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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3160680600.a', 'ambient_counter': 1, 'ambient_order': 3160680600, 'ambient_tex': '\\PSL(2,1849)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 3160680600, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 3675210, 'label': '3160680600.a.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '1.A', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': True, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3160680600.a', 'subgroup_hash': None, 'subgroup_order': 3160680600, 'subgroup_tex': '\\PSL(2,1849)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '3160680600.a', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3988780083962, 143591533], 'label': '3160680600.a.1.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': False, 'almost_simple': True, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[3988780083962, 143591533], [2990485461073, 3350639226840], [409543303375, 7841608201885], [3703146372299, 2125290605913], [6669842743641, 1781306188652], [7290846228701, 1761610407679], [3439171311683, 10668843767327]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 12642722400, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1710325, 1, 1], [3, 3420650, 1, 1], [4, 3420650, 1, 1], [5, 3416952, 2, 1], [6, 3420650, 1, 1], [7, 3420650, 1, 3], [11, 3420650, 1, 5], [12, 3420650, 2, 1], [14, 3420650, 1, 3], [21, 3420650, 1, 6], [22, 3420650, 1, 5], [25, 3416952, 2, 5], [28, 3420650, 2, 3], [33, 3420650, 2, 5], [37, 3416952, 2, 9], [42, 3420650, 1, 6], [43, 1709400, 2, 1], [44, 3420650, 1, 10], [66, 3420650, 2, 5], [77, 3420650, 2, 15], [84, 3420650, 2, 6], [132, 3420650, 2, 10], [154, 3420650, 2, 15], [185, 3416952, 2, 36], [231, 3420650, 2, 30], [308, 3420650, 2, 30], [462, 3420650, 2, 30], [924, 3420650, 2, 60], [925, 3416952, 2, 180]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1710325, 1], [3, 3420650, 1], [4, 3420650, 1], [5, 3416952, 2], [6, 3420650, 1], [7, 3420650, 3], [11, 3420650, 5], [12, 3420650, 2], [14, 3420650, 3], [21, 3420650, 6], [22, 3420650, 5], [25, 3416952, 10], [28, 3420650, 6], [33, 3420650, 10], [37, 3416952, 18], [42, 3420650, 6], [43, 1709400, 2], [44, 3420650, 10], [66, 3420650, 10], [77, 3420650, 30], [84, 3420650, 12], [132, 3420650, 20], [154, 3420650, 30], [185, 3416952, 72], [231, 3420650, 60], [308, 3420650, 60], [462, 3420650, 60], [924, 3420650, 120], [925, 3416952, 360]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '3160680600.a', 'commutator_count': 1, 'commutator_label': '3160680600.a', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['3160680600.a'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1710325, 1, 1], [3, 3420650, 1, 1], [4, 3420650, 1, 1], [5, 3416952, 2, 1], [6, 3420650, 1, 1], [7, 3420650, 3, 1], [11, 3420650, 5, 1], [12, 3420650, 2, 1], [14, 3420650, 3, 1], [21, 3420650, 6, 1], [22, 3420650, 5, 1], [25, 3416952, 10, 1], [28, 3420650, 6, 1], [33, 3420650, 10, 1], [37, 3416952, 18, 1], [42, 3420650, 6, 1], [43, 1709400, 1, 2], [44, 3420650, 10, 1], [66, 3420650, 10, 1], [77, 3420650, 30, 1], [84, 3420650, 12, 1], [132, 3420650, 20, 1], [154, 3420650, 30, 1], [185, 3416952, 72, 1], [231, 3420650, 60, 1], [308, 3420650, 60, 1], [462, 3420650, 60, 1], [924, 3420650, 120, 1], [925, 3416952, 360, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': None, 'exponent': 36752100, 'exponents_of_order': [3, 2, 2, 1, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7, 11, 37, 43], 'factors_of_order': [2, 3, 5, 7, 11, 37, 43], 'faithful_reps': [[925, 1, 2], [1848, 1, 462], [1849, 1, 1], [1850, 1, 461]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '3160680600.a', 'hash': 4568413250399914240, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': '\\PSL(2,1849)', 'inner_used': None, 'irrC_degree': 925, 'irrQ_degree': 925, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 1], [925, 2], [1848, 462], [1849, 1], [1850, 461]], 'label': '3160680600.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': False, 'metacyclic': False, 'monomial': False, 'name': 'PSL(2,1849)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 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'old_label': None, 'order': 3160680600, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1710325], [3, 3420650], [4, 3420650], [5, 6833904], [6, 3420650], [7, 10261950], [11, 17103250], [12, 6841300], [14, 10261950], [21, 20523900], [22, 17103250], [25, 34169520], [28, 20523900], [33, 34206500], [37, 61505136], [42, 20523900], [43, 3418800], [44, 34206500], [66, 34206500], [77, 102619500], [84, 41047800], [132, 68413000], [154, 102619500], [185, 246020544], [231, 205239000], [308, 205239000], [462, 205239000], [924, 410478000], [925, 1230102720]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 4, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': True, 'permutation_degree': 1850, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 1], [925, 2], [1849, 1], [1850, 3], [3696, 1], [3700, 1], [5550, 2], [9250, 2], [11100, 3], [18480, 1], [18500, 3], [22200, 1], [33264, 1], [37000, 1], [55500, 2], [111000, 3], [133056, 1], [222000, 1], [665280, 1]], 'representations': {'Lie': [{'d': 2, 'q': 1849, 'gens': [3988780083962, 143591533], 'family': 'PSL'}, {'d': 2, 'q': 1849, 'family': 'PSU'}, {'d': 3, 'q': 1849, 'family': 'Omega'}, {'d': 4, 'q': 43, 'family': 'OmegaMinus'}, {'d': 3, 'q': 1849, 'family': 'POmega'}, {'d': 4, 'q': 43, 'family': 'POmegaMinus'}], 'Perm': {'d': 1850, 'gens': 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'schur_multiplier': None, 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 3160680600, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PSL(2,1849)', 'transitive_degree': 1850, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': False, 'almost_simple': True, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[3988780083962, 143591533], [2990485461073, 3350639226840], [409543303375, 7841608201885], [3703146372299, 2125290605913], [6669842743641, 1781306188652], [7290846228701, 1761610407679], [3439171311683, 10668843767327]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 12642722400, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1710325, 1, 1], [3, 3420650, 1, 1], [4, 3420650, 1, 1], [5, 3416952, 2, 1], [6, 3420650, 1, 1], [7, 3420650, 1, 3], [11, 3420650, 1, 5], [12, 3420650, 2, 1], [14, 3420650, 1, 3], [21, 3420650, 1, 6], [22, 3420650, 1, 5], [25, 3416952, 2, 5], [28, 3420650, 2, 3], [33, 3420650, 2, 5], [37, 3416952, 2, 9], [42, 3420650, 1, 6], [43, 1709400, 2, 1], [44, 3420650, 1, 10], [66, 3420650, 2, 5], [77, 3420650, 2, 15], [84, 3420650, 2, 6], [132, 3420650, 2, 10], [154, 3420650, 2, 15], [185, 3416952, 2, 36], [231, 3420650, 2, 30], [308, 3420650, 2, 30], [462, 3420650, 2, 30], [924, 3420650, 2, 60], [925, 3416952, 2, 180]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1710325, 1], [3, 3420650, 1], [4, 3420650, 1], [5, 3416952, 2], [6, 3420650, 1], [7, 3420650, 3], [11, 3420650, 5], [12, 3420650, 2], [14, 3420650, 3], [21, 3420650, 6], [22, 3420650, 5], [25, 3416952, 10], [28, 3420650, 6], [33, 3420650, 10], [37, 3416952, 18], [42, 3420650, 6], [43, 1709400, 2], [44, 3420650, 10], [66, 3420650, 10], [77, 3420650, 30], [84, 3420650, 12], [132, 3420650, 20], [154, 3420650, 30], [185, 3416952, 72], [231, 3420650, 60], [308, 3420650, 60], [462, 3420650, 60], [924, 3420650, 120], [925, 3416952, 360]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '3160680600.a', 'commutator_count': 1, 'commutator_label': '3160680600.a', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['3160680600.a'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1710325, 1, 1], [3, 3420650, 1, 1], [4, 3420650, 1, 1], [5, 3416952, 2, 1], [6, 3420650, 1, 1], [7, 3420650, 3, 1], [11, 3420650, 5, 1], [12, 3420650, 2, 1], [14, 3420650, 3, 1], [21, 3420650, 6, 1], [22, 3420650, 5, 1], [25, 3416952, 10, 1], [28, 3420650, 6, 1], [33, 3420650, 10, 1], [37, 3416952, 18, 1], [42, 3420650, 6, 1], [43, 1709400, 1, 2], [44, 3420650, 10, 1], [66, 3420650, 10, 1], [77, 3420650, 30, 1], [84, 3420650, 12, 1], [132, 3420650, 20, 1], [154, 3420650, 30, 1], [185, 3416952, 72, 1], [231, 3420650, 60, 1], [308, 3420650, 60, 1], [462, 3420650, 60, 1], [924, 3420650, 120, 1], [925, 3416952, 360, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': None, 'exponent': 36752100, 'exponents_of_order': [3, 2, 2, 1, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7, 11, 37, 43], 'factors_of_order': [2, 3, 5, 7, 11, 37, 43], 'faithful_reps': [[925, 1, 2], [1848, 1, 462], [1849, 1, 1], [1850, 1, 461]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '3160680600.a', 'hash': 4568413250399914240, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': '\\PSL(2,1849)', 'inner_used': None, 'irrC_degree': 925, 'irrQ_degree': 925, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 1], [925, 2], [1848, 462], [1849, 1], [1850, 461]], 'label': '3160680600.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': False, 'metacyclic': False, 'monomial': False, 'name': 'PSL(2,1849)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 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'old_label': None, 'order': 3160680600, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1710325], [3, 3420650], [4, 3420650], [5, 6833904], [6, 3420650], [7, 10261950], [11, 17103250], [12, 6841300], [14, 10261950], [21, 20523900], [22, 17103250], [25, 34169520], [28, 20523900], [33, 34206500], [37, 61505136], [42, 20523900], [43, 3418800], [44, 34206500], [66, 34206500], [77, 102619500], [84, 41047800], [132, 68413000], [154, 102619500], [185, 246020544], [231, 205239000], [308, 205239000], [462, 205239000], [924, 410478000], [925, 1230102720]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 4, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': True, 'permutation_degree': 1850, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 1], [925, 2], [1849, 1], [1850, 3], [3696, 1], [3700, 1], [5550, 2], [9250, 2], [11100, 3], [18480, 1], [18500, 3], [22200, 1], [33264, 1], [37000, 1], [55500, 2], [111000, 3], [133056, 1], [222000, 1], [665280, 1]], 'representations': {'Lie': [{'d': 2, 'q': 1849, 'gens': [3988780083962, 143591533], 'family': 'PSL'}, {'d': 2, 'q': 1849, 'family': 'PSU'}, {'d': 3, 'q': 1849, 'family': 'Omega'}, {'d': 4, 'q': 43, 'family': 'OmegaMinus'}, {'d': 3, 'q': 1849, 'family': 'POmega'}, {'d': 4, 'q': 43, 'family': 'POmegaMinus'}], 'Perm': {'d': 1850, 'gens': 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'schur_multiplier': None, 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 3160680600, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PSL(2,1849)', 'transitive_degree': 1850, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1.1', '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': [], '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]], '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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 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': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, 'wreath_data': None, 'wreath_product': False}
