4], [6, 720, 2, 2], [6, 810, 1, 2], [6, 810, 2, 1], [6, 1080, 1, 4], [6, 1440, 1, 4], [6, 1440, 2, 2], [6, 1620, 1, 1], [6, 1620, 2, 1], [6, 2160, 1, 4], [6, 2160, 2, 2], [6, 2430, 1, 1], [6, 3240, 1, 3], [6, 4320, 1, 2], [6, 4320, 2, 2], [6, 6480, 1, 2], [6, 8640, 1, 2], [9, 72, 2, 1], [9, 2880, 2, 2], [10, 2592, 1, 1], [10, 3888, 1, 1], [12, 360, 2, 2], [12, 540, 1, 2], [12, 1080, 1, 2], [12, 1620, 2, 2], [12, 3240, 1, 2], [12, 3240, 2, 2], [12, 4860, 1, 2], [12, 6480, 1, 4], [12, 19440, 1, 2], [15, 576, 2, 1], [15, 864, 1, 1], [15, 1728, 1, 1], [15, 10368, 1, 1], [18, 1080, 2, 2], [18, 3240, 2, 1], [18, 8640, 2, 2], [20, 23328, 1, 1], [30, 2592, 2, 1], [30, 5184, 1, 1], [30, 5184, 2, 1], [30, 7776, 1, 1], [36, 6480, 2, 2], [45, 10368, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 180, 'exponents_of_order': [7, 6, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[20, 0, 16], [30, 0, 8], [30, 1, 8], [36, 0, 8], [40, 0, 16], [54, 0, 4], [54, 1, 4], [60, 0, 4], [60, 1, 12], [64, 0, 4], [72, 0, 4], [80, 0, 4], [96, 0, 2], [96, 1, 2], [108, 1, 4], [120, 1, 4], [128, 0, 2], [192, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '466560.s', 'hash': 6285179920648805424, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 180, 'inner_gen_orders': [3, 30, 4, 3, 3, 2, 2, 6, 3], 'inner_gens': [[147, 93924276210, 224162, 362424, 80784, 122, 40440, 3674610, 240], [147, 93924276210, 362877, 224375, 80643, 269, 5045, 442641069810, 4], [45364, 93924593255, 178565, 138959, 45504, 85685, 85800, 3991655, 80640], [80784, 93924409084, 277196, 316920, 80643, 5304, 5042, 3807484, 45360], [147, 93924276453, 178709, 281643, 80784, 125, 85800, 3674853, 240], [244, 93924276210, 183869, 322080, 80880, 269, 40584, 3674610, 144], [243, 93924311759, 224165, 276749, 45600, 269, 40584, 3710159, 144], [147, 93967821810, 362877, 224375, 80643, 269, 5045, 3674610, 4], [147, 93924276358, 143429, 316828, 80784, 29, 40344, 3674758, 240]], 'inner_hash': 6285179920648805424, 'inner_nilpotent': False, 'inner_order': 466560, 'inner_split': True, 'inner_tex': 'C_3^3:S_4\\times S_6', 'inner_used': [1, 2, 3, 8], 'irrC_degree': 20, 'irrQ_degree': 30, 'irrQ_dim': 30, 'irrR_degree': 30, 'irrep_stats': [[1, 4], [2, 2], [3, 4], [4, 8], [5, 8], [6, 8], [8, 4], [9, 4], [10, 8], [12, 4], [15, 8], [16, 2], [18, 2], [20, 18], [27, 4], [30, 20], [32, 1], [36, 8], [40, 16], [48, 2], [54, 8], [60, 16], [64, 4], [72, 4], [80, 4], [96, 4], [108, 4], [120, 4], [128, 2], [192, 2]], 'label': '466560.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': False, 'name': 'C3^3:S4*S6', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 104, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 187, 'number_divisions': 143, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 6698, 'number_subgroup_classes': 11092, 'number_subgroups': 9778520, 'old_label': None, 'order': 466560, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 3495], [3, 8018], [4, 49752], [5, 144], [6, 123918], [9, 11664], [10, 6480], [12, 105120], [15, 14112], [18, 45360], [20, 23328], [30, 28512], [36, 25920], [45, 20736]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [105859353600, 0], 'outer_gens': [[147, 355023693810, 178565, 316920, 80784, 269, 40584, 448908007410, 240], [244, 93924311638, 224069, 281788, 45600, 29, 5064, 3710038, 144]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [3, 4], [5, 8], [6, 4], [8, 4], [9, 4], [10, 8], [12, 6], [15, 8], [16, 4], [18, 2], [20, 2], [27, 4], [30, 12], [32, 1], [40, 8], [48, 2], [54, 4], [60, 16], [72, 4], [80, 8], [96, 2], [108, 6], [120, 6], [128, 2], [144, 2], [160, 2], [192, 3], [256, 1]], 'representations': {'Perm': {'d': 15, 'gens': [147, 93924276210, 178565, 316920, 80784, 269, 40584, 3674610, 240]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 640, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3:S_4\\times S_6', 'transitive_degree': 54, 'wreath_data': None, 'wreath_product': False}
