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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.1492', 'ambient_counter': 1492, 'ambient_order': 960, 'ambient_tex': 'C_{20}.(S_3\\times Q_8)', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 2, 'counter': 191, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.1492.480.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '480.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '480.500', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 500, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{30}:Q_8', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.1492', 'aut_centralizer_order': 30720, 'aut_label': '480.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 30720, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '160.c1.a1', '240.a1.a1', '240.b1.a1', '240.c1.a1', '240.i1.a1', '240.i1.b1'], 'contains': ['960.a1.a1'], 'core': '480.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6943, 4258, 8643, 5148, 6907, 5140, 7210, 4765], 'generators': [96], 'label': '960.1492.480.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '480.c1.a1', 'normal_contained_in': ['96.c1.a1', '160.c1.a1', '240.a1.a1', '240.b1.a1', '240.c1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '480.c1.a1', 'projective_image': '480.500', 'quotient_action_image': '1.1', 'quotient_action_kernel': '480.500', 'quotient_action_kernel_order': 480, 'quotient_fusion': None, 'short_label': '480.c1.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': '2.1', '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': [[1]], '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], [2, 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], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], '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, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 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': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, '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': 60, 'aut_gen_orders': [4, 4, 10, 2, 4, 2, 4, 2, 4, 60], 'aut_gens': [[1, 2, 8, 192], [1, 102, 904, 384], [1, 54, 664, 384], [1, 146, 764, 192], [101, 2, 732, 768], [5, 98, 200, 384], [101, 2, 588, 768], [97, 98, 572, 384], [133, 98, 88, 192], [5, 150, 200, 768], [133, 54, 680, 192]], 'aut_group': None, 'aut_hash': 7312598050044633167, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 30720, 'aut_permdeg': 60, 'aut_perms': [4085376209459534433156274019623716740216037878124371908288454062575034354662007099, 5331172998145928479304943319224266061589868257670654782586834077597980616907525179, 4374493838045490281984765191133184710232789603077744729015061678818585827657686352, 1130178649371894214460436250454993028701798548296485849123962213991943927716258519, 3963471258895845192099554690066901661861206531578116379809066102532961011423817608, 8320662329573915686163166383730163733843141925931994237238113893847521272012616919, 2253706349260025362984679028918535224493481674690163651787497539620971876628517073, 5642307544213165901429613800186801533055572705503944039010526210042248997323527040, 6182411229727728256358957738110781595272087710794015890986119348220560729913731831, 5785687515210142002271313173001011991454529509418839241719785287203200611119167416], 'aut_phi_ratio': 120.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 6, 2, 1], [4, 8, 1, 1], [4, 12, 1, 1], [4, 20, 2, 1], [4, 24, 1, 1], [4, 60, 2, 1], [5, 2, 2, 1], [6, 2, 1, 3], [8, 20, 2, 1], [8, 60, 2, 1], [10, 2, 2, 3], [12, 4, 1, 2], [12, 8, 2, 1], [12, 40, 2, 1], [15, 4, 2, 1], [20, 4, 2, 2], [20, 8, 4, 1], [20, 12, 4, 2], [20, 24, 4, 1], [24, 20, 4, 1], [30, 4, 2, 3], [60, 8, 2, 2], [60, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{15}:(C_2^2.C_2^6.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': 60, 'autcentquo_group': '480.1197', 'autcentquo_hash': 1197, 'autcentquo_nilpotent': False, 'autcentquo_order': 480, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [4, 2, 2], [4, 6, 2], [4, 8, 1], [4, 12, 1], [4, 20, 2], [4, 24, 1], [4, 60, 2], [5, 2, 2], [6, 2, 3], [8, 20, 2], [8, 60, 2], [10, 2, 6], [12, 4, 2], [12, 8, 2], [12, 40, 2], [15, 4, 2], [20, 4, 4], [20, 8, 4], [20, 12, 8], [20, 24, 4], [24, 20, 4], [30, 4, 6], [60, 8, 12]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '240.150', 'commutator_count': 2, 'commutator_label': '120.31', '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', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 1492, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 6, 1, 2], [4, 8, 1, 1], [4, 12, 1, 1], [4, 20, 2, 1], [4, 24, 1, 1], [4, 60, 1, 2], [5, 2, 2, 1], [6, 2, 1, 3], [8, 20, 2, 1], [8, 60, 2, 1], [10, 2, 2, 3], [12, 4, 1, 2], [12, 8, 2, 1], [12, 40, 2, 1], [15, 4, 2, 1], [20, 4, 2, 2], [20, 8, 4, 1], [20, 12, 2, 2], [20, 12, 4, 1], [20, 24, 4, 1], [24, 20, 4, 1], [30, 4, 2, 3], [60, 8, 2, 2], [60, 8, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8064, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '120.42', 'hash': 1492, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 2, 12, 5], 'inner_gens': [[1, 6, 140, 192], [5, 2, 152, 192], [69, 50, 8, 768], [1, 2, 392, 192]], 'inner_hash': 150, 'inner_nilpotent': False, 'inner_order': 240, 'inner_split': True, 'inner_tex': 'D_6:D_{10}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 34], [4, 35], [8, 4]], 'label': '960.1492', 'linC_count': 320, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 126, 'linQ_dim': 14, 'linQ_dim_count': 104, 'linR_count': 8, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C20.(S3*Q8)', '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': 40, 'number_characteristic_subgroups': 60, 'number_conjugacy_classes': 81, 'number_divisions': 43, 'number_normal_subgroups': 66, 'number_subgroup_autclasses': 176, 'number_subgroup_classes': 192, 'number_subgroups': 984, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 220], [5, 4], [6, 6], [8, 160], [10, 12], [12, 104], [15, 8], [20, 240], [24, 80], [30, 24], [60, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 136, 192], [97, 2, 8, 192], [1, 2, 104, 192], [5, 2, 8, 192], [1, 6, 8, 192], [1, 2, 8, 384]], 'outer_group': '128.2319', 'outer_hash': 2319, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 14, 'outer_perms': [362880, 6227020800, 39916800, 127, 5040, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 24, '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, 10], [8, 11], [16, 6]], 'representations': {'PC': {'code': 4167902786921102508603304010772777000506800431890439, 'gens': [1, 2, 4, 8], 'pres': [8, -2, -2, -2, 2, -2, -2, -3, -5, 32, 97, 41, 4483, 2443, 91, 3204, 2252, 116, 7685, 141, 7174, 6175]}, 'Perm': {'d': 24, 'gens': [27083077961278184254824, 55085780431078738750081, 4557190755194842423680, 83436746068083220606080, 4302991486080, 55085780429570322432000, 3, 6504]}}, 'schur_multiplier': [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_{20}.(S_3\\times Q_8)', 'transitive_degree': 960, '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': 60, 'aut_gen_orders': [6, 4, 2, 10, 2, 6, 12, 10, 4], 'aut_gens': [[1, 2, 4, 8], [401, 166, 4, 152], [5, 294, 4, 344], [325, 470, 4, 236], [5, 146, 4, 12], [165, 454, 4, 236], [325, 134, 4, 152], [81, 86, 4, 348], [5, 390, 4, 88], [1, 338, 4, 188]], 'aut_group': None, 'aut_hash': 814302305876374217, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7680, 'aut_permdeg': 36, 'aut_perms': [354618608291552645675402997951573821166959, 281598574912209897398481647743068610994406, 282189386178521437253322220823886892937527, 286026968049692418949721806071318778578002, 310513496320266967944392980195604588165284, 310514285182272049318549330698225084145565, 366123199105008727894759451773618462587574, 327924394892039578780792441178464310055481, 61096686223297473101066066274428284879280], 'aut_phi_ratio': 60.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 30, 2, 1], [3, 2, 1, 1], [4, 4, 1, 1], [4, 6, 2, 1], [4, 10, 2, 1], [4, 12, 1, 1], [4, 20, 1, 1], [4, 60, 1, 1], [5, 2, 2, 1], [6, 2, 1, 3], [10, 2, 2, 3], [12, 4, 2, 1], [12, 20, 2, 2], [15, 4, 2, 1], [20, 4, 4, 1], [20, 12, 4, 2], [30, 4, 2, 3], [60, 4, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6\\times S_3\\times F_5', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '120.36', 'autcentquo_hash': 36, 'autcentquo_nilpotent': False, 'autcentquo_order': 120, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 30, 2], [3, 2, 1], [4, 4, 1], [4, 6, 2], [4, 10, 2], [4, 12, 1], [4, 20, 1], [4, 60, 1], [5, 2, 2], [6, 2, 3], [10, 2, 6], [12, 4, 2], [12, 20, 4], [15, 4, 2], [20, 4, 4], [20, 12, 8], [30, 4, 6], [60, 4, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '120.42', 'commutator_count': 1, 'commutator_label': '60.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 500, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 30, 1, 2], [3, 2, 1, 1], [4, 4, 1, 1], [4, 6, 1, 2], [4, 10, 2, 1], [4, 12, 1, 1], [4, 20, 1, 1], [4, 60, 1, 1], [5, 2, 2, 1], [6, 2, 1, 3], [10, 2, 2, 3], [12, 4, 2, 1], [12, 20, 2, 2], [15, 4, 2, 1], [20, 4, 4, 1], [20, 12, 2, 2], [20, 12, 4, 1], [30, 4, 2, 3], [60, 4, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4032, 'exponent': 60, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '120.42', 'hash': 500, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 2, 1, 30], 'inner_gens': [[1, 2, 4, 88], [1, 2, 4, 236], [1, 2, 4, 8], [401, 262, 4, 8]], 'inner_hash': 42, 'inner_nilpotent': False, 'inner_order': 120, 'inner_split': True, 'inner_tex': 'S_3\\times D_{10}', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 30], [4, 22]], 'label': '480.500', 'linC_count': 32, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 80, 'linQ_dim': 12, 'linQ_dim_count': 117, 'linR_count': 8, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D30:Q8', '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': 30, 'number_characteristic_subgroups': 44, 'number_conjugacy_classes': 60, 'number_divisions': 33, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 128, 'number_subgroup_classes': 148, 'number_subgroups': 780, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 63], [3, 2], [4, 128], [5, 4], [6, 6], [10, 12], [12, 88], [15, 8], [20, 112], [30, 24], [60, 32]], 'outer_abelian': True, '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': [[1, 2, 4, 328], [5, 2, 4, 8], [241, 2, 4, 8], [1, 242, 4, 8], [1, 2, 4, 296]], 'outer_group': '64.260', 'outer_hash': 260, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 12, 'outer_perms': [127, 39916800, 362880, 5040, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 20, '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], [8, 7], [16, 3]], 'representations': {'PC': {'code': 4310008959936876933011467833517479444487, 'gens': [1, 2, 3, 4], 'pres': [7, -2, -2, -2, 2, -2, -3, -5, 1680, 2467, 3314, 80, 6164, 8131, 102, 14789, 9420, 166, 9421]}, 'GLZN': {'d': 2, 'p': 66, 'gens': [6612431, 433456, 14195425, 980031, 11174576, 2331376, 12362371]}, 'Perm': {'d': 20, 'gens': [135936679803729961, 135936679807353607, 263295183882931216, 392327162440012807, 392327162440012800, 43545600, 50520]}}, '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': 'D_{30}:Q_8', 'transitive_degree': 240, 'wreath_data': None, 'wreath_product': False}
