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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4200.m', 'ambient_counter': 13, 'ambient_order': 4200, 'ambient_tex': 'C_{105}:C_{40}', 'central': False, 'central_factor': False, 'centralizer_order': 2100, 'characteristic': True, 'core_order': 60, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '4200.m.70.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '70.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '70.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 70, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{35}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '4200.m', 'aut_centralizer_order': 5040, 'aut_label': '70.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 5040, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '14.a1.a1', '35.a1.a1'], 'contains': ['140.a1.a1', '210.a1.a1', '350.a1.a1'], 'core': '70.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8503, 3090, 8050, 6548, 6391, 3088, 7225, 2042], 'generators': [10, 8, 20, 2800], 'label': '4200.m.70.a1.a1', 'mobius_quo': 0, 'mobius_sub': -35, 'normal_closure': '70.a1.a1', 'normal_contained_in': ['10.a1.a1', '14.a1.a1'], 'normal_contains': ['140.a1.a1', '210.a1.a1', '350.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '70.a1.a1', 'projective_image': '210.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '35.1', 'quotient_action_kernel_order': 35, 'quotient_fusion': None, 'short_label': '70.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': '60.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 4], 'aut_gens': [[1], [31], [41], [37]], 'aut_group': '16.10', 'aut_hash': 10, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 16, 'aut_permdeg': 8, 'aut_perms': [5040, 120, 9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [5, 1, 4, 1], [6, 1, 2, 1], [10, 1, 4, 1], [12, 1, 4, 1], [15, 1, 8, 1], [20, 1, 8, 1], [30, 1, 8, 1], [60, 1, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times C_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.10', 'autcent_hash': 10, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_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, 1], [3, 1, 2], [4, 1, 2], [5, 1, 4], [6, 1, 2], [10, 1, 4], [12, 1, 4], [15, 1, 8], [20, 1, 8], [30, 1, 8], [60, 1, 16]], 'center_label': '60.4', 'center_order': 60, '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', '3.1', '5.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['4.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [5, 1, 4, 1], [6, 1, 2, 1], [10, 1, 4, 1], [12, 1, 4, 1], [15, 1, 8, 1], [20, 1, 8, 1], [30, 1, 8, 1], [60, 1, 16, 1]], 'element_repr_type': 'PC', 'elementary': 30, 'eulerian_function': 1, 'exponent': 60, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[1, 0, 16]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '30.4', 'hash': 4, 'hyperelementary': 30, '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': 16, 'irrQ_dim': 16, 'irrR_degree': 2, 'irrep_stats': [[1, 60]], 'label': '60.4', 'linC_count': 16, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 6, 'linQ_dim': 8, 'linQ_dim_count': 6, 'linR_count': 8, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C60', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 12, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 60, 'number_divisions': 12, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 12, 'number_subgroups': 12, 'old_label': None, 'order': 60, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [5, 4], [6, 2], [10, 4], [12, 4], [15, 8], [20, 8], [30, 8], [60, 16]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[31], [41], [37]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [4, 3, 5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 3], [8, 3], [16, 1]], 'representations': {'PC': {'code': 513148679, 'gens': [1], 'pres': [4, -2, -2, -3, -5, 8, 21, 46]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [14343]}, 'Perm': {'d': 12, 'gens': [127008000, 10080, 96, 40279680]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [60], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{60}', 'transitive_degree': 60, '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': '40.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [84, 6, 12, 42, 12, 12, 140], 'aut_gens': [[1, 40], [477, 880], [951, 3560], [1603, 80], [2239, 2560], [2973, 2960], [2837, 160], [193, 2840]], 'aut_group': None, 'aut_hash': 5292214774166627756, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 80640, 'aut_permdeg': 424, 'aut_perms': 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1, 1], [2, 1, 1, 1], [3, 2, 1, 1], [4, 1, 2, 1], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 8, 1], [6, 2, 1, 1], [7, 2, 3, 1], [8, 105, 4, 1], [10, 1, 4, 1], [10, 2, 2, 1], [10, 2, 8, 1], [12, 2, 2, 1], [14, 2, 3, 1], [15, 2, 4, 2], [15, 2, 16, 1], [20, 1, 8, 1], [20, 2, 4, 1], [20, 2, 16, 1], [21, 2, 6, 1], [28, 2, 6, 1], [30, 2, 4, 2], [30, 2, 16, 1], [35, 2, 12, 2], [35, 2, 48, 1], [40, 105, 16, 1], [42, 2, 6, 1], [60, 2, 8, 2], [60, 2, 32, 1], [70, 2, 12, 2], [70, 2, 48, 1], [84, 2, 12, 1], [105, 2, 24, 2], [105, 2, 96, 1], [140, 2, 24, 2], [140, 2, 96, 1], [210, 2, 24, 2], [210, 2, 96, 1], [420, 2, 48, 2], [420, 2, 192, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times C_4\\times F_5\\times S_3\\times F_7', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.10', 'autcent_hash': 10, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': '5040.bh', 'autcentquo_hash': 3346192685167362256, 'autcentquo_nilpotent': False, 'autcentquo_order': 5040, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_5\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 2, 1], [4, 1, 2], [5, 1, 4], [5, 2, 10], [6, 2, 1], [7, 2, 3], [8, 105, 4], [10, 1, 4], [10, 2, 10], [12, 2, 2], [14, 2, 3], [15, 2, 24], [20, 1, 8], [20, 2, 20], [21, 2, 6], [28, 2, 6], [30, 2, 24], [35, 2, 72], [40, 105, 16], [42, 2, 6], [60, 2, 48], [70, 2, 72], [84, 2, 12], [105, 2, 144], [140, 2, 144], [210, 2, 144], [420, 2, 288]], 'center_label': '20.2', 'center_order': 20, 'central_product': True, 'central_quotient': '210.11', 'commutator_count': 1, 'commutator_label': '105.2', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1', '5.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 13, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['5.1', 1], ['840.11', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 2, 1, 1], [4, 1, 2, 1], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 4, 2], [6, 2, 1, 1], [7, 2, 3, 1], [8, 105, 4, 1], [10, 1, 4, 1], [10, 2, 2, 1], [10, 2, 4, 2], [12, 2, 2, 1], [14, 2, 3, 1], [15, 2, 4, 2], [15, 2, 8, 2], [20, 1, 8, 1], [20, 2, 4, 1], [20, 2, 8, 2], [21, 2, 6, 1], [28, 2, 6, 1], [30, 2, 4, 2], [30, 2, 8, 2], [35, 2, 12, 2], [35, 2, 24, 2], [40, 105, 16, 1], [42, 2, 6, 1], [60, 2, 8, 2], [60, 2, 16, 2], [70, 2, 12, 2], [70, 2, 24, 2], [84, 2, 12, 1], [105, 2, 24, 2], [105, 2, 48, 2], [140, 2, 24, 2], [140, 2, 48, 2], [210, 2, 24, 2], [210, 2, 48, 2], [420, 2, 48, 2], [420, 2, 96, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 840, 'exponents_of_order': [3, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7], 'faithful_reps': [[2, 0, 192]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '1050.37', 'hash': 4885601148649830834, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 210, 'inner_gen_orders': [2, 105], 'inner_gens': [[1, 4160], [81, 40]], 'inner_hash': 11, 'inner_nilpotent': False, 'inner_order': 210, 'inner_split': True, 'inner_tex': 'D_{105}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 192, 'irrQ_dim': 192, 'irrR_degree': None, 'irrep_stats': [[1, 40], [2, 1040]], 'label': '4200.m', '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': 'C105:C40', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 50, 'number_characteristic_subgroups': 50, 'number_conjugacy_classes': 1080, 'number_divisions': 62, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 76, 'number_subgroup_classes': 88, 'number_subgroups': 480, 'old_label': None, 'order': 4200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [5, 24], [6, 2], [7, 6], [8, 420], [10, 24], [12, 4], [14, 6], [15, 48], [20, 48], [21, 12], [28, 12], [30, 48], [35, 144], [40, 1680], [42, 12], [60, 96], [70, 144], [84, 24], [105, 288], [140, 288], [210, 288], [420, 576]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 4, 12], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[21, 40], [1, 2840], [11, 40], [1, 1720], [33, 2440]], 'outer_group': '384.19878', 'outer_hash': 19878, 'outer_nilpotent': True, 'outer_order': 384, 'outer_permdeg': 17, 'outer_perms': [20922789888000, 486985704, 87178291200, 4032000, 2403], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_4\\times C_{12}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 28, 'pgroup': 0, 'primary_abelian_invariants': [8, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 6], [6, 2], [8, 10], [12, 3], [16, 9], [24, 5], [32, 2], [48, 10], [96, 8], [192, 2]], 'representations': {'PC': {'code': '4336526773255188049304680991963869606211', 'gens': [1, 5], 'pres': [7, -2, -2, -2, -5, -3, -5, -7, 14, 36, 58, 145604, 137, 171365, 250, 176406]}, 'GLFp': {'d': 2, 'p': 421, 'gens': [240812, 18206904486, 23579433680]}, 'Perm': {'d': 28, 'gens': [11324451255549898769107953153, 23020551001671363717901561504, 34341896592228333368781450720]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [40], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{105}:C_{40}', 'transitive_degree': 840, 'wreath_data': None, 'wreath_product': False}
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [2, 12, 35], 'aut_gens': [[1, 2], [1, 12], [1, 46], [65, 2]], 'aut_group': '840.139', 'aut_hash': 139, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 840, 'aut_permdeg': 12, 'aut_perms': [15729840, 8427613, 258013504], 'aut_phi_ratio': 35.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 35, 1, 1], [5, 2, 2, 1], [7, 2, 3, 1], [35, 2, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_5\\times F_7', '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': 420, 'autcentquo_group': '840.139', 'autcentquo_hash': 139, 'autcentquo_nilpotent': False, 'autcentquo_order': 840, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_5\\times F_7', 'cc_stats': [[1, 1, 1], [2, 35, 1], [5, 2, 2], [7, 2, 3], [35, 2, 12]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '70.3', 'commutator_count': 1, 'commutator_label': '35.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '5.1', '7.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 35, 1, 1], [5, 2, 2, 1], [7, 2, 3, 1], [35, 2, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 70, 'exponents_of_order': [1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 5, 7], 'faithful_reps': [[2, 1, 12]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '70.3', 'hash': 3, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 70, 'inner_gen_orders': [2, 35], 'inner_gens': [[1, 68], [5, 2]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 70, 'inner_split': True, 'inner_tex': 'D_{35}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 2, 'irrep_stats': [[1, 2], [2, 17]], 'label': '70.3', 'linC_count': 12, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 1, 'linQ_dim': 10, 'linQ_dim_count': 1, 'linR_count': 12, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D35', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 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': 19, 'number_divisions': 5, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 52, 'old_label': None, 'order': 70, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 35], [5, 4], [7, 6], [35, 24]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [12], 'outer_gen_pows': [0], 'outer_gens': [[1, 34]], 'outer_group': '12.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [867], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{12}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 1], [6, 1], [24, 1]], 'representations': {'PC': {'code': 182417639, 'gens': [1, 2], 'pres': [3, -2, -5, -7, 409, 34, 542]}, 'GLFp': {'d': 2, 'p': 71, 'gens': [10379468, 5112]}, 'Perm': {'d': 12, 'gens': [3669847, 37, 47255760]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{35}', 'transitive_degree': 35, 'wreath_data': None, 'wreath_product': False}
