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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3415', 'ambient_counter': 3415, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 2, 'counter': 130, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.3415.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.750', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 750, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^4:C_2^3', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1296.3415', 'aut_centralizer_order': 2985984, 'aut_label': '648.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2985984, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.b1', '324.a1', '324.b1', '324.c1', '324.d1', '324.e1'], 'contains': ['1296.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5106, 6483, 4739, 7313], 'generators': [648], 'label': '1296.3415.648.a1', 'mobius_quo': -1, 'mobius_sub': -5832, 'normal_closure': '648.a1', 'normal_contained_in': ['216.a1', '324.a1'], 'normal_contains': ['1296.a1'], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': '648.750', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.750', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], '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, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 6, 'aut_exponent': 48, 'aut_gen_orders': [8, 12, 12, 8, 16], 'aut_gens': [[1, 2, 12, 36, 216], [21, 886, 8, 396, 360], [186, 277, 144, 120, 664], [906, 993, 144, 768, 668], [1, 34, 16, 324, 360], [402, 845, 864, 788, 656]], 'aut_group': None, 'aut_hash': 455835253681380774, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2985984, 'aut_permdeg': 38, 'aut_perms': [501364051170104304911650807943882813944840101, 194504527037394681214988224830027284674336258, 25850807553564026970026788954394363225306240, 62949318402315402405583937586008461419156897, 337255182783437193602249784390645676196863050], 'aut_phi_ratio': 6912.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 18, 2, 1], [3, 2, 8, 1], [3, 4, 16, 1], [4, 18, 2, 1], [4, 81, 2, 1], [4, 162, 1, 1], [6, 2, 8, 1], [6, 4, 8, 1], [6, 4, 16, 1], [6, 4, 32, 1], [6, 36, 8, 1], [12, 36, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.Q_8^2.D_6^2.C_2^2', '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': 48, 'autcentquo_group': '373248.b', 'autcentquo_hash': 4345101132123987080, 'autcentquo_nilpotent': False, 'autcentquo_order': 373248, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:\\GL(2,3)\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 18, 2], [3, 2, 8], [3, 4, 16], [4, 18, 2], [4, 81, 2], [4, 162, 1], [6, 2, 8], [6, 4, 56], [6, 36, 8], [12, 36, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '648.750', 'commutator_count': 1, 'commutator_label': '162.55', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3415, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 18, 1, 2], [3, 2, 1, 8], [3, 4, 1, 16], [4, 18, 1, 2], [4, 81, 2, 1], [4, 162, 1, 1], [6, 2, 1, 8], [6, 4, 1, 56], [6, 36, 1, 8], [12, 36, 1, 8]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 84, 'exponent': 12, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '648.750', 'hash': 3415, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 3, 6, 3], 'inner_gens': [[1, 10, 24, 684, 216], [5, 2, 12, 828, 1080], [25, 2, 12, 36, 216], [649, 722, 12, 36, 216], [1, 434, 12, 36, 216]], 'inner_hash': 750, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': False, 'inner_tex': 'C_3^4:C_2^3', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 34], [4, 72]], 'label': '1296.3415', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'C6^2.S3^2', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 114, 'number_divisions': 113, 'number_normal_subgroups': 152, 'number_subgroup_autclasses': 133, 'number_subgroup_classes': 1424, 'number_subgroups': 12156, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 39], [3, 80], [4, 360], [6, 528], [12, 288]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [8, 12, 24, 4], 'outer_gen_pows': [7, 0, 0, 7], 'outer_gens': [[762, 541, 576, 136, 680], [1, 666, 28, 540, 792], [649, 658, 28, 396, 792], [649, 682, 32, 324, 360]], 'outer_group': None, 'outer_hash': 5654329661307977825, 'outer_nilpotent': False, 'outer_order': 4608, 'outer_permdeg': 34, 'outer_perms': [195702848277144947555815325402626508671, 68327978632085856561689378756819521735, 177709260551714833434172473962578377985, 245271541357665757407464343212827052520], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\SL(2,3):A_4.D_4.C_2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 32], [4, 73]], 'representations': {'PC': {'code': 152621625098049469991362958696782631950818464565, 'gens': [1, 2, 4, 5, 7], 'pres': [8, -2, -2, -3, -3, -2, -3, -2, -3, 5184, 161, 41, 194, 771, 27364, 16572, 116, 3469, 30254, 166, 27663]}, 'Perm': {'d': 20, 'gens': [6403681383815544, 487445281, 1624320, 12501360, 128069704578816000, 243290200817664000, 6706022403, 6706022404]}}, 'schur_multiplier': [6, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.S_3^2', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 6, 'aut_exponent': 48, 'aut_gen_orders': [12, 8, 12], 'aut_gens': [[24577758, 26172358, 2939606, 14159168, 25633100, 28816400, 34663142], [20699780, 13041911, 37043725, 14325240, 17128748, 28816400, 21380924], [7192025, 24423882, 24898809, 11660736, 17347803, 28816400, 13833109], [6920336, 15629446, 32864349, 14725868, 39306280, 28816400, 4102068]], 'aut_group': '1492992.c', 'aut_hash': 4827064521911694658, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1492992, 'aut_permdeg': 36, 'aut_perms': [259565405465656465194210411898631932819236, 87374739313573195735476507136205101564660, 62594172425999563671323355277358889611399], 'aut_phi_ratio': 6912.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 4, 1], [2, 81, 2, 1], [3, 2, 8, 1], [3, 4, 16, 1], [6, 2, 8, 1], [6, 4, 16, 1], [6, 18, 16, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_3^2\\times C_6^2).\\GL(2,3)\\wr C_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': 48, 'autcentquo_group': '373248.b', 'autcentquo_hash': 4345101132123987080, 'autcentquo_nilpotent': False, 'autcentquo_order': 373248, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:\\GL(2,3)\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 9, 4], [2, 81, 2], [3, 2, 8], [3, 4, 16], [6, 2, 8], [6, 4, 16], [6, 18, 16]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '324.169', 'commutator_count': 1, 'commutator_label': '81.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 750, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['18.4', 2], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 1, 4], [2, 81, 1, 2], [3, 2, 1, 8], [3, 4, 1, 16], [6, 2, 1, 8], [6, 4, 1, 16], [6, 18, 1, 16]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 21, 'exponent': 6, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '648.750', 'hash': 750, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [3, 6, 3, 2, 3, 1, 3], 'inner_gens': [[24577758, 13089749, 2939606, 8188666, 25633100, 28816400, 34663142], [43014227, 26172358, 32864349, 34924766, 8092874, 28816400, 13939616], [24577758, 39825765, 2939606, 39300942, 25633100, 28816400, 34663142], [20201582, 8733253, 32864349, 14159168, 8092874, 28816400, 38915318], [24577758, 29363677, 2939606, 17350487, 25633100, 28816400, 34663142], [24577758, 26172358, 2939606, 14159168, 25633100, 28816400, 34663142], [24577758, 8640151, 2939606, 8314856, 25633100, 28816400, 34663142]], 'inner_hash': 169, 'inner_nilpotent': False, 'inner_order': 324, 'inner_split': False, 'inner_tex': 'C_3^2:S_3^2', 'inner_used': [1, 2, 4, 5, 7], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 32], [4, 32]], 'label': '648.750', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^4:C2^3', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 72, 'number_divisions': 72, 'number_normal_subgroups': 116, 'number_subgroup_autclasses': 70, 'number_subgroup_classes': 1016, 'number_subgroups': 10992, 'old_label': None, 'order': 648, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 199], [3, 80], [6, 368]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 3, 2, 2], 'outer_gen_pows': [32319731, 32319731, 14408200, 14408200], 'outer_gens': [[20426712, 24297695, 2939606, 11394961, 25633100, 28816400, 14251946], [7138662, 8733253, 2939606, 34924766, 25633100, 28816400, 39233480], [7138662, 12603968, 2939606, 24676207, 25633100, 28816400, 14251946], [24577758, 29361018, 37043725, 29131384, 14038559, 28816400, 28765467]], 'outer_group': '4608.bs', 'outer_hash': 3000911920882418164, 'outer_nilpotent': False, 'outer_order': 4608, 'outer_permdeg': 12, 'outer_perms': [98064107, 3736, 98065489, 223806840], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4^2:D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 32], [4, 32]], 'representations': {'PC': {'code': 826779042919613010057025876525, 'gens': [1, 2, 3, 5, 6], 'pres': [7, -2, -3, -2, -3, -3, -2, -3, 57, 632, 58, 675, 438, 3799, 124, 3548]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [24577758, 26172358, 2939606, 14159168, 25633100, 28816400, 34663142]}, 'Perm': {'d': 14, 'gens': [482635440, 25, 3628800, 147, 240, 6706067760, 45360]}}, 'schur_multiplier': [2, 6, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:C_2^3', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
