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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5500.a', 'ambient_counter': 1, 'ambient_order': 5500, 'ambient_tex': 'C_5\\times C_{55}:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 2750, 'characteristic': True, 'core_order': 5, 'counter': 58, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '5500.a.1100.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1100.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1100.19', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 19, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1100, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{220}:C_5', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '5500.a', 'aut_centralizer_order': None, 'aut_label': '1100.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': ['5.c1'], 'conjugacy_class_count': 1, 'contained_in': ['100.b1', '220.a1', '220.d1', '550.b1'], 'contains': ['5500.a1'], 'core': '1100.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3796, 6879, 3930, 6887], 'generators': [1100], 'label': '5500.a.1100.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1100.b1', 'normal_contained_in': ['100.b1', '220.a1', '550.b1'], 'normal_contains': ['5500.a1'], 'normalizer': '1.a1', 'old_label': '1100.b1', 'projective_image': '5500.a', 'quotient_action_image': '2.1', 'quotient_action_kernel': '550.10', 'quotient_action_kernel_order': 550, 'quotient_fusion': None, 'short_label': '1100.b1', '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': '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}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '100.8', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 220, 'aut_gen_orders': [10, 20, 10, 20, 20], 'aut_gens': [[1, 5, 100], [1, 5109, 5400], [3, 2507, 4200], [4, 1306, 1600], [2, 4707, 900], [1, 4056, 800]], 'aut_group': None, 'aut_hash': 9029674209157533335, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 88000, 'aut_permdeg': 65, 'aut_perms': [2306189787178934340249945646084349849792451367080693244126124878272527135302429657590912584, 5278981974351819326252331301197374545591170486417403600656833402340514246564167593151390405, 5152127086223985183246878176844248761269102902540456542128653121022100563885099782500227538, 5157979925224022834066162220550218624396899795593192419759124469227307820857778627868619891, 1290870528647873770669417742494393668037088831179833170534427147278787641747351003552991812], 'aut_phi_ratio': 44.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 5, 2, 1], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 8, 1], [5, 11, 5, 4], [5, 22, 10, 4], [10, 1, 4, 1], [10, 2, 2, 1], [10, 2, 8, 1], [10, 11, 5, 4], [10, 22, 10, 4], [11, 5, 2, 1], [20, 5, 8, 1], [20, 55, 10, 4], [22, 5, 2, 1], [44, 25, 4, 1], [55, 5, 8, 1], [55, 10, 4, 1], [55, 10, 16, 1], [110, 5, 8, 1], [110, 10, 4, 1], [110, 10, 16, 1], [220, 25, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{55}.(C_{20}\\times D_5).C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '40.12', 'autcent_hash': 12, 'autcent_nilpotent': False, 'autcent_order': 40, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': '2200.be', 'autcentquo_hash': 5423566900542061453, 'autcentquo_nilpotent': False, 'autcentquo_order': 2200, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_5\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [4, 5, 2], [5, 1, 4], [5, 2, 10], [5, 11, 20], [5, 22, 40], [10, 1, 4], [10, 2, 10], [10, 11, 20], [10, 22, 40], [11, 5, 2], [20, 5, 8], [20, 55, 40], [22, 5, 2], [44, 25, 4], [55, 5, 8], [55, 10, 20], [110, 5, 8], [110, 10, 20], [220, 25, 16]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '550.8', 'commutator_count': 1, 'commutator_label': '55.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '5.1', '5.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['20.1', 1], ['5.1', 1], ['55.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 5, 2, 1], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 4, 2], [5, 11, 4, 5], [5, 22, 4, 10], [10, 1, 4, 1], [10, 2, 2, 1], [10, 2, 4, 2], [10, 11, 4, 5], [10, 22, 4, 10], [11, 5, 2, 1], [20, 5, 8, 1], [20, 55, 8, 5], [22, 5, 2, 1], [44, 25, 4, 1], [55, 5, 8, 1], [55, 10, 4, 1], [55, 10, 8, 2], [110, 5, 8, 1], [110, 10, 4, 1], [110, 10, 8, 2], [220, 25, 16, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 220, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 0, 16]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2750.d', 'hash': 7176339576926168759, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [1, 10, 55], 'inner_gens': [[1, 5, 100], [1, 5, 4900], [1, 705, 100]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 550, 'inner_split': False, 'inner_tex': 'C_{55}:C_{10}', 'inner_used': [2, 3], 'irrC_degree': 10, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 20, 'irrep_stats': [[1, 100], [2, 100], [5, 40], [10, 40]], 'label': '5500.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': False, 'monomial': True, 'name': 'C5*C55:C20', 'ngens': 6, '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': 40, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 280, 'number_divisions': 59, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 64, 'number_subgroup_classes': 192, 'number_subgroups': 1832, 'old_label': None, 'order': 5500, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1], [4, 10], [5, 1124], [10, 1124], [11, 10], [20, 2240], [22, 10], [44, 100], [55, 240], [110, 240], [220, 400]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 20, 'outer_gen_orders': [2, 2, 4, 10], 'outer_gen_pows': [1100, 25, 0, 0], 'outer_gens': [[1, 1105, 2100], [1, 5, 4300], [3, 5, 2100], [1, 57, 2100]], 'outer_group': '160.236', 'outer_hash': 236, 'outer_nilpotent': False, 'outer_order': 160, 'outer_permdeg': 11, 'outer_perms': [126, 1, 731089, 8064288], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times F_5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [4, 5, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 14], [8, 30], [10, 2], [20, 1], [40, 4], [80, 5]], 'representations': {'PC': {'code': '7025069704124447927553522980907102230300339', 'gens': [1, 2, 5], 'pres': [6, -5, -2, -2, -5, -5, -11, 31, 50, 29410, 10816, 4672, 178, 18011, 5417, 8123]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 2223827614270807, 40144423758791283, 37678710548104341, 36687300164533435, 8388386403068862]}, 'Perm': {'d': 25, 'gens': [1407311804138, 674451527608736324933069, 1319576854410911416320000, 1913100451620447828700755, 2484041864839335457233622, 1284626]}}, 'schur_multiplier': [5], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [5, 20], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times C_{55}:C_{20}', 'transitive_degree': 220, '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': '100.8', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 220, 'aut_gen_orders': [4, 10, 110], 'aut_gens': [[1, 5], [221, 985], [1, 505], [121, 555]], 'aut_group': '4400.r', 'aut_hash': 3690388632023574097, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4400, 'aut_permdeg': 57, 'aut_perms': [552177193327368596654017085942357817688391572855886588656427788613773164687, 331744024647865077884773496468222514952908633936920622364143262719468981721, 33453142282050453399316860010159861191778300937354515526373447781095490124912], 'aut_phi_ratio': 11.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [5, 1, 4, 1], [5, 11, 5, 4], [10, 1, 4, 1], [10, 11, 5, 4], [11, 5, 2, 1], [20, 1, 8, 1], [20, 11, 10, 4], [22, 5, 2, 1], [44, 5, 4, 1], [55, 5, 8, 1], [110, 5, 8, 1], [220, 5, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_{110}:C_{20}', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '40.12', 'autcent_hash': 12, 'autcent_nilpotent': False, 'autcent_order': 40, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [4, 1, 2], [5, 1, 4], [5, 11, 20], [10, 1, 4], [10, 11, 20], [11, 5, 2], [20, 1, 8], [20, 11, 40], [22, 5, 2], [44, 5, 4], [55, 5, 8], [110, 5, 8], [220, 5, 16]], 'center_label': '20.2', 'center_order': 20, 'central_product': True, 'central_quotient': '55.1', 'commutator_count': 1, 'commutator_label': '11.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '5.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 19, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['5.1', 1], ['55.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [5, 1, 4, 1], [5, 11, 4, 5], [10, 1, 4, 1], [10, 11, 4, 5], [11, 5, 2, 1], [20, 1, 8, 1], [20, 11, 8, 5], [22, 5, 2, 1], [44, 5, 4, 1], [55, 5, 8, 1], [110, 5, 8, 1], [220, 5, 16, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 220, 'exponents_of_order': [2, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[5, 0, 16]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '550.10', 'hash': 19, 'hyperelementary': 5, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 55, 'inner_gen_orders': [5, 11], 'inner_gens': [[1, 405], [701, 5]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 55, 'inner_split': True, 'inner_tex': 'C_{11}:C_5', 'inner_used': [1, 2], 'irrC_degree': 5, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 10, 'irrep_stats': [[1, 100], [5, 40]], 'label': '1100.19', 'linC_count': 16, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 20, 'linQ_dim': 16, 'linQ_dim_count': 20, 'linR_count': 8, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C220:C5', 'ngens': 5, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 24, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 140, 'number_divisions': 27, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 48, 'number_subgroups': 228, 'old_label': None, 'order': 1100, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1], [4, 2], [5, 224], [10, 224], [11, 10], [20, 448], [22, 10], [44, 20], [55, 40], [110, 40], [220, 80]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 20, 'outer_gen_orders': [2, 4, 10], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 655], [441, 765], [221, 305]], 'outer_group': '80.50', 'outer_hash': 50, 'outer_nilpotent': False, 'outer_order': 80, 'outer_permdeg': 9, 'outer_perms': [7, 5896, 122536], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times F_5', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [4, 5, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 12], [8, 6], [10, 2], [20, 1], [40, 2], [80, 1]], 'representations': {'PC': {'code': 8720789124096363978777430039, 'gens': [1, 2], 'pres': [5, -5, -2, -2, -5, -11, 4051, 26, 12152, 42, 10403, 118, 10004]}, 'GLFq': {'d': 2, 'q': 121, 'gens': [15680518, 143403964, 15944058, 83263414, 17715620]}, 'Perm': {'d': 20, 'gens': [9, 7159866360647160, 96480, 16, 135229490543347200]}}, 'schur_multiplier': [5], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [5, 20], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{220}:C_5', 'transitive_degree': 220, 'wreath_data': None, 'wreath_product': False}
