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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9240.a', 'ambient_counter': 1, 'ambient_order': 9240, 'ambient_tex': 'C_{11}\\times D_{420}', 'central': False, 'central_factor': False, 'centralizer_order': 4620, 'characteristic': True, 'core_order': 462, 'counter': 26, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '9240.a.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '462.12', 'subgroup_hash': 12, 'subgroup_order': 462, 'subgroup_tex': 'C_{462}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '9240.a', 'aut_centralizer_order': None, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.b1.b1'], 'contains': ['40.a1.a1', '60.a1.a1', '140.a1.a1', '220.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5249, 4588, 5115, 4370, 2863, 5321, 5279, 4571], 'generators': [4620, 2640, 840, 3080], 'label': '9240.a.20.a1.a1', 'mobius_quo': 1, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.a1', '60.a1.a1', '140.a1.a1', '220.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '420.40', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '462.12', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 30, 'aut_gen_orders': [2, 2, 30], 'aut_gens': [[1], [155], [265], [277]], 'aut_group': '120.47', 'aut_hash': 47, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 120, 'aut_permdeg': 18, 'aut_perms': [3223511245342080, 20922789899520, 202374917156534], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1], [7, 1, 6, 1], [11, 1, 10, 1], [14, 1, 6, 1], [21, 1, 12, 1], [22, 1, 10, 1], [33, 1, 20, 1], [42, 1, 12, 1], [66, 1, 20, 1], [77, 1, 60, 1], [154, 1, 60, 1], [231, 1, 120, 1], [462, 1, 120, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times C_{30}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 30, 'autcent_group': '120.47', 'autcent_hash': 47, 'autcent_nilpotent': True, 'autcent_order': 120, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_{30}', '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], [3, 1, 2], [6, 1, 2], [7, 1, 6], [11, 1, 10], [14, 1, 6], [21, 1, 12], [22, 1, 10], [33, 1, 20], [42, 1, 12], [66, 1, 20], [77, 1, 60], [154, 1, 60], [231, 1, 120], [462, 1, 120]], 'center_label': '462.12', 'center_order': 462, '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', '3.1', '7.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 12, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['2.1', 1], ['3.1', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1], [7, 1, 6, 1], [11, 1, 10, 1], [14, 1, 6, 1], [21, 1, 12, 1], [22, 1, 10, 1], [33, 1, 20, 1], [42, 1, 12, 1], [66, 1, 20, 1], [77, 1, 60, 1], [154, 1, 60, 1], [231, 1, 120, 1], [462, 1, 120, 1]], 'element_repr_type': 'PC', 'elementary': 462, 'eulerian_function': 1, 'exponent': 462, 'exponents_of_order': [1, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 7, 11], 'faithful_reps': [[1, 0, 120]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '462.12', 'hash': 12, 'hyperelementary': 462, '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': 120, 'irrQ_dim': 120, 'irrR_degree': 2, 'irrep_stats': [[1, 462]], 'label': '462.12', 'linC_count': 120, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 7, 'linQ_dim': 18, 'linQ_dim_count': 7, 'linR_count': 60, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C462', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, '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': 16, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 462, 'number_divisions': 16, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 16, 'number_subgroups': 16, 'old_label': None, 'order': 462, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2], [7, 6], [11, 10], [14, 6], [21, 12], [22, 10], [33, 20], [42, 12], [66, 20], [77, 60], [154, 60], [231, 120], [462, 120]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 2, 30], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[155], [265], [277]], 'outer_group': '120.47', 'outer_hash': 47, 'outer_nilpotent': True, 'outer_order': 120, 'outer_permdeg': 18, 'outer_perms': [3223511245342080, 20922789899520, 202374917156534], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{30}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 7, 11], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [6, 2], [10, 2], [12, 2], [20, 2], [60, 2], [120, 2]], 'representations': {'PC': {'code': 1119247430159, 'gens': [1], 'pres': [4, -2, -3, -7, -11, 8, 29, 94]}, 'GLFp': {'d': 2, 'p': 43, 'gens': [481004]}, 'Perm': {'d': 23, 'gens': [1124000727777607680000, 4865804016353280000, 2134124568576000, 36288000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [462], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{462}', 'transitive_degree': 462, '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': '44.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [60, 140, 140, 10, 30, 30, 140], 'aut_gens': [[1, 2], [3125, 386], [6601, 6106], [3301, 6386], [6865, 2182], [859, 358], [1013, 3482], [1519, 1682]], 'aut_group': '10000.dd', 'aut_hash': 4562266160802583006, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 403200, 'aut_permdeg': 430, 'aut_perms': 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'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 210, 2, 1], [3, 2, 1, 1], [4, 2, 1, 1], [5, 2, 2, 1], [6, 2, 1, 1], [7, 2, 3, 1], [10, 2, 2, 1], [11, 1, 10, 1], [12, 2, 2, 1], [14, 2, 3, 1], [15, 2, 4, 1], [20, 2, 4, 1], [21, 2, 6, 1], [22, 1, 10, 1], [22, 210, 20, 1], [28, 2, 6, 1], [30, 2, 4, 1], [33, 2, 10, 1], [35, 2, 12, 1], [42, 2, 6, 1], [44, 2, 10, 1], [55, 2, 20, 1], [60, 2, 8, 1], [66, 2, 10, 1], [70, 2, 12, 1], [77, 2, 30, 1], [84, 2, 12, 1], [105, 2, 24, 1], [110, 2, 20, 1], [132, 2, 20, 1], [140, 2, 24, 1], [154, 2, 30, 1], [165, 2, 40, 1], [210, 2, 24, 1], [220, 2, 40, 1], [231, 2, 60, 1], [308, 2, 60, 1], [330, 2, 40, 1], [385, 2, 120, 1], [420, 2, 48, 1], [462, 2, 60, 1], [660, 2, 80, 1], [770, 2, 120, 1], [924, 2, 120, 1], [1155, 2, 240, 1], [1540, 2, 240, 1], [2310, 2, 240, 1], [4620, 2, 480, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_5^4.C_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 10, 'autcent_group': '40.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 40, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': None, 'autcentquo_hash': 2285439238770837057, 'autcentquo_nilpotent': False, 'autcentquo_order': 10080, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_5\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 210, 2], [3, 2, 1], [4, 2, 1], [5, 2, 2], [6, 2, 1], [7, 2, 3], [10, 2, 2], [11, 1, 10], [12, 2, 2], [14, 2, 3], [15, 2, 4], [20, 2, 4], [21, 2, 6], [22, 1, 10], [22, 210, 20], [28, 2, 6], [30, 2, 4], [33, 2, 10], [35, 2, 12], [42, 2, 6], [44, 2, 10], [55, 2, 20], [60, 2, 8], [66, 2, 10], [70, 2, 12], [77, 2, 30], [84, 2, 12], [105, 2, 24], [110, 2, 20], [132, 2, 20], [140, 2, 24], [154, 2, 30], [165, 2, 40], [210, 2, 24], [220, 2, 40], [231, 2, 60], [308, 2, 60], [330, 2, 40], [385, 2, 120], [420, 2, 48], [462, 2, 60], [660, 2, 80], [770, 2, 120], [924, 2, 120], [1155, 2, 240], [1540, 2, 240], [2310, 2, 240], [4620, 2, 480]], 'center_label': '22.2', 'center_order': 22, 'central_product': True, 'central_quotient': '420.40', 'commutator_count': 1, 'commutator_label': '210.12', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1', '7.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['840.128', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 210, 1, 2], [3, 2, 1, 1], [4, 2, 1, 1], [5, 2, 2, 1], [6, 2, 1, 1], [7, 2, 3, 1], [10, 2, 2, 1], [11, 1, 10, 1], [12, 2, 2, 1], [14, 2, 3, 1], [15, 2, 4, 1], [20, 2, 4, 1], [21, 2, 6, 1], [22, 1, 10, 1], [22, 210, 10, 2], [28, 2, 6, 1], [30, 2, 4, 1], [33, 2, 10, 1], [35, 2, 12, 1], [42, 2, 6, 1], [44, 2, 10, 1], [55, 2, 20, 1], [60, 2, 8, 1], [66, 2, 10, 1], [70, 2, 12, 1], [77, 2, 30, 1], [84, 2, 12, 1], [105, 2, 24, 1], [110, 2, 20, 1], [132, 2, 20, 1], [140, 2, 24, 1], [154, 2, 30, 1], [165, 2, 40, 1], [210, 2, 24, 1], [220, 2, 40, 1], [231, 2, 60, 1], [308, 2, 60, 1], [330, 2, 40, 1], [385, 2, 120, 1], [420, 2, 48, 1], [462, 2, 60, 1], [660, 2, 80, 1], [770, 2, 120, 1], [924, 2, 120, 1], [1155, 2, 240, 1], [1540, 2, 240, 1], [2310, 2, 240, 1], [4620, 2, 480, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 4620, 'exponents_of_order': [3, 1, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7, 11], 'faithful_reps': [[2, 0, 480]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '4620.a', 'hash': 6816930612416858155, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 210, 'inner_gen_orders': [2, 210], 'inner_gens': [[1, 838], [8405, 2]], 'inner_hash': 40, 'inner_nilpotent': False, 'inner_order': 420, 'inner_split': True, 'inner_tex': 'D_{210}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 960, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 44], [2, 2299]], 'label': '9240.a', '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': True, 'monomial': True, 'name': 'C11*D420', '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, 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, 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': 50, 'number_characteristic_subgroups': 50, 'number_conjugacy_classes': 2343, 'number_divisions': 52, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 96, 'number_subgroup_classes': 128, 'number_subgroups': 2736, 'old_label': None, 'order': 9240, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 421], [3, 2], [4, 2], [5, 4], [6, 2], [7, 6], [10, 4], [11, 10], [12, 4], [14, 6], [15, 8], [20, 8], [21, 12], [22, 4210], [28, 12], [30, 8], [33, 20], [35, 24], [42, 12], [44, 20], [55, 40], [60, 16], [66, 20], [70, 24], [77, 60], [84, 24], [105, 48], [110, 40], [132, 40], [140, 48], [154, 60], [165, 80], [210, 48], [220, 80], [231, 120], [308, 120], [330, 80], [385, 240], [420, 96], [462, 120], [660, 160], [770, 240], [924, 240], [1155, 480], [1540, 480], [2310, 480], [4620, 960]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 60, 'outer_gen_orders': [2, 2, 2, 2, 60], 'outer_gen_pows': [0, 0, 9030, 0, 0], 'outer_gens': [[1, 8402], [1, 3082], [2311, 8402], [1, 7702], [1, 4586]], 'outer_group': '960.11348', 'outer_hash': 11348, 'outer_nilpotent': True, 'outer_order': 960, 'outer_permdeg': 20, 'outer_perms': [1307761459200, 355693655116800, 121645100408832000, 6227020800, 6270935073], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_{60}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 3], [4, 3], [6, 2], [8, 3], [10, 4], [12, 3], [16, 1], [20, 3], [24, 3], [40, 3], [48, 3], [60, 2], [80, 3], [96, 1], [120, 3], [160, 1], [240, 3], [480, 3], [960, 1]], 'representations': {'PC': {'code': '38899698737788854599812578737067875291784826860001359', 'gens': [1, 2], 'pres': [7, -2, -2, -2, -3, -5, -7, -11, 11733, 36, 35198, 58, 93859, 108, 28564, 207, 171365, 334]}, 'GLFp': {'d': 2, 'p': 419, 'gens': [30748104663, 13916081265]}, 'Perm': {'d': 30, 'gens': [9168459100849992178781577164194, 642474319994769439457367091936]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 22], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}\\times D_{420}', 'transitive_degree': 4620, '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': 20, 'aut_gen_orders': [4, 10], 'aut_gens': [[1, 2], [1, 6], [7, 2]], 'aut_group': '40.12', 'aut_hash': 12, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 40, 'aut_permdeg': 7, 'aut_perms': [169, 2929], 'aut_phi_ratio': 5.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 2, 1], [5, 2, 2, 1], [10, 2, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times F_5', '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': 20, 'autcentquo_group': '20.3', 'autcentquo_hash': 3, 'autcentquo_nilpotent': False, 'autcentquo_order': 20, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 5, 2], [5, 2, 2], [10, 2, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '10.1', 'commutator_count': 1, 'commutator_label': '5.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [['10.1', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 1, 2], [5, 2, 2, 1], [10, 2, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 10, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[2, 1, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '20.4', 'hash': 4, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 10, 'inner_gen_orders': [2, 5], 'inner_gens': [[1, 18], [5, 2]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 10, 'inner_split': False, 'inner_tex': 'D_5', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 4], [2, 4]], 'label': '20.4', 'linC_count': 2, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D10', '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': 8, 'number_divisions': 6, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 10, 'number_subgroups': 22, 'old_label': None, 'order': 20, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 11], [5, 4], [10, 4]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [1, 0], 'outer_gens': [[1, 6], [11, 2]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 2]], 'representations': {'PC': {'code': 2624387, 'gens': [1, 2], 'pres': [3, -2, -2, -5, 109, 16, 146]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [7430093, 16717348]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [131, 504, 501]}, 'Perm': {'d': 7, 'gens': [126, 1, 966]}}, '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_{10}', 'transitive_degree': 10, 'wreath_data': None, 'wreath_product': False}
