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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2916.ev', 'ambient_counter': 126, 'ambient_order': 2916, 'ambient_tex': 'C_9^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 243, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2916.ev.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.31', 'subgroup_hash': 31, 'subgroup_order': 243, 'subgroup_tex': 'C_3\\times C_9^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '2916.ev', 'aut_centralizer_order': 243, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '108.42', 'aut_weyl_index': 243, 'centralizer': '12.b1.a1', 'complements': ['243.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.c1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['36.a1.a1', '36.c1.a1', '36.f1.a1', '36.l1.a1', '36.m1.a1', '36.n1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3954, 7040, 5627, 2896, 7845, 5731, 6951, 2868], 'generators': [2604, 252, 2268], 'label': '2916.ev.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.c1.a1'], 'normal_contains': ['36.a1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '2916.ev', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '243.31', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 6, 'aut_exponent': 72, 'aut_gen_orders': [6, 6, 12, 4, 3, 3, 3, 3, 3, 3, 3, 3], 'aut_gens': [[1, 3, 27], [2, 186, 207], [2, 93, 132], [1, 222, 52], [1, 109, 8], [181, 183, 27], [1, 21, 189], [1, 175, 207], [100, 4, 47], [91, 4, 191], [100, 166, 47], [10, 165, 108], [19, 93, 207]], 'aut_group': '629856.lf', 'aut_hash': 9120032771072783391, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 629856, 'aut_permdeg': 65, 'aut_perms': [1023561438233204727306998525206406952798557479635474802680559633383884637900571955381794080, 1650413416996166131692117522391172814941241413361425414051079568079598038554546929493952095, 4376671015498473525274882040914042269778091072312205746480132338315074740975961782807022048, 1047419192740014414553317984120052979491894764095780594940595102422237974647261561467642888, 13910244249264788944998469978205423530573490257392756408389713819528891183494087663042504, 1222934822600510437989348604368, 1430127066712564314807868062499023625797267599198917146535903183257763015886307422877533454, 420376921588431233932508956394474631235112049548138369753007060238010519240103518569753368, 547546083618930691785369798333962458052076106068589637511822454261166889994692027132752304, 12211385033284770681305012506706410250285508008727800603104118083798201961207390569753368, 14193990048533629578632503298517248334495631056441785569450845472486687709275776274356726, 14162521302753289466132576643583823247322198182405362234803251520227993605017130690905224], 'aut_phi_ratio': 3888.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 8, 1], [3, 1, 18, 1], [9, 1, 216, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.(C_2\\times C_3^4:\\GL(2,3))', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 72, 'autcent_group': '629856.lf', 'autcent_hash': 9120032771072783391, 'autcent_nilpotent': False, 'autcent_order': 629856, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_3^4.(C_2\\times C_3^4:\\GL(2,3))', '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], [3, 1, 26], [9, 1, 216]], 'center_label': '243.31', 'center_order': 243, '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': ['3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 31, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['9.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 13], [9, 1, 6, 36]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 13, 'exponent': 9, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '27.5', 'hash': 31, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 3, 27], [1, 3, 27], [1, 3, 27]], '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, 243]], 'label': '243.31', 'linC_count': 1364688, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 4374, 'linQ_dim': 14, 'linQ_dim_count': 4374, 'linR_count': 170586, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3*C9^2', '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': 243, 'number_divisions': 50, 'number_normal_subgroups': 126, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 126, 'number_subgroups': 126, 'old_label': None, 'order': 243, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 26], [9, 216]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 72, 'outer_gen_orders': [6, 6, 12, 4, 3, 3, 3, 3, 3, 3, 3, 3], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[2, 186, 207], [2, 93, 132], [1, 222, 52], [1, 109, 8], [181, 183, 27], [1, 21, 189], [1, 175, 207], [100, 4, 47], [91, 4, 191], [100, 166, 47], [10, 165, 108], [19, 93, 207]], 'outer_group': '629856.lf', 'outer_hash': 9120032771072783391, 'outer_nilpotent': False, 'outer_order': 629856, 'outer_permdeg': 65, 'outer_perms': [1023561438233204727306998525206406952798557479635474802680559633383884637900571955381794080, 1650413416996166131692117522391172814941241413361425414051079568079598038554546929493952095, 4376671015498473525274882040914042269778091072312205746480132338315074740975961782807022048, 1047419192740014414553317984120052979491894764095780594940595102422237974647261561467642888, 13910244249264788944998469978205423530573490257392756408389713819528891183494087663042504, 1222934822600510437989348604368, 1430127066712564314807868062499023625797267599198917146535903183257763015886307422877533454, 420376921588431233932508956394474631235112049548138369753007060238010519240103518569753368, 547546083618930691785369798333962458052076106068589637511822454261166889994692027132752304, 12211385033284770681305012506706410250285508008727800603104118083798201961207390569753368, 14193990048533629578632503298517248334495631056441785569450845472486687709275776274356726, 14162521302753289466132576643583823247322198182405362234803251520227993605017130690905224], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_3^4.(C_2\\times C_3^4:\\GL(2,3))', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 21, 'pgroup': 3, 'primary_abelian_invariants': [3, 9, 9], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 13], [6, 36]], 'representations': {'PC': {'code': 4128778, 'gens': [1, 2, 4], 'pres': [5, 3, 3, 3, 3, 3, 36, 78]}, 'GLZN': {'d': 2, 'p': 38, 'gens': [54881, 54879, 384111, 493857, 247669]}, 'GLZq': {'d': 2, 'q': 27, 'gens': [140464, 196840, 203896, 78736, 19927]}, 'Perm': {'d': 21, 'gens': [2978882210304000, 357120, 4865804016353280000, 711549292608000, 80884]}}, 'schur_multiplier': [3, 3, 9], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 9, 9], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_9^2', 'transitive_degree': 243, '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': 3, 'aut_exponent': 18, 'aut_gen_orders': [18, 3, 6], 'aut_gens': [[1, 2, 12, 36, 324], [1205, 262, 1968, 792, 1728], [1757, 62, 228, 1656, 1404], [1293, 142, 2172, 2880, 324]], 'aut_group': None, 'aut_hash': 1415438368598865940, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 26244, 'aut_permdeg': 108, 'aut_perms': [137342979149916079220739251304326734595566297902824269596750947599258432044861198433607852100130479792789929965013570084968071817663114232356611852110827958019922668001275672, 90043010124294963280031501447884637625465217917251357549485027598641062368039961974290857582813204615391443317684991825549087790917653951863754659563650676592586831409784795, 118470645692172679890084881117654532674096509691635847388690911682872660785867472588124845130274900176076522015603566046522995169054689456359026303595857799870019905786542126], 'aut_phi_ratio': 27.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 27, 1, 1], [2, 81, 1, 1], [2, 243, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 6, 3, 1], [3, 54, 1, 1], [3, 108, 1, 1], [6, 54, 1, 1], [6, 54, 3, 1], [6, 162, 1, 1], [6, 486, 1, 1], [9, 2, 3, 1], [9, 6, 3, 3], [9, 12, 1, 1], [9, 12, 3, 1], [9, 12, 9, 1], [9, 108, 1, 3], [18, 54, 3, 3], [18, 162, 3, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_3\\times C_9).C_3^5.C_2^2', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': None, 'autcentquo_hash': 1415438368598865940, 'autcentquo_nilpotent': False, 'autcentquo_order': 26244, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': '\\He_3:C_3.C_3^4.C_2^2', 'cc_stats': [[1, 1, 1], [2, 27, 1], [2, 81, 1], [2, 243, 1], [3, 2, 1], [3, 6, 4], [3, 54, 1], [3, 108, 1], [6, 54, 4], [6, 162, 1], [6, 486, 1], [9, 2, 3], [9, 6, 9], [9, 12, 13], [9, 108, 3], [18, 54, 9], [18, 162, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '2916.ev', 'commutator_count': 1, 'commutator_label': '729.397', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 126, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 27, 1, 1], [2, 81, 1, 1], [2, 243, 1, 1], [3, 2, 1, 1], [3, 6, 1, 4], [3, 54, 1, 1], [3, 108, 1, 1], [6, 54, 1, 4], [6, 162, 1, 1], [6, 486, 1, 1], [9, 2, 3, 1], [9, 6, 3, 3], [9, 12, 1, 1], [9, 12, 3, 4], [9, 108, 1, 1], [9, 108, 2, 1], [18, 54, 3, 3], [18, 162, 3, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 18, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 1, 18], [12, 1, 9]], 'familial': False, 'frattini_label': '27.2', 'frattini_quotient': '108.40', 'hash': 6714582029697048367, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [18, 6, 3, 9, 9], 'inner_gens': [[1, 286, 240, 36, 2808], [845, 2, 2076, 396, 2808], [133, 1214, 12, 36, 324], [1, 2882, 12, 36, 324], [757, 758, 12, 36, 324]], 'inner_hash': 6714582029697048367, 'inner_nilpotent': False, 'inner_order': 2916, 'inner_split': True, 'inner_tex': 'C_9^2.S_3^2', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 18, 'irrQ_dim': 18, 'irrR_degree': 6, 'irrep_stats': [[1, 4], [2, 6], [4, 5], [6, 30], [12, 12]], 'label': '2916.ev', 'linC_count': 18, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 6, 'linQ_dim': 18, 'linQ_dim_count': 6, 'linR_count': 18, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C9^2.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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 57, 'number_divisions': 32, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 224, 'number_subgroup_classes': 262, 'number_subgroups': 9245, 'old_label': None, 'order': 2916, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 351], [3, 188], [6, 864], [9, 540], [18, 972]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 3, 'outer_gen_orders': [3, 3], 'outer_gen_pows': [1465, 0], 'outer_gens': [[1633, 10, 2184, 36, 2808], [217, 2, 984, 144, 1296]], 'outer_group': '9.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 9, 'outer_permdeg': 6, 'outer_perms': [3, 144], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 3], [6, 6], [8, 1], [18, 8], [36, 4]], 'representations': {'PC': {'code': '14018937435406837908756861921671689613873177463828156009359945471775462207', 'gens': [1, 2, 4, 5, 7], 'pres': [8, -2, -2, -3, -3, -3, -3, 3, -3, 288, 4577, 41, 18338, 7683, 33227, 979, 7932, 3620, 156, 28525, 12981, 157254, 78638, 34798, 222, 124423, 62223]}, 'Perm': {'d': 27, 'gens': [6694988457505281749541106563, 6307183476091692578629100285]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_9^2.S_3^2', 'transitive_degree': 27, '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': '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, 6], 'aut_gens': [[1, 2], [1, 10], [3, 2]], 'aut_group': '12.4', 'aut_hash': 4, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12, 'aut_permdeg': 5, 'aut_perms': [6, 49], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 2, 1], [3, 2, 1, 1], [6, 2, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': '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, 1], [2, 3, 2], [3, 2, 1], [6, 2, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [['2.1', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [6, 2, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 6, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '12.4', 'hash': 4, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 10], [5, 2]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 4], [2, 2]], 'label': '12.4', 'linC_count': 1, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D6', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 6, 'number_divisions': 6, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 10, 'number_subgroups': 16, 'old_label': None, 'order': 12, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 7], [3, 2], [6, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[7, 2]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 5, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2]], 'representations': {'PC': {'code': 43377, 'gens': [1, 2], 'pres': [3, -2, -2, -3, 61, 16, 74]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [17, 35]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [31, 55, 56]}, 'Perm': {'d': 5, 'gens': [6, 1, 30]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_6', 'transitive_degree': 6, 'wreath_data': None, 'wreath_product': False}
