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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5160.b', 'ambient_counter': 2, 'ambient_order': 5160, 'ambient_tex': 'C_{5160}', 'central': True, 'central_factor': False, 'centralizer_order': 5160, 'characteristic': True, 'core_order': 24, 'counter': 21, 'cyclic': True, 'direct': True, 'hall': 6, 'label': '5160.b.215.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '215.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '215.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 215, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{215}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '5160.b', 'aut_centralizer_order': None, 'aut_label': '215.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['24.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '43.a1.a1'], 'contains': ['430.a1.a1', '645.a1.a1'], 'core': '215.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [935, 935, 9706, 9706, 8573, 8573, 9596, 9596], 'generators': [645, 3440, 1290, 2580], 'label': '5160.b.215.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '215.a1.a1', 'normal_contained_in': ['5.a1.a1', '43.a1.a1'], 'normal_contains': ['430.a1.a1', '645.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '215.a1.a1', 'projective_image': '215.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '215.1', 'quotient_action_kernel_order': 215, 'quotient_fusion': None, 'short_label': '215.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': '24.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2, 2, 2], 'aut_gens': [[1], [17], [13], [19]], 'aut_group': '8.5', 'aut_hash': 5, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 8, 'aut_permdeg': 6, 'aut_perms': [1, 6, 120], '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], [6, 1, 2, 1], [8, 1, 4, 1], [12, 1, 4, 1], [24, 1, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', '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], [6, 1, 2], [8, 1, 4], [12, 1, 4], [24, 1, 8]], 'center_label': '24.2', 'center_order': 24, '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', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [6, 1, 2, 1], [8, 1, 4, 1], [12, 1, 4, 1], [24, 1, 8, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 24, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 8]], 'familial': True, 'frattini_label': '4.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, '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, 24]], 'label': '24.2', 'linC_count': 8, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 2, 'linQ_dim': 6, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C24', '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': 24, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 24, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [6, 2], [8, 4], [12, 4], [24, 8]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[17], [13], [19]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [8, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 2], [8, 1]], 'representations': {'PC': {'code': 5357681, 'gens': [1], 'pres': [4, -2, -2, -2, -3, 8, 21, 34]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [108470311826960419]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [584]}, 'Perm': {'d': 11, 'gens': [27760320, 4, 11614560, 3669864]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [24], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{24}', 'transitive_degree': 24, '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': '5160.b', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 84, 'aut_gen_orders': [2, 2, 2, 2, 84], 'aut_gens': [[1], [1291], [2581], [1721], [601], [2927]], 'aut_group': '1344.11677', 'aut_hash': 11677, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 1344, 'aut_permdeg': 52, 'aut_perms': [9574684900420033599460032394348489424526411390255787872902400, 5953959519263679070462369448585436558168215177000234193542400, 1497600, 992481070945831143772316649597849214710221610049031760736353339599, 25843318598430841016224889750089803607424358224558199939456921908328], '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], [20, 1, 8, 1], [24, 1, 8, 1], [30, 1, 8, 1], [40, 1, 16, 1], [43, 1, 42, 1], [60, 1, 16, 1], [86, 1, 42, 1], [120, 1, 32, 1], [129, 1, 84, 1], [172, 1, 84, 1], [215, 1, 168, 1], [258, 1, 84, 1], [344, 1, 168, 1], [430, 1, 168, 1], [516, 1, 168, 1], [645, 1, 336, 1], [860, 1, 336, 1], [1032, 1, 336, 1], [1290, 1, 336, 1], [1720, 1, 672, 1], [2580, 1, 672, 1], [5160, 1, 1344, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4\\times C_{84}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 84, 'autcent_group': '1344.11677', 'autcent_hash': 11677, 'autcent_nilpotent': True, 'autcent_order': 1344, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\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], [20, 1, 8], [24, 1, 8], [30, 1, 8], [40, 1, 16], [43, 1, 42], [60, 1, 16], [86, 1, 42], [120, 1, 32], [129, 1, 84], [172, 1, 84], [215, 1, 168], [258, 1, 84], [344, 1, 168], [430, 1, 168], [516, 1, 168], [645, 1, 336], [860, 1, 336], [1032, 1, 336], [1290, 1, 336], [1720, 1, 672], [2580, 1, 672], [5160, 1, 1344]], 'center_label': '5160.b', 'center_order': 5160, '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', '3.1', '5.1', '43.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['43.1', 1], ['5.1', 1], ['8.1', 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], [20, 1, 8, 1], [24, 1, 8, 1], [30, 1, 8, 1], [40, 1, 16, 1], [43, 1, 42, 1], [60, 1, 16, 1], [86, 1, 42, 1], [120, 1, 32, 1], [129, 1, 84, 1], [172, 1, 84, 1], [215, 1, 168, 1], [258, 1, 84, 1], [344, 1, 168, 1], [430, 1, 168, 1], [516, 1, 168, 1], [645, 1, 336, 1], [860, 1, 336, 1], [1032, 1, 336, 1], [1290, 1, 336, 1], [1720, 1, 672, 1], [2580, 1, 672, 1], [5160, 1, 1344, 1]], 'element_repr_type': 'PC', 'elementary': 1290, 'eulerian_function': 1, 'exponent': 5160, 'exponents_of_order': [3, 1, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 5, 43], 'faithful_reps': [[1, 0, 1344]], 'familial': True, 'frattini_label': '4.1', 'frattini_quotient': '1290.12', 'hash': 997006023, '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': 1344, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 5160]], 'label': '5160.b', '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': 'C5160', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 32, 'number_characteristic_subgroups': 32, 'number_conjugacy_classes': 5160, 'number_divisions': 32, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 32, 'number_subgroups': 32, 'old_label': None, 'order': 5160, '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], [20, 8], [24, 8], [30, 8], [40, 16], [43, 42], [60, 16], [86, 42], [120, 32], [129, 84], [172, 84], [215, 168], [258, 84], [344, 168], [430, 168], [516, 168], [645, 336], [860, 336], [1032, 336], [1290, 336], [1720, 672], [2580, 672], [5160, 1344]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 84, 'outer_gen_orders': [2, 2, 2, 2, 84], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1291], [2581], [1721], [601], [2927]], 'outer_group': '1344.11677', 'outer_hash': 11677, 'outer_nilpotent': True, 'outer_order': 1344, 'outer_permdeg': 52, 'outer_perms': [9574684900420033599460032394348489424526411390255787872902400, 5953959519263679070462369448585436558168215177000234193542400, 1497600, 992481070945831143772316649597849214710221610049031760736353339599, 25843318598430841016224889750089803607424358224558199939456921908328], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_{84}', 'pc_rank': None, 'perfect': False, 'permutation_degree': 59, 'pgroup': 0, 'primary_abelian_invariants': [8, 3, 5, 43], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [2, 3], [4, 4], [8, 4], [16, 2], [32, 1], [42, 2], [84, 3], [168, 4], [336, 4], [672, 2], [1344, 1]], 'representations': {'PC': {'code': '4114357889917116344739652916555', 'gens': [1], 'pres': [6, -2, -2, -2, -3, -5, -43, 12, 31, 50, 93, 178]}, 'GLFp': {'d': 2, 'p': 431, 'gens': [3721606173]}, 'Perm': {'d': 59, 'gens': [2391812180978184131424599331379555888500771355812946093403582957914648420940313]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [5160], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{5160}', 'transitive_degree': 5160, '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': '215.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 84, 'aut_gen_orders': [2, 84], 'aut_gens': [[1], [171], [212]], 'aut_group': '168.39', 'aut_hash': 39, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 168, 'aut_permdeg': 16, 'aut_perms': [1321086412800, 6746343273], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [5, 1, 4, 1], [43, 1, 42, 1], [215, 1, 168, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_{84}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 84, 'autcent_group': '168.39', 'autcent_hash': 39, 'autcent_nilpotent': True, 'autcent_order': 168, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\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], [5, 1, 4], [43, 1, 42], [215, 1, 168]], 'center_label': '215.1', 'center_order': 215, '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': ['5.1', '43.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['43.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [5, 1, 4, 1], [43, 1, 42, 1], [215, 1, 168, 1]], 'element_repr_type': 'PC', 'elementary': 215, 'eulerian_function': 1, 'exponent': 215, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [5, 43], 'faithful_reps': [[1, 0, 168]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '215.1', 'hash': 1, 'hyperelementary': 215, '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, 215]], 'label': '215.1', 'linC_count': 168, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 46, 'linQ_degree_count': 1, 'linQ_dim': 46, 'linQ_dim_count': 1, 'linR_count': 84, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C215', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 215, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 215, 'order_factorization_type': 11, 'order_stats': [[1, 1], [5, 4], [43, 42], [215, 168]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 84, 'outer_gen_orders': [2, 84], 'outer_gen_pows': [0, 0], 'outer_gens': [[171], [212]], 'outer_group': '168.39', 'outer_hash': 39, 'outer_nilpotent': True, 'outer_order': 168, 'outer_permdeg': 16, 'outer_perms': [1321086412800, 6746343273], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{84}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 48, 'pgroup': 0, 'primary_abelian_invariants': [5, 43], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1], [42, 1], [168, 1]], 'representations': {'PC': {'code': 8987, 'gens': [1], 'pres': [2, -5, -43, 10]}, 'GLFp': {'d': 2, 'p': 431, 'gens': [10248063175]}, 'Perm': {'d': 48, 'gens': [1034492966044672722571857420614447919876790529556480000000000, 59010256945620955738811989462269485937328128000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [215], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{215}', 'transitive_degree': 215, 'wreath_data': None, 'wreath_product': False}
