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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': 720, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '466560.s.36.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12960.bi', 'subgroup_hash': 1730392048136745174, 'subgroup_order': 12960, 'subgroup_tex': 'C_3\\times S_3\\times S_6', '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': '36.F', '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': ['12.D'], 'contains': ['72.E', '72.L', '72.BC', '108.E', '108.I', '216.C', '360.CL', '540.DQ'], 'core': '648.A', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [199348209094, 93924311494, 316828, 178680, 45604], 'label': '466560.s.36.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.F', 'old_label': '36.f1', 'projective_image': '466560.s', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.F', 'subgroup_fusion': None, 'weyl_group': '4320.bg'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 120, 'aut_gen_orders': [2, 24, 2, 2, 3, 6, 2], 'aut_gens': [[811567, 43948953], [44680259, 160115913], [203656770, 44639660], [203656770, 119836783], [811567, 43949400], [812099, 43949503], [127008450, 80962765], [811567, 43949180]], 'aut_group': '17280.dj', 'aut_hash': 2660302502921319895, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 17280, 'aut_permdeg': 35, 'aut_perms': [61075012181267576509856018518852573249, 10026466680207829056163551598290540527870, 212906552516553760370628077859383106843, 22181030361963309957120000000, 4584633462923350926981014323200, 4766852984118921155522545767067981527888, 4584633488775367665865990963200], 'aut_phi_ratio': 5.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 15, 2, 1], [2, 45, 1, 1], [2, 45, 2, 1], [2, 135, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 40, 2, 1], [3, 40, 4, 1], [3, 80, 2, 1], [3, 80, 4, 1], [4, 90, 1, 2], [4, 270, 1, 2], [5, 144, 1, 1], [6, 3, 2, 1], [6, 15, 4, 1], [6, 30, 2, 1], [6, 30, 4, 1], [6, 45, 2, 1], [6, 45, 4, 1], [6, 90, 1, 1], [6, 90, 2, 1], [6, 120, 2, 2], [6, 120, 4, 2], [6, 135, 2, 1], [6, 240, 2, 1], [6, 240, 4, 1], [6, 360, 2, 1], [6, 360, 4, 1], [10, 432, 1, 1], [12, 90, 2, 2], [12, 180, 1, 2], [12, 180, 2, 2], [12, 270, 2, 2], [15, 144, 2, 1], [15, 288, 1, 1], [15, 288, 2, 1], [30, 432, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times S_6:D_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': 120, 'autcentquo_group': '8640.q', 'autcentquo_hash': 2989818192655253003, 'autcentquo_nilpotent': False, 'autcentquo_order': 8640, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_6:D_6', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 15, 2], [2, 45, 3], [2, 135, 1], [3, 1, 2], [3, 2, 3], [3, 40, 6], [3, 80, 6], [4, 90, 2], [4, 270, 2], [5, 144, 1], [6, 3, 2], [6, 15, 4], [6, 30, 6], [6, 45, 6], [6, 90, 3], [6, 120, 12], [6, 135, 2], [6, 240, 6], [6, 360, 6], [10, 432, 1], [12, 90, 4], [12, 180, 6], [12, 270, 4], [15, 144, 2], [15, 288, 3], [30, 432, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '4320.bg', 'commutator_count': 1, 'commutator_label': '1080.487', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '360.118'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 35, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['6.1', 1], ['720.763', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 15, 1, 2], [2, 45, 1, 3], [2, 135, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 40, 1, 2], [3, 40, 2, 2], [3, 80, 1, 2], [3, 80, 2, 2], [4, 90, 1, 2], [4, 270, 1, 2], [5, 144, 1, 1], [6, 3, 2, 1], [6, 15, 2, 2], [6, 30, 1, 2], [6, 30, 2, 2], [6, 45, 2, 3], [6, 90, 1, 1], [6, 90, 2, 1], [6, 120, 1, 4], [6, 120, 2, 4], [6, 135, 2, 1], [6, 240, 1, 2], [6, 240, 2, 2], [6, 360, 1, 2], [6, 360, 2, 2], [10, 432, 1, 1], [12, 90, 2, 2], [12, 180, 1, 2], [12, 180, 2, 2], [12, 270, 2, 2], [15, 144, 2, 1], [15, 288, 1, 1], [15, 288, 2, 1], [30, 432, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1272, 'exponent': 60, 'exponents_of_order': [5, 4, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[10, 0, 8], [18, 0, 4], [20, 0, 4], [32, 0, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '12960.bi', 'hash': 1730392048136745174, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [4, 10], 'inner_gens': [[811567, 51171500], [163664579, 43948953]], 'inner_hash': 8915526446794886175, 'inner_nilpotent': False, 'inner_order': 4320, 'inner_split': True, 'inner_tex': 'S_3\\times S_6', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 20, 'irrep_stats': [[1, 12], [2, 6], [5, 24], [9, 12], [10, 24], [16, 6], [18, 6], [20, 6], [32, 3]], 'label': '12960.bi', 'linC_count': 128, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 80, 'linQ_dim': 9, 'linQ_dim_count': 80, 'linR_count': 80, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C3*S3*S6', 'ngens': 2, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 48, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 99, 'number_divisions': 66, 'number_normal_subgroups': 20, 'number_subgroup_autclasses': 608, 'number_subgroup_classes': 982, 'number_subgroups': 59250, 'old_label': None, 'order': 12960, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 303], [3, 728], [4, 720], [5, 144], [6, 6096], [10, 432], [12, 2520], [15, 1152], [30, 864]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [50848560, 0], 'outer_gens': [[14958847, 94752153], [811567, 43949400]], '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': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 2], [5, 8], [9, 4], [10, 16], [16, 2], [18, 6], [20, 10], [32, 3], [36, 2], [40, 2], [64, 1]], 'representations': {'Perm': {'d': 12, 'gens': [811567, 43948953]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times S_3\\times S_6', 'transitive_degree': 36, '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}
