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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.414', 'ambient_counter': 414, 'ambient_order': 960, 'ambient_tex': 'C_{15}:\\SD_{64}', 'central': False, 'central_factor': True, 'centralizer_order': 10, 'characteristic': True, 'core_order': 192, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '960.414.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.79', 'subgroup_hash': 79, 'subgroup_order': 192, 'subgroup_tex': 'C_3:\\SD_{64}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.414', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.15044535', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '15.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9150, 3899, 9868, 3495, 8626, 3469, 8626, 3469], 'generators': [1, 32, 48, 2, 640, 28, 8], 'label': '960.414.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '480.145', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.33'}
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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': 2, 'aut_exponent': 48, 'aut_gen_orders': [2, 2, 8, 48], 'aut_gens': [[1, 2, 64], [1, 2, 128], [9, 62, 64], [21, 38, 64], [29, 98, 64]], 'aut_group': '1536.15044535', 'aut_hash': 5277401465989707296, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536, 'aut_permdeg': 27, 'aut_perms': [405233734404542293905177601, 1293023717172742440996633600, 5869733527356305763524625384, 1710764327137057940882534403], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 16, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 48, 1, 1], [6, 2, 1, 1], [6, 16, 2, 1], [8, 2, 2, 1], [12, 4, 1, 1], [16, 2, 4, 1], [24, 4, 2, 1], [32, 6, 8, 1], [48, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3\\times D_{16}:C_8', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '384.12439', 'autcentquo_hash': 12439, 'autcentquo_nilpotent': False, 'autcentquo_order': 384, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_8:C_4\\times S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 16, 1], [3, 2, 1], [4, 2, 1], [4, 48, 1], [6, 2, 1], [6, 16, 2], [8, 2, 2], [12, 4, 1], [16, 2, 4], [24, 4, 2], [32, 6, 8], [48, 4, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '96.33', 'commutator_count': 1, 'commutator_label': '48.2', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 79, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 16, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 48, 1, 1], [6, 2, 1, 1], [6, 16, 2, 1], [8, 2, 2, 1], [12, 4, 1, 1], [16, 2, 4, 1], [24, 4, 2, 1], [32, 6, 8, 1], [48, 4, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 96, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, -1, 4]], 'familial': False, 'frattini_label': '16.1', 'frattini_quotient': '12.4', 'hash': 79, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 48, 'inner_gen_orders': [2, 16, 3], 'inner_gens': [[1, 30, 64], [37, 2, 128], [1, 130, 64]], 'inner_hash': 33, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': True, 'inner_tex': 'C_3:D_{16}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 32, 'irrR_degree': 8, 'irrep_stats': [[1, 4], [2, 19], [4, 7]], 'label': '192.79', 'linC_count': 36, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 1, 'linQ_dim': 18, 'linQ_dim_count': 2, 'linR_count': 8, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3:SD64', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 14, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 30, 'number_divisions': 14, 'number_normal_subgroups': 15, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 32, 'number_subgroups': 140, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 17], [3, 2], [4, 50], [6, 34], [8, 4], [12, 4], [16, 8], [24, 8], [32, 48], [48, 16]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 8, 'outer_gen_orders': [2, 8], 'outer_gen_pows': [60, 0], 'outer_gens': [[29, 2, 64], [1, 10, 64]], 'outer_group': '16.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 10, 'outer_perms': [362880, 18551], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_8', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 3], [8, 2], [16, 2]], 'representations': {'PC': {'code': 32230625330158958157215428353, 'gens': [1, 2, 7], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 421, 36, 1262, 58, 1571, 80, 1684, 102, 3149]}, 'GLZN': {'d': 2, 'p': 94, 'gens': [77244405, 830677, 19309175, 23063531, 71396769, 1250342, 39345063]}, 'Perm': {'d': 35, 'gens': [331121045577926953912110296908399694065, 45861989620767997046472807040812311520, 645273284954738719426046969779309758480, 948959192284879930255774445132585047704, 1253375567419352152550981300797478393784, 1557589996604749737697137337663830037224, 3]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3:\\SD_{64}', 'transitive_degree': 96, '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': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 48, 'aut_gen_orders': [6, 12, 8, 12, 16, 8], 'aut_gens': [[1, 2, 64], [25, 350, 256], [53, 366, 64], [25, 678, 704], [45, 382, 832], [21, 10, 64], [57, 690, 128]], 'aut_group': None, 'aut_hash': 6950560539663341654, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 68, 'aut_perms': [2461780145879062200730792622449939043551955063681635858637599709449468411784282345376169275012474, 1014792707258886901549527036773705070028667494378949901602854452484321887321276942372250287482494, 1549972735519110186835926131041640578426084462831704262078638580788456188760199712054293706079575, 1916982968239194572648954821156502651934227945607364819368652182351650046027396293078305119893995, 221280448575936090142466024486558205174523782380114951677095945069073012347942129759940644562530, 1435301145371438351489557142525859388431071726080906858613440863209014863986458531306482401281267], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 16, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 48, 1, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 16, 2, 1], [8, 2, 2, 1], [10, 1, 4, 1], [10, 16, 4, 1], [12, 4, 1, 1], [15, 2, 4, 1], [16, 2, 4, 1], [20, 2, 4, 1], [20, 48, 4, 1], [24, 4, 2, 1], [30, 2, 4, 1], [30, 16, 8, 1], [32, 6, 8, 1], [40, 2, 8, 1], [48, 4, 4, 1], [60, 4, 4, 1], [80, 2, 16, 1], [120, 4, 8, 1], [160, 6, 32, 1], [240, 4, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:((C_2\\times C_4\\times C_8).C_2^5)', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '384.12439', 'autcentquo_hash': 12439, 'autcentquo_nilpotent': False, 'autcentquo_order': 384, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_8:C_4\\times S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 16, 1], [3, 2, 1], [4, 2, 1], [4, 48, 1], [5, 1, 4], [6, 2, 1], [6, 16, 2], [8, 2, 2], [10, 1, 4], [10, 16, 4], [12, 4, 1], [15, 2, 4], [16, 2, 4], [20, 2, 4], [20, 48, 4], [24, 4, 2], [30, 2, 4], [30, 16, 8], [32, 6, 8], [40, 2, 8], [48, 4, 4], [60, 4, 4], [80, 2, 16], [120, 4, 8], [160, 6, 32], [240, 4, 16]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '96.33', 'commutator_count': 1, 'commutator_label': '48.2', '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': 414, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['192.79', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 16, 1, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 48, 1, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 16, 2, 1], [8, 2, 2, 1], [10, 1, 4, 1], [10, 16, 4, 1], [12, 4, 1, 1], [15, 2, 4, 1], [16, 2, 4, 1], [20, 2, 4, 1], [20, 48, 4, 1], [24, 4, 2, 1], [30, 2, 4, 1], [30, 16, 8, 1], [32, 6, 8, 1], [40, 2, 8, 1], [48, 4, 4, 1], [60, 4, 4, 1], [80, 2, 16, 1], [120, 4, 8, 1], [160, 6, 32, 1], [240, 4, 16, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 480, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 0, 16]], 'familial': False, 'frattini_label': '16.1', 'frattini_quotient': '60.11', 'hash': 414, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 48, 'inner_gen_orders': [2, 16, 3], 'inner_gens': [[1, 30, 64], [37, 2, 704], [1, 322, 64]], 'inner_hash': 33, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': True, 'inner_tex': 'C_3:D_{16}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 64, 'irrQ_dim': 128, 'irrR_degree': 8, 'irrep_stats': [[1, 20], [2, 95], [4, 35]], 'label': '960.414', 'linC_count': 784, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 4, 'linQ_dim': 22, 'linQ_dim_count': 8, 'linR_count': 32, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C15:SD64', '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': 28, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 150, 'number_divisions': 28, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 64, 'number_subgroup_classes': 64, 'number_subgroups': 280, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 17], [3, 2], [4, 50], [5, 4], [6, 34], [8, 4], [10, 68], [12, 4], [15, 8], [16, 8], [20, 200], [24, 8], [30, 136], [32, 48], [40, 16], [48, 16], [60, 16], [80, 32], [120, 32], [160, 192], [240, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 8, 'outer_gen_orders': [2, 4, 8], 'outer_gen_pows': [60, 0, 0], 'outer_gens': [[29, 2, 64], [1, 2, 448], [1, 10, 64]], 'outer_group': '64.83', 'outer_hash': 83, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 14, 'outer_perms': [6227020800, 43908480, 18551], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4\\times C_8', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 40, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 7], [8, 5], [16, 5], [32, 2], [64, 2]], 'representations': {'PC': {'code': 12500026086317505159869450276054114573877255, 'gens': [1, 2, 7], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -5, 481, 41, 1442, 66, 1795, 91, 1924, 116, 19726, 222]}, 'Perm': {'d': 40, 'gens': [22549638304972078078917952527688210704718885200, 2742459984884017090663705661449868715685996800, 33, 44074981004299847962731929876229936143673523200, 64983610912345163270973308885219756218504702080, 85930875187807345334493624000829403491086737280, 106867121372654151338721916856919182376937514880, 5760]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}:\\SD_{64}', 'transitive_degree': 480, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '5.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [4], 'aut_gens': [[1], [2]], 'aut_group': '4.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [5, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': '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], [5, 1, 4]], 'center_label': '5.1', 'center_order': 5, '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': ['5.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [5, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 5, 'eulerian_function': 1, 'exponent': 5, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [5], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '5.1', 'hash': 1, 'hyperelementary': 5, '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': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 5]], 'label': '5.1', 'linC_count': 4, 'linC_degree': 1, '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': 'C5', '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': 5, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 5, 'order_factorization_type': 1, 'order_stats': [[1, 1], [5, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 5, 'primary_abelian_invariants': [5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -5]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [26329372]}, 'Lie': [{'d': 1, 'q': 5, 'gens': [33], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 5, 'gens': [131]}, 'Perm': {'d': 5, 'gens': [96]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [5], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5', 'transitive_degree': 5, 'wreath_data': None, 'wreath_product': False}
