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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '10320.d', 'ambient_counter': 4, 'ambient_order': 10320, 'ambient_tex': 'C_{10320}', 'central': True, 'central_factor': False, 'centralizer_order': 10320, 'characteristic': True, 'core_order': 30, 'counter': 27, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '10320.d.344.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '344.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '344.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 344, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{344}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '10320.d', 'aut_centralizer_order': None, 'aut_label': '344.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '172.a1.a1'], 'contains': ['688.a1.a1', '1032.a1.a1', '1720.a1.a1'], 'core': '344.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6641, 6641, 2890, 2890, 1927, 1927, 1927, 1927], 'generators': [5160, 4128, 6880], 'label': '10320.d.344.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '344.a1.a1', 'normal_contained_in': ['8.a1.a1', '172.a1.a1'], 'normal_contains': ['688.a1.a1', '1032.a1.a1', '1720.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '344.a1.a1', 'projective_image': '344.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '344.2', 'quotient_action_kernel_order': 344, 'quotient_fusion': None, 'short_label': '344.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '30.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [2, 4], 'aut_gens': [[1], [11], [7]], 'aut_group': '8.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 8, 'aut_permdeg': 6, 'aut_perms': [120, 9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [5, 1, 4, 1], [6, 1, 2, 1], [10, 1, 4, 1], [15, 1, 8, 1], [30, 1, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_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], [5, 1, 4], [6, 1, 2], [10, 1, 4], [15, 1, 8], [30, 1, 8]], 'center_label': '30.4', 'center_order': 30, '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', '5.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [5, 1, 4, 1], [6, 1, 2, 1], [10, 1, 4, 1], [15, 1, 8, 1], [30, 1, 8, 1]], 'element_repr_type': 'PC', 'elementary': 30, 'eulerian_function': 1, 'exponent': 30, 'exponents_of_order': [1, 1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[1, 0, 8]], 'familial': True, 'frattini_label': '1.1', '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': 8, 'irrQ_dim': 8, 'irrR_degree': 2, 'irrep_stats': [[1, 30]], 'label': '30.4', 'linC_count': 8, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 3, 'linQ_dim': 6, 'linQ_dim_count': 3, 'linR_count': 4, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C30', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, '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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 30, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 30, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [5, 4], [6, 2], [10, 4], [15, 8], [30, 8]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[11], [7]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [4, 2], [8, 2]], 'representations': {'PC': {'code': 71879, 'gens': [1], 'pres': [3, -2, -3, -5, 6, 22]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [58415888370979138]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [11393]}, 'Perm': {'d': 10, 'gens': [362880, 10080, 96]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [30], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{30}', 'transitive_degree': 30, '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': '10320.d', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 84, 'aut_gen_orders': [4, 4, 2, 2, 4, 42], 'aut_gens': [[1], [6451], [2581], [5161], [6881], [8257], [4561]], 'aut_group': None, 'aut_hash': 3183331083131895313, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2688, 'aut_permdeg': 56, 'aut_perms': [2485604821532080240780310072288838359841888421535434519680, 4359687686764054375130964812196795340658933513117385834240, 4529842391950011595618053255038912386741912404184622325120, 14917791311334074950220313, 8314730227825727183366688291474474465328364669760078627290878951723008000, 343257083448766191518628796435478939017245359838703302744605243771278388336], '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], [8, 1, 4, 1], [10, 1, 4, 1], [12, 1, 4, 1], [15, 1, 8, 1], [16, 1, 8, 1], [20, 1, 8, 1], [24, 1, 8, 1], [30, 1, 8, 1], [40, 1, 16, 1], [43, 1, 42, 1], [48, 1, 16, 1], [60, 1, 16, 1], [80, 1, 32, 1], [86, 1, 42, 1], [120, 1, 32, 1], [129, 1, 84, 1], [172, 1, 84, 1], [215, 1, 168, 1], [240, 1, 64, 1], [258, 1, 84, 1], [344, 1, 168, 1], [430, 1, 168, 1], [516, 1, 168, 1], [645, 1, 336, 1], [688, 1, 336, 1], [860, 1, 336, 1], [1032, 1, 336, 1], [1290, 1, 336, 1], [1720, 1, 672, 1], [2064, 1, 672, 1], [2580, 1, 672, 1], [3440, 1, 1344, 1], [5160, 1, 1344, 1], [10320, 1, 2688, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3\\times C_4\\times C_{84}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 84, 'autcent_group': None, 'autcent_hash': 3183331083131895313, 'autcent_nilpotent': True, 'autcent_order': 2688, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_4\\times C_{84}', '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], [8, 1, 4], [10, 1, 4], [12, 1, 4], [15, 1, 8], [16, 1, 8], [20, 1, 8], [24, 1, 8], [30, 1, 8], [40, 1, 16], [43, 1, 42], [48, 1, 16], [60, 1, 16], [80, 1, 32], [86, 1, 42], [120, 1, 32], [129, 1, 84], [172, 1, 84], [215, 1, 168], [240, 1, 64], [258, 1, 84], [344, 1, 168], [430, 1, 168], [516, 1, 168], [645, 1, 336], [688, 1, 336], [860, 1, 336], [1032, 1, 336], [1290, 1, 336], [1720, 1, 672], [2064, 1, 672], [2580, 1, 672], [3440, 1, 1344], [5160, 1, 1344], [10320, 1, 2688]], 'center_label': '10320.d', 'center_order': 10320, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1', '43.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['16.1', 1], ['3.1', 1], ['43.1', 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], [8, 1, 4, 1], [10, 1, 4, 1], [12, 1, 4, 1], [15, 1, 8, 1], [16, 1, 8, 1], [20, 1, 8, 1], [24, 1, 8, 1], [30, 1, 8, 1], [40, 1, 16, 1], [43, 1, 42, 1], [48, 1, 16, 1], [60, 1, 16, 1], [80, 1, 32, 1], [86, 1, 42, 1], [120, 1, 32, 1], [129, 1, 84, 1], [172, 1, 84, 1], [215, 1, 168, 1], [240, 1, 64, 1], [258, 1, 84, 1], [344, 1, 168, 1], [430, 1, 168, 1], [516, 1, 168, 1], [645, 1, 336, 1], [688, 1, 336, 1], [860, 1, 336, 1], [1032, 1, 336, 1], [1290, 1, 336, 1], [1720, 1, 672, 1], [2064, 1, 672, 1], [2580, 1, 672, 1], [3440, 1, 1344, 1], [5160, 1, 1344, 1], [10320, 1, 2688, 1]], 'element_repr_type': 'PC', 'elementary': 1290, 'eulerian_function': 1, 'exponent': 10320, 'exponents_of_order': [4, 1, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 5, 43], 'faithful_reps': [[1, 0, 2688]], 'familial': True, 'frattini_label': '8.1', 'frattini_quotient': '1290.12', 'hash': 997009087, 'hyperelementary': 1290, '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': 2688, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 10320]], 'label': '10320.d', 'linC_count': None, 'linC_degree': 1, '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': 'C10320', 'ngens': 7, 'nilpotency_class': 1, 'nilpotent': True, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 40, 'number_characteristic_subgroups': 40, 'number_conjugacy_classes': 10320, 'number_divisions': 40, 'number_normal_subgroups': 40, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 40, 'number_subgroups': 40, 'old_label': None, 'order': 10320, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [5, 4], [6, 2], [8, 4], [10, 4], [12, 4], [15, 8], [16, 8], [20, 8], [24, 8], [30, 8], [40, 16], [43, 42], [48, 16], [60, 16], [80, 32], [86, 42], [120, 32], [129, 84], [172, 84], [215, 168], [240, 64], [258, 84], [344, 168], [430, 168], [516, 168], [645, 336], [688, 336], [860, 336], [1032, 336], [1290, 336], [1720, 672], [2064, 672], [2580, 672], [3440, 1344], [5160, 1344], [10320, 2688]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 84, 'outer_gen_orders': [4, 4, 2, 2, 4, 42], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[6451], [2581], [5161], [6881], [8257], [4561]], 'outer_group': None, 'outer_hash': 3183331083131895313, 'outer_nilpotent': True, 'outer_order': 2688, 'outer_permdeg': 56, 'outer_perms': [2485604821532080240780310072288838359841888421535434519680, 4359687686764054375130964812196795340658933513117385834240, 4529842391950011595618053255038912386741912404184622325120, 14917791311334074950220313, 8314730227825727183366688291474474465328364669760078627290878951723008000, 343257083448766191518628796435478939017245359838703302744605243771278388336], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_4\\times C_{84}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 67, 'pgroup': 0, 'primary_abelian_invariants': [16, 3, 5, 43], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [2, 3], [4, 4], [8, 5], [16, 3], [32, 2], [42, 2], [64, 1], [84, 3], [168, 4], [336, 5], [672, 3], [1344, 2], [2688, 1]], 'representations': {'PC': {'code': '3637140487642037098079019419677087275275', 'gens': [1], 'pres': [7, -2, -2, -2, -2, -3, -5, -43, 14, 36, 58, 80, 137, 250]}, 'GLFp': {'d': 2, 'p': 431, 'gens': [17413321695]}, 'Perm': {'d': 67, 'gens': [552721491196042359583250342708796644205084181811282986987367099771692554233776474648420940313]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10320], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{10320}', 'transitive_degree': 10320, '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': '344.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 42, 'aut_gen_orders': [2, 2, 42], 'aut_gens': [[1], [259], [173], [89]], 'aut_group': '168.57', 'aut_hash': 57, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 168, 'aut_permdeg': 46, 'aut_perms': [109050989124884473699447170889578704597969879389173989904, 87784816526576883555098164401461777476264286867995897104, 242091245115638712176566319733838055767028510100114067212], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [8, 1, 4, 1], [43, 1, 42, 1], [86, 1, 42, 1], [172, 1, 84, 1], [344, 1, 168, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times C_{42}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 42, 'autcent_group': '168.57', 'autcent_hash': 57, 'autcent_nilpotent': True, 'autcent_order': 168, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_{42}', '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], [4, 1, 2], [8, 1, 4], [43, 1, 42], [86, 1, 42], [172, 1, 84], [344, 1, 168]], 'center_label': '344.2', 'center_order': 344, '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', '2.1', '43.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['43.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [8, 1, 4, 1], [43, 1, 42, 1], [86, 1, 42, 1], [172, 1, 84, 1], [344, 1, 168, 1]], 'element_repr_type': 'PC', 'elementary': 86, 'eulerian_function': 1, 'exponent': 344, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 43], 'faithful_reps': [[1, 0, 168]], 'familial': True, 'frattini_label': '4.1', 'frattini_quotient': '86.2', 'hash': 2, 'hyperelementary': 86, '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': 168, 'irrQ_dim': 168, 'irrR_degree': 2, 'irrep_stats': [[1, 344]], 'label': '344.2', 'linC_count': 168, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 46, 'linQ_degree_count': 2, 'linQ_dim': 46, 'linQ_dim_count': 2, 'linR_count': 84, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C344', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, '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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 344, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 344, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 1], [4, 2], [8, 4], [43, 42], [86, 42], [172, 84], [344, 168]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 42, 'outer_gen_orders': [2, 2, 42], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[259], [173], [89]], 'outer_group': '168.57', 'outer_hash': 57, 'outer_nilpotent': True, 'outer_order': 168, 'outer_permdeg': 46, 'outer_perms': [109050989124884473699447170889578704597969879389173989904, 87784816526576883555098164401461777476264286867995897104, 242091245115638712176566319733838055767028510100114067212], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{42}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 51, 'pgroup': 0, 'primary_abelian_invariants': [8, 43], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 1], [42, 2], [84, 1], [168, 1]], 'representations': {'PC': {'code': 212235014905241, 'gens': [1], 'pres': [4, -2, -2, -2, -43, 8, 21, 34]}, 'GLFp': {'d': 2, 'p': 173, 'gens': [2210075]}, 'Perm': {'d': 51, 'gens': [216599033751535440633927791155991262120042770706947112960000000000, 59010256945620955738811989462269485937328128000000000, 92458860080319590419809567499679506678988139383362682880000000000, 30426512622586345503160869073461196830685671907286581248000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [344], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{344}', 'transitive_degree': 344, 'wreath_data': None, 'wreath_product': False}
