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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.46792', 'ambient_counter': 46792, 'ambient_order': 1728, 'ambient_tex': 'C_6\\times D_6:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': True, 'core_order': 4, 'counter': 1222, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46792.432.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.656', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 656, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2.D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.46792', 'aut_centralizer_order': 1536, 'aut_label': '432.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1536, 'centralizer': '6.a1.a1', 'complements': ['4.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.e1.a1', '144.f1.a1', '144.cr1.a1', '144.cs1.a1', '144.ct1.a1', '144.cu1.a1', '216.a1.a1', '216.a1.b1', '216.b1.a1', '216.bi1.a1', '216.bi1.b1', '216.bj1.a1', '216.bj1.b1'], 'contains': ['864.d1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1647, 6693, 8483, 5845, 1486, 5117, 1743, 4623], 'generators': [340271, 329687], 'label': '1728.46792.432.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.b1.a1', 'normal_contained_in': ['144.d1.a1', '144.e1.a1', '144.f1.a1', '216.a1.b1', '216.a1.a1', '216.b1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.b1.a1', 'projective_image': '1728.46792', 'quotient_action_image': '6.1', 'quotient_action_kernel': '72.48', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, '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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 4, 2, 4, 4, 12, 6], 'aut_gens': [[475167, 253045, 302434, 340271, 505311], [155757, 433961, 137409, 329687, 252459], [475167, 82717, 455727, 329687, 515895], [171549, 214435, 148777, 329687, 515895], [463071, 576838, 455713, 340271, 208945], [162253, 253045, 291472, 340271, 241875], [481663, 247361, 137423, 329687, 252459], [463071, 390059, 148777, 329687, 515895]], 'aut_group': None, 'aut_hash': 8765063099206293740, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 9216, 'aut_permdeg': 38, 'aut_perms': [185163755288831865707677454424195430956905699, 134861313930016066097640794949232515051662, 117120843371763078478302937723081664156428432, 474357350108297944324312588536101685586499210, 246589982606673548069204649716483718901587129, 16680195737189322481806969651675860163860741, 469374372451192677283920555801517105072569431], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 6, 2, 1], [2, 18, 2, 1], [2, 36, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 8, 1, 1], [3, 8, 2, 1], [3, 16, 1, 1], [3, 16, 2, 1], [4, 12, 2, 2], [4, 36, 2, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 2], [6, 2, 4, 1], [6, 3, 2, 2], [6, 3, 4, 1], [6, 6, 1, 2], [6, 6, 2, 3], [6, 6, 4, 2], [6, 8, 1, 1], [6, 8, 2, 2], [6, 8, 4, 1], [6, 16, 1, 1], [6, 16, 2, 2], [6, 16, 4, 1], [6, 18, 4, 1], [6, 24, 4, 1], [6, 24, 8, 1], [6, 36, 4, 1], [12, 12, 4, 4], [12, 12, 8, 2], [12, 36, 4, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_6\\times A_4).C_2^6.C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.202', 'autcent_hash': 202, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '144.183', 'autcentquo_hash': 183, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [2, 6, 2], [2, 18, 2], [2, 36, 2], [3, 1, 2], [3, 2, 3], [3, 8, 3], [3, 16, 3], [4, 12, 4], [4, 36, 2], [6, 1, 6], [6, 2, 9], [6, 3, 8], [6, 6, 16], [6, 8, 9], [6, 16, 9], [6, 18, 4], [6, 24, 12], [6, 36, 4], [12, 12, 32], [12, 36, 4]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '144.183', 'commutator_count': 1, 'commutator_label': '72.47', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 46792, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['288.858', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [2, 6, 1, 2], [2, 18, 1, 2], [2, 36, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 8, 1, 1], [3, 8, 2, 1], [3, 16, 1, 1], [3, 16, 2, 1], [4, 12, 1, 4], [4, 36, 1, 2], [6, 1, 2, 3], [6, 2, 1, 3], [6, 2, 2, 3], [6, 3, 2, 4], [6, 6, 1, 4], [6, 6, 2, 6], [6, 8, 1, 3], [6, 8, 2, 3], [6, 16, 1, 3], [6, 16, 2, 3], [6, 18, 2, 2], [6, 24, 2, 6], [6, 36, 2, 2], [12, 12, 2, 8], [12, 12, 4, 4], [12, 36, 2, 2]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 131040, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '864.4690', 'hash': 46792, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 3, 2, 2], 'inner_gens': [[475167, 208751, 302434, 340271, 505311], [155757, 253045, 137409, 33321, 505311], [475167, 93900, 302434, 329687, 208945], [475167, 560387, 598800, 340271, 505311], [475167, 253045, 609384, 340271, 505311]], 'inner_hash': 183, 'inner_nilpotent': False, 'inner_order': 144, 'inner_split': True, 'inner_tex': 'S_3\\times S_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 54], [3, 24], [4, 12], [6, 30]], 'label': '1728.46792', 'linC_count': 128, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 832, 'linQ_dim': 9, 'linQ_dim_count': 832, 'linR_count': 208, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6*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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 54, 'number_characteristic_subgroups': 50, 'number_conjugacy_classes': 144, 'number_divisions': 86, 'number_normal_subgroups': 106, 'number_subgroup_autclasses': 685, 'number_subgroup_classes': 1295, 'number_subgroups': 10196, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 135], [3, 80], [4, 120], [6, 864], [12, 528]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [21953, 21953, 21953, 21953, 21953], 'outer_gens': [[167853, 77425, 137409, 33321, 241875], [469567, 516485, 302434, 340271, 241875], [475167, 516485, 302434, 340271, 241875], [475167, 516485, 302434, 340271, 505311], [469567, 516485, 598394, 340271, 241875]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [368056, 5063, 368040, 7, 1169302], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 18], [3, 8], [4, 22], [6, 14], [8, 6], [12, 8], [24, 2]], 'representations': {'PC': {'code': 110346604231798676622955622245682015596865631320831614200873, 'gens': [1, 2, 5, 7, 8], 'pres': [9, -2, -2, -2, -3, -2, -3, -2, 2, -3, 397, 46, 542, 74, 579, 2713, 130, 2606, 31767, 2310, 1374, 1339, 1996, 214]}, 'GLZN': {'d': 2, 'p': 28, 'gens': [214622, 22149, 548825, 475167, 167853, 22345, 21977, 33321, 285389]}, 'Perm': {'d': 16, 'gens': [5165, 180583603209, 120, 43545600, 16, 93405312000, 45360, 1313901388800, 2789705318400]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6\\times D_6:S_4', 'transitive_degree': 144, '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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 6, 12, 2, 6, 6, 2], 'aut_gens': [[1, 6, 72], [37, 282, 108], [25, 390, 72], [5, 114, 108], [13, 318, 396], [29, 186, 72], [269, 258, 360], [13, 30, 72]], 'aut_group': None, 'aut_hash': 8142848205473677161, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2304, 'aut_permdeg': 26, 'aut_perms': [196860533720901685151935352, 2515258693556483882215439, 530945821627064109220250, 240345314731180084867106349, 77736912152298522939625096, 97439727930265472931925075, 240556576587829282165235904], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 6, 2, 1], [2, 18, 2, 1], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [4, 6, 2, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 1, 2], [6, 2, 2, 4], [6, 2, 4, 2], [6, 4, 1, 1], [6, 4, 2, 2], [6, 4, 4, 1], [6, 6, 4, 2], [6, 6, 8, 1], [6, 18, 4, 1], [12, 6, 4, 2], [12, 6, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_6^2.C_2^5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.202', 'autcent_hash': 202, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '36.10', 'autcentquo_hash': 10, 'autcentquo_nilpotent': False, 'autcentquo_order': 36, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 2], [2, 18, 2], [3, 1, 2], [3, 2, 6], [3, 4, 3], [4, 6, 2], [6, 1, 6], [6, 2, 18], [6, 4, 9], [6, 6, 16], [6, 18, 4], [12, 6, 16]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '36.10', 'commutator_count': 1, 'commutator_label': '18.5', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 656, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['72.23', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 2], [2, 18, 1, 2], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [4, 6, 1, 2], [6, 1, 2, 3], [6, 2, 1, 6], [6, 2, 2, 6], [6, 4, 1, 3], [6, 4, 2, 3], [6, 6, 2, 8], [6, 18, 2, 2], [12, 6, 2, 4], [12, 6, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8736, 'exponent': 12, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '216.170', 'hash': 656, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 3], 'inner_gens': [[1, 66, 72], [13, 6, 360], [1, 150, 72]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 36, 'inner_split': True, 'inner_tex': 'S_3^2', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 54], [4, 12]], 'label': '432.656', 'linC_count': 192, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 16, 'linQ_dim': 6, 'linQ_dim_count': 16, 'linR_count': 136, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6^2.D6', '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': 34, 'number_characteristic_subgroups': 36, 'number_conjugacy_classes': 90, 'number_divisions': 54, 'number_normal_subgroups': 80, 'number_subgroup_autclasses': 180, 'number_subgroup_classes': 306, 'number_subgroups': 1120, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 51], [3, 26], [4, 12], [6, 246], [12, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[221, 222, 360], [217, 6, 72], [5, 6, 72], [1, 30, 360], [221, 6, 108]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [766096, 23, 806520, 806407, 1174342], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 18], [4, 22], [8, 6]], 'representations': {'PC': {'code': 20936774360428536126890953528997, 'gens': [1, 3, 6], 'pres': [7, -2, -3, -2, -2, -3, -2, -3, 14, 1388, 58, 1683, 80, 1684, 2539, 124, 2372]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101736038821652, 24992906222180337, 41624323485457081]}, 'GLZN': {'d': 2, 'p': 18, 'gens': [99161, 68839, 40831, 6083, 5941, 5995, 42997]}, 'Perm': {'d': 15, 'gens': [41064, 1465, 39916800, 93405312000, 2424, 3, 403200]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.D_6', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
