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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.3509', 'ambient_counter': 3509, 'ambient_order': 1344, 'ambient_tex': 'C_{28}.(S_3\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 28, 'counter': 132, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.3509.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.3509', 'aut_centralizer_order': 10752, 'aut_label': '48.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 10752, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1', '336.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2985, 8015, 2521, 8844, 3177, 8020, 7031, 3230], 'generators': [8, 192, 672], 'label': '1344.3509.48.a1.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normal_contains': ['96.a1.a1', '96.c1.a1', '96.b1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '336.157', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.14', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '28.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [6, 6], 'aut_gens': [[1, 2], [14, 9], [15, 13]], 'aut_group': '36.12', 'aut_hash': 12, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 36, 'aut_permdeg': 8, 'aut_perms': [750, 10081], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [7, 1, 6, 1], [14, 1, 18, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_6\\times S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '36.12', 'autcent_hash': 12, 'autcent_nilpotent': False, 'autcent_order': 36, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_6\\times 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], [7, 1, 6], [14, 1, 18]], 'center_label': '28.4', 'center_order': 28, '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', '7.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [7, 1, 6, 1], [14, 1, 6, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 8, 'exponent': 14, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '28.4', 'hash': 4, '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, 28]], 'label': '28.4', 'linC_count': 144, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 6, 'linQ_dim': 7, 'linQ_dim_count': 6, 'linR_count': 18, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C14', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 28, 'number_divisions': 8, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 10, 'number_subgroups': 10, 'old_label': None, 'order': 28, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 3], [7, 6], [14, 18]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[14, 9], [15, 13]], 'outer_group': '36.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 36, 'outer_permdeg': 8, 'outer_perms': [750, 10081], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [6, 4]], 'representations': {'PC': {'code': 7349, 'gens': [1, 2], 'pres': [3, -2, -2, -7, 16]}, 'GLFp': {'d': 2, 'p': 29, 'gens': [536562, 682893]}, 'Perm': {'d': 11, 'gens': [3628800, 40320, 4320]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 14], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{14}', 'transitive_degree': 28, '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': 2, 'aut_exponent': 84, 'aut_gen_orders': [6, 6, 6, 12, 2, 6, 12, 14, 6, 6], 'aut_gens': [[1, 2, 4, 16], [105, 2, 796, 1264], [537, 10, 1132, 368], [1249, 10, 676, 848], [625, 10, 1236, 80], [1065, 10, 12, 208], [729, 2, 452, 752], [1017, 682, 124, 272], [433, 682, 1124, 1136], [193, 10, 116, 496], [1057, 2, 684, 1168]], 'aut_group': None, 'aut_hash': 5255589997166976132, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 64512, 'aut_permdeg': 84, 'aut_perms': [1275401750957261115136721669845171474287515341701916626487102097004900864939811119590980417274102522317429914595737117178442253, 1615451947090416047143376101051695426949697630465964504259896127158530081847569489959764595592444154956700196810288602944959155, 663540086784795003296884443720249094778173736276876854718531663879871622053419957639381848052520033582279384810824643538311673, 643939399952014131051436515280700647064069906253641737944359209331676196469811753598761001944714973272371014577849671131124453, 635618228240932936629191149841448065095996002364321009559182245882858929868044776192108959453567130427359472744074129108307007, 1297520952894362232514989005676540117588595193358690370198814784353213082226532806130901080455069378532946415195084568030922605, 1593413775528483602321951357997219616014071685977473307326611561968456608515551587259117020168993136823866703579160256417890318, 644901186325416876085412252132345073822403268719447560369429830921238064185370740931152334142814084932902457187468379991919380, 1616696961118547536329066163904475706881505188708836710080480223141675516567762398958505495660320482539678846805586285996770530, 36092897539408620692241934244904489575148169599017927536069167075085105187667698503115214501610164932008311632437042457285107], 'aut_phi_ratio': 168.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [2, 56, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 24, 1, 2], [4, 56, 1, 1], [6, 2, 1, 3], [6, 4, 2, 1], [6, 56, 2, 1], [7, 2, 3, 1], [8, 84, 2, 2], [12, 4, 1, 2], [12, 4, 2, 1], [12, 56, 2, 1], [14, 2, 3, 3], [14, 4, 6, 1], [21, 4, 3, 1], [28, 4, 3, 2], [28, 4, 6, 1], [28, 24, 6, 2], [42, 4, 3, 3], [42, 4, 12, 1], [84, 4, 6, 2], [84, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '1008.906', 'autcentquo_hash': 906, 'autcentquo_nilpotent': False, 'autcentquo_order': 1008, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [2, 56, 1], [3, 2, 1], [4, 2, 2], [4, 4, 1], [4, 24, 2], [4, 56, 1], [6, 2, 3], [6, 4, 2], [6, 56, 2], [7, 2, 3], [8, 84, 4], [12, 4, 4], [12, 56, 2], [14, 2, 9], [14, 4, 6], [21, 4, 3], [28, 4, 12], [28, 24, 12], [42, 4, 21], [84, 4, 24]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '336.157', 'commutator_count': 2, 'commutator_label': '168.39', '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', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3509, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [2, 56, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 24, 1, 2], [4, 56, 1, 1], [6, 2, 1, 3], [6, 4, 2, 1], [6, 56, 2, 1], [7, 2, 3, 1], [8, 84, 1, 2], [8, 84, 2, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 56, 2, 1], [14, 2, 3, 3], [14, 4, 6, 1], [21, 4, 3, 1], [28, 4, 3, 2], [28, 4, 6, 1], [28, 24, 6, 2], [42, 4, 3, 3], [42, 4, 12, 1], [84, 4, 6, 2], [84, 4, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 10752, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '168.50', 'hash': 3509, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 2, 42], 'inner_gens': [[1, 10, 340, 880], [9, 2, 684, 16], [1009, 682, 4, 1136], [481, 2, 228, 16]], 'inner_hash': 157, 'inner_nilpotent': False, 'inner_order': 336, 'inner_split': True, 'inner_tex': 'C_{42}:D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 38], [4, 74]], 'label': '1344.3509', 'linC_count': 96, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 80, 'linQ_dim': 14, 'linQ_dim_count': 36, 'linR_count': 96, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C28.(S3*D4)', '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, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 42, 'number_characteristic_subgroups': 64, 'number_conjugacy_classes': 120, 'number_divisions': 43, 'number_normal_subgroups': 66, 'number_subgroup_autclasses': 224, 'number_subgroup_classes': 240, 'number_subgroups': 1684, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 63], [3, 2], [4, 112], [6, 126], [7, 6], [8, 336], [12, 128], [14, 42], [21, 12], [28, 336], [42, 84], [84, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 4, 464], [673, 2, 4, 16], [337, 10, 4, 688], [9, 2, 4, 16], [1, 10, 4, 16], [1, 2, 4, 1168]], 'outer_group': '192.1543', 'outer_hash': 1543, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 15, 'outer_perms': [482671464, 3628800, 41064, 87178291200, 744, 27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 7], [6, 4], [8, 2], [12, 8], [24, 4], [48, 2]], 'representations': {'PC': {'code': 24285089844316068224240353832642649091516840465318086865931, 'gens': [1, 2, 3, 5], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -7, 161, 8162, 8218, 66, 35204, 11380, 116, 19973, 11157, 141, 46598, 7190, 222, 73735]}, 'Perm': {'d': 22, 'gens': [2439325304684676007, 6276135616, 14933642, 23, 91578240, 135732240, 93405312000, 55969571858264064000]}}, 'schur_multiplier': [2, 2], '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_{28}.(S_3\\times D_4)', 'transitive_degree': 672, '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': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 12], 'aut_gens': [[1, 2, 8], [25, 26, 8], [1, 2, 12], [1, 2, 40], [5, 6, 8], [25, 18, 12]], 'aut_group': '192.1147', 'aut_hash': 1147, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 192, 'aut_permdeg': 11, 'aut_perms': [21144, 12501360, 8361601, 15301704, 19436403], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 6, 2, 1], [3, 2, 1, 1], [4, 6, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 2, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4:D_6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 6, 2], [3, 2, 1], [4, 6, 2], [6, 2, 7]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 43, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['24.8', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 6, 1, 2], [3, 2, 1, 1], [4, 6, 1, 2], [6, 2, 1, 3], [6, 2, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 168, 'exponent': 12, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '24.14', 'hash': 43, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 3], 'inner_gens': [[1, 6, 8], [5, 2, 40], [1, 18, 8]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': False, 'inner_tex': 'D_6', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 10]], 'label': '48.43', 'linC_count': 16, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 4, 'linQ_dim': 4, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6:D4', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 10, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 18, 'number_divisions': 16, 'number_normal_subgroups': 27, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 54, 'number_subgroups': 108, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 19], [3, 2], [4, 12], [6, 14]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[25, 26, 8], [1, 2, 12], [5, 26, 8], [5, 2, 8]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [6, 289, 1, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 2]], 'representations': {'PC': {'code': 2906379043649, 'gens': [1, 2, 4], 'pres': [5, -2, -2, -2, -2, -3, 61, 26, 408, 58, 409]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16563488, 35813463, 7233663]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [34720862, 6536214, 34603218, 16771677, 34409418]}, 'Perm': {'d': 9, 'gens': [5045, 120, 127, 16, 45360]}}, 'schur_multiplier': [2, 2, 2], '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:D_4', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
