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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.8726', 'ambient_counter': 8726, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 8, 'counter': 202, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8726.168.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '168.16', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.8726', 'aut_centralizer_order': None, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '56.c1', '84.a1', '84.d1', '84.g1'], 'contains': ['336.a1', '336.d1'], 'core': '168.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [56, 1008], 'label': '1344.8726.168.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '168.c1', 'normal_contained_in': ['24.c1', '56.c1', '84.a1'], 'normal_contains': ['336.a1', '336.d1'], 'normalizer': '1.a1', 'old_label': '168.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 4], 'aut_gens': [[1, 2], [1, 3], [5, 3]], 'aut_group': '8.3', 'aut_hash': 3, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 8, 'aut_permdeg': 4, 'aut_perms': [1, 22], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [4, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.3', 'autcent_hash': 3, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_4', '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], [4, 1, 4]], 'center_label': '8.2', 'center_order': 8, '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', '2.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 1, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 3, 'exponent': 4, 'exponents_of_order': [3], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '2.1', '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, 8]], 'label': '8.2', 'linC_count': 12, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 4, 'linQ_dim': 3, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C4', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 8, 'number_divisions': 6, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 3], [4, 4]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 3], [5, 3]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [1, 22], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 6, 'pgroup': 2, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2]], 'representations': {'PC': {'code': 34, 'gens': [1, 2], 'pres': [3, -2, 2, -2, 16]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [3362, 16426]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [251, 504]}, 'Perm': {'d': 6, 'gens': [22, 120, 7]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], '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_4', 'transitive_degree': 8, '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, 14, 2, 6, 12, 42, 12, 12], 'aut_gens': [[1, 2, 56, 112], [781, 250, 56, 840], [49, 626, 728, 784], [81, 282, 56, 1232], [721, 1314, 56, 1232], [65, 374, 56, 1232], [41, 1006, 728, 840], [717, 254, 728, 784], [717, 554, 56, 112], [109, 614, 56, 840]], 'aut_group': None, 'aut_hash': 2121436511852193631, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 258048, 'aut_permdeg': 104, 'aut_perms': [8303840898389705740484928163542103387139684783917088888470437693258948262677976031224606134098561325954991621511247304422769044590705518131629535650078121269282060131, 4299024950704383476744776773576073624481889943420956992318805961342786812895181445336316227531810387058189185895754757367879874540161867771127997985865720948812213441, 9501918946219961557304185376334742901092414578091346815198162269000413364899701234718267294782069668456065834965780227593994521736298136554088926009672238805044086172, 4101922582500150168662498425373799360540585441056483023095382516042522508969630664502550078960679288963934318977075403121483181387893389922380205816545823805907167571, 3599991216078086301323184158971678660390324179937130213321250721882632795464269163420721259183067795231386810986065415185278890169740678042414954666949081522477793667, 196118515601451655116599616821251569987491127748712835424044129198031226545883961506591587248331016575984368933289663334366405015102530707899462973478095100532600967, 196121925269386275467281937915151991582038656899249651937611562607069560031675049411551317391969074187533560692938698705956718176390506281482817714132195268253560967, 9503834997700215542452098731315049096647975788705810566733896559977279075469758693343421823627815825821164559239415834933593751001082057620871625736642390163194662411, 4397097079500648341021430275165820567800288473609763804153162008763937417222093988331895932379844683157668555970945606887322784882896886525423123578084865260877786157], 'aut_phi_ratio': 672.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 28, 2, 1], [2, 84, 4, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 28, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 4, 2, 1], [6, 28, 4, 1], [7, 2, 3, 1], [8, 12, 4, 1], [12, 2, 4, 1], [12, 4, 1, 2], [12, 28, 4, 1], [14, 2, 3, 1], [14, 2, 6, 1], [14, 4, 6, 1], [21, 4, 3, 1], [28, 2, 6, 2], [28, 4, 6, 1], [42, 4, 3, 1], [42, 4, 6, 1], [42, 4, 12, 1], [56, 12, 24, 1], [84, 4, 6, 2], [84, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^4\\times C_6).C_2^6', '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': None, 'autcentquo_hash': 5451351369529179689, 'autcentquo_nilpotent': False, 'autcentquo_order': 2016, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^3\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 28, 2], [2, 84, 4], [3, 2, 1], [4, 2, 4], [4, 28, 2], [6, 2, 3], [6, 4, 2], [6, 28, 4], [7, 2, 3], [8, 12, 4], [12, 2, 4], [12, 4, 2], [12, 28, 4], [14, 2, 9], [14, 4, 6], [21, 4, 3], [28, 2, 12], [28, 4, 6], [42, 4, 21], [56, 12, 24], [84, 4, 24]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '336.158', 'commutator_count': 1, 'commutator_label': '84.6', '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': 8726, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['672.445', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 28, 1, 2], [2, 84, 1, 4], [3, 2, 1, 1], [4, 2, 1, 4], [4, 28, 1, 2], [6, 2, 1, 3], [6, 4, 1, 2], [6, 28, 2, 2], [7, 2, 3, 1], [8, 12, 1, 4], [12, 2, 2, 2], [12, 4, 1, 2], [12, 28, 2, 2], [14, 2, 3, 3], [14, 4, 3, 2], [21, 4, 3, 1], [28, 2, 6, 2], [28, 4, 3, 2], [42, 4, 3, 3], [42, 4, 6, 2], [56, 12, 6, 4], [84, 4, 6, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3734640, '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': '4.1', 'frattini_quotient': '336.219', 'hash': 8726, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 28, 1, 6], 'inner_gens': [[1, 726, 56, 112], [5, 2, 56, 1232], [1, 2, 56, 112], [1, 226, 56, 112]], 'inner_hash': 158, 'inner_nilpotent': False, 'inner_order': 336, 'inner_split': False, 'inner_tex': 'C_6:D_{28}', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 68], [4, 66]], 'label': '1344.8726', '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': 'C84.C2^4', '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': 35, 'number_characteristic_subgroups': 46, 'number_conjugacy_classes': 150, 'number_divisions': 60, 'number_normal_subgroups': 160, 'number_subgroup_autclasses': 244, 'number_subgroup_classes': 596, 'number_subgroups': 6388, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 399], [3, 2], [4, 64], [6, 126], [7, 6], [8, 48], [12, 128], [14, 42], [21, 12], [28, 48], [42, 84], [56, 288], [84, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 4, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 336], 'outer_gens': [[57, 734, 56, 168], [57, 58, 728, 168], [1, 2, 56, 560], [29, 30, 56, 112], [1, 58, 56, 112], [57, 30, 56, 112], [1, 394, 56, 112]], 'outer_group': '768.55643', 'outer_hash': 55643, 'outer_nilpotent': True, 'outer_order': 768, 'outer_permdeg': 17, 'outer_perms': [47096395405923, 47358013651200, 24, 90720, 67040185766400, 131784, 355499061840], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^7:C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 20, '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, 6], [6, 8], [8, 2], [12, 12], [24, 2], [48, 2]], 'representations': {'PC': {'code': 1111474624969616811960896991009111401741858293585, 'gens': [1, 2, 5, 6], 'pres': [8, -2, -2, -2, -7, -2, -2, -2, -3, 11617, 41, 17378, 66, 23043, 2715, 29581, 141, 31374, 166, 28687]}, 'Perm': {'d': 20, 'gens': [6423383674282369, 40650529, 1, 1297471, 1658430, 2084766, 518918400, 134491780578355200]}}, 'schur_multiplier': [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': 'C_{84}.C_2^4', 'transitive_degree': 336, '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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 42, 'aut_gen_orders': [2, 2, 6, 42], 'aut_gens': [[1, 2, 56], [29, 2, 56], [1, 2, 112], [1, 34, 112], [41, 142, 56]], 'aut_group': '1008.906', 'aut_hash': 906, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1008, 'aut_permdeg': 14, 'aut_perms': [7, 127, 2405934847, 14530119856], 'aut_phi_ratio': 21.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 14, 1, 1], [2, 42, 1, 1], [3, 2, 1, 1], [4, 6, 1, 1], [6, 2, 1, 1], [6, 14, 2, 1], [7, 2, 3, 1], [14, 2, 3, 1], [21, 4, 3, 1], [28, 6, 6, 1], [42, 4, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_6\\times F_7', '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': 42, 'autcentquo_group': '252.26', 'autcentquo_hash': 26, 'autcentquo_nilpotent': False, 'autcentquo_order': 252, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 14, 1], [2, 42, 1], [3, 2, 1], [4, 6, 1], [6, 2, 1], [6, 14, 2], [7, 2, 3], [14, 2, 3], [21, 4, 3], [28, 6, 6], [42, 4, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '84.8', 'commutator_count': 1, 'commutator_label': '42.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 16, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 14, 1, 1], [2, 42, 1, 1], [3, 2, 1, 1], [4, 6, 1, 1], [6, 2, 1, 1], [6, 14, 2, 1], [7, 2, 3, 1], [14, 2, 3, 1], [21, 4, 3, 1], [28, 6, 6, 1], [42, 4, 3, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 84, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[4, 1, 3]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '84.8', 'hash': 16, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [2, 14, 3], 'inner_gens': [[1, 54, 56], [5, 2, 112], [1, 114, 56]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 84, 'inner_split': True, 'inner_tex': 'S_3\\times D_7', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 17], [4, 6]], 'label': '168.16', 'linC_count': 39, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 6, 'linQ_dim': 10, 'linQ_dim_count': 6, 'linR_count': 15, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3:D28', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 13, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 27, 'number_divisions': 13, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 32, 'number_subgroups': 192, 'old_label': None, 'order': 168, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 57], [3, 2], [4, 6], [6, 30], [7, 6], [14, 6], [21, 12], [28, 36], [42, 12]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 30, 56], [1, 6, 112]], 'outer_group': '12.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [24, 724], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 1], [6, 2], [12, 3]], 'representations': {'PC': {'code': 18583259141820612703, 'gens': [1, 2, 5], 'pres': [5, -2, -2, -2, -7, -3, 541, 26, 782, 42, 963, 1409]}, 'GLZN': {'d': 2, 'p': 28, 'gens': [137866, 329295, 22065, 27658, 598597]}, 'Perm': {'d': 14, 'gens': [6266937727, 12493998720, 19678982400, 403200, 973]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [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:D_{28}', 'transitive_degree': 84, 'wreath_data': None, 'wreath_product': False}
