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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1142', 'ambient_counter': 1142, 'ambient_order': 672, 'ambient_tex': 'D_{12}:D_{14}', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 1, 'counter': 136, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '672.1142.672.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '672.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '672.1142', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1142, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}:D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
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{'ambient': '672.1142', 'aut_centralizer_order': None, 'aut_label': '672.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '224.a1', '336.a1', '336.b1', '336.c1', '336.d1', '336.e1'], 'contains': [], 'core': '672.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7962, 4569, 2349, 5963], 'generators': [], 'label': '672.1142.672.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '672.a1', 'normal_contained_in': ['96.a1', '224.a1', '336.a1', '336.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '672.a1', 'projective_image': '672.1142', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.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': '1.1', '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': [], '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]], '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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 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': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, '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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [12, 12, 12, 12, 12, 4, 28], 'aut_gens': [[1, 2, 4, 8], [1, 59, 172, 105], [337, 619, 604, 184], [337, 282, 653, 89], [337, 562, 197, 137], [337, 2, 197, 200], [337, 507, 28, 328], [1, 59, 220, 233]], 'aut_group': None, 'aut_hash': 8662371451100837692, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 64512, 'aut_permdeg': 80, 'aut_perms': [32664639212577316333381797207535151298202153286629216931136858717095929074771401374423178247788525446562436088750669529, 53278242344887085974062059437011752747801434179762500616680129220672384381673344911150465770076102202981402005999478606, 57048905165874532556914336251469491853406795764984225369062854654425547071152123701800747070295734902843463775674181865, 37101315673896065253613100128794800388500900425778935245142207148421965044108474715494137459035416835611189310944575581, 9293653620839170149510107227906095974627926733950646129045784489170198652313426030525208897859673210775072541650736, 4314990469141745317786664265141713999302771927808913417668324193843366081740635154651596310922565164233352396897552635, 32664639212433815415389099609245116753560850946618469012186228783321235424303010445324094426234814447556031076301933671], 'aut_phi_ratio': 336.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 6, 4, 1], [2, 14, 4, 1], [2, 21, 4, 1], [3, 2, 1, 1], [4, 2, 2, 1], [4, 42, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 28, 4, 1], [7, 2, 3, 1], [12, 4, 2, 1], [14, 2, 3, 1], [14, 2, 6, 1], [14, 12, 12, 1], [21, 4, 3, 1], [28, 4, 6, 1], [42, 4, 3, 1], [42, 4, 6, 1], [84, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1578', 'autcent_hash': 1578, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '504.162', 'autcentquo_hash': 162, 'autcentquo_nilpotent': False, 'autcentquo_order': 504, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 4], [2, 14, 4], [2, 21, 4], [3, 2, 1], [4, 2, 2], [4, 42, 2], [6, 2, 3], [6, 28, 4], [7, 2, 3], [12, 4, 2], [14, 2, 9], [14, 12, 12], [21, 4, 3], [28, 4, 6], [42, 4, 9], [84, 4, 12]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '168.50', 'commutator_count': 1, 'commutator_label': '42.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1142, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['336.150', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 4], [2, 14, 1, 4], [2, 21, 1, 4], [3, 2, 1, 1], [4, 2, 1, 2], [4, 42, 1, 2], [6, 2, 1, 3], [6, 28, 1, 4], [7, 2, 3, 1], [12, 4, 1, 2], [14, 2, 3, 3], [14, 12, 3, 4], [21, 4, 3, 1], [28, 4, 3, 2], [42, 4, 3, 3], [84, 4, 6, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 933660, 'exponent': 84, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '336.219', 'hash': 1142, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [1, 2, 2, 42], 'inner_gens': [[1, 2, 4, 8], [1, 2, 4, 568], [1, 2, 4, 440], [1, 114, 244, 8]], 'inner_hash': 50, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': False, 'inner_tex': 'S_3\\times D_{14}', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 36], [4, 32]], 'label': '672.1142', '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': 'D12:D14', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 22, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 84, 'number_divisions': 46, 'number_normal_subgroups': 124, 'number_subgroup_autclasses': 136, 'number_subgroup_classes': 472, 'number_subgroups': 3752, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 167], [3, 2], [4, 88], [6, 118], [7, 6], [12, 8], [14, 162], [21, 12], [28, 24], [42, 36], [84, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 4, 4, 6], 'outer_gen_pows': [504, 0, 0, 0, 0], 'outer_gens': [[1, 170, 172, 8], [337, 2, 4, 8], [337, 171, 508, 344], [1, 171, 173, 9], [1, 2, 4, 584]], 'outer_group': '384.16843', 'outer_hash': 16843, 'outer_nilpotent': True, 'outer_order': 384, 'outer_permdeg': 15, 'outer_perms': [19200343680, 31661644560, 25434261600, 126616453200, 295076598508], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6.D_4^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 2], [6, 8], [12, 6], [24, 2]], 'representations': {'PC': {'code': 5256288577215877918352049933340291052555, 'gens': [1, 2, 3, 4], 'pres': [7, -2, -2, -2, -2, -2, -3, -7, 7962, 3097, 80, 8131, 1838, 102, 5388, 4387, 166, 7076]}, 'GLZN': {'d': 2, 'p': 42, 'gens': [963157, 2173837, 74411, 2148581, 74341, 1667863, 963271]}, 'Perm': {'d': 16, 'gens': [6227025966, 6230649600, 1313901388801, 2795932339201, 1313901388800, 43545600, 50646]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{12}:D_{14}', 'transitive_degree': 168, '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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [12, 12, 12, 12, 12, 4, 28], 'aut_gens': [[1, 2, 4, 8], [1, 59, 172, 105], [337, 619, 604, 184], [337, 282, 653, 89], [337, 562, 197, 137], [337, 2, 197, 200], [337, 507, 28, 328], [1, 59, 220, 233]], 'aut_group': None, 'aut_hash': 8662371451100837692, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 64512, 'aut_permdeg': 80, 'aut_perms': [32664639212577316333381797207535151298202153286629216931136858717095929074771401374423178247788525446562436088750669529, 53278242344887085974062059437011752747801434179762500616680129220672384381673344911150465770076102202981402005999478606, 57048905165874532556914336251469491853406795764984225369062854654425547071152123701800747070295734902843463775674181865, 37101315673896065253613100128794800388500900425778935245142207148421965044108474715494137459035416835611189310944575581, 9293653620839170149510107227906095974627926733950646129045784489170198652313426030525208897859673210775072541650736, 4314990469141745317786664265141713999302771927808913417668324193843366081740635154651596310922565164233352396897552635, 32664639212433815415389099609245116753560850946618469012186228783321235424303010445324094426234814447556031076301933671], 'aut_phi_ratio': 336.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 6, 4, 1], [2, 14, 4, 1], [2, 21, 4, 1], [3, 2, 1, 1], [4, 2, 2, 1], [4, 42, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 28, 4, 1], [7, 2, 3, 1], [12, 4, 2, 1], [14, 2, 3, 1], [14, 2, 6, 1], [14, 12, 12, 1], [21, 4, 3, 1], [28, 4, 6, 1], [42, 4, 3, 1], [42, 4, 6, 1], [84, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1578', 'autcent_hash': 1578, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '504.162', 'autcentquo_hash': 162, 'autcentquo_nilpotent': False, 'autcentquo_order': 504, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 4], [2, 14, 4], [2, 21, 4], [3, 2, 1], [4, 2, 2], [4, 42, 2], [6, 2, 3], [6, 28, 4], [7, 2, 3], [12, 4, 2], [14, 2, 9], [14, 12, 12], [21, 4, 3], [28, 4, 6], [42, 4, 9], [84, 4, 12]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '168.50', 'commutator_count': 1, 'commutator_label': '42.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1142, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['336.150', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 4], [2, 14, 1, 4], [2, 21, 1, 4], [3, 2, 1, 1], [4, 2, 1, 2], [4, 42, 1, 2], [6, 2, 1, 3], [6, 28, 1, 4], [7, 2, 3, 1], [12, 4, 1, 2], [14, 2, 3, 3], [14, 12, 3, 4], [21, 4, 3, 1], [28, 4, 3, 2], [42, 4, 3, 3], [84, 4, 6, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 933660, 'exponent': 84, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '336.219', 'hash': 1142, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [1, 2, 2, 42], 'inner_gens': [[1, 2, 4, 8], [1, 2, 4, 568], [1, 2, 4, 440], [1, 114, 244, 8]], 'inner_hash': 50, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': False, 'inner_tex': 'S_3\\times D_{14}', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 36], [4, 32]], 'label': '672.1142', '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': 'D12:D14', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 22, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 84, 'number_divisions': 46, 'number_normal_subgroups': 124, 'number_subgroup_autclasses': 136, 'number_subgroup_classes': 472, 'number_subgroups': 3752, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 167], [3, 2], [4, 88], [6, 118], [7, 6], [12, 8], [14, 162], [21, 12], [28, 24], [42, 36], [84, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 4, 4, 6], 'outer_gen_pows': [504, 0, 0, 0, 0], 'outer_gens': [[1, 170, 172, 8], [337, 2, 4, 8], [337, 171, 508, 344], [1, 171, 173, 9], [1, 2, 4, 584]], 'outer_group': '384.16843', 'outer_hash': 16843, 'outer_nilpotent': True, 'outer_order': 384, 'outer_permdeg': 15, 'outer_perms': [19200343680, 31661644560, 25434261600, 126616453200, 295076598508], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6.D_4^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 2], [6, 8], [12, 6], [24, 2]], 'representations': {'PC': {'code': 5256288577215877918352049933340291052555, 'gens': [1, 2, 3, 4], 'pres': [7, -2, -2, -2, -2, -2, -3, -7, 7962, 3097, 80, 8131, 1838, 102, 5388, 4387, 166, 7076]}, 'GLZN': {'d': 2, 'p': 42, 'gens': [963157, 2173837, 74411, 2148581, 74341, 1667863, 963271]}, 'Perm': {'d': 16, 'gens': [6227025966, 6230649600, 1313901388801, 2795932339201, 1313901388800, 43545600, 50646]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{12}:D_{14}', 'transitive_degree': 168, 'wreath_data': None, 'wreath_product': False}
