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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '111168.a', 'ambient_counter': 1, 'ambient_order': 111168, 'ambient_tex': 'C_3\\times F_{193}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 6948, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '111168.a.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6948.a', 'subgroup_hash': 163829408175284635, 'subgroup_order': 6948, 'subgroup_tex': 'C_{579}:C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '111168.a', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '37056.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.b1.b1', '48.b1.c1', '3088.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6817, 7769, 2884, 6947, 2431, 2015, 2153, 7919], 'generators': [96, 576, 37056, 64, 48], 'label': '111168.a.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.b1.b1', '48.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '37056.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '37056.a'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '36.8', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [96, 192, 3], 'aut_gens': [[1, 12], [6541, 5280], [2941, 264], [457, 3612]], 'aut_group': None, 'aut_hash': 9034218873832238734, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 222336, 'aut_permdeg': 772, 'aut_perms': 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'aut_phi_ratio': 96.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 193, 1, 1], [3, 1, 2, 1], [3, 193, 3, 2], [4, 193, 1, 2], [6, 193, 2, 1], [6, 193, 3, 2], [12, 193, 2, 2], [12, 193, 3, 4], [193, 12, 16, 1], [579, 12, 32, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{579}.C_{192}.C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [2, 193, 1], [3, 1, 2], [3, 193, 6], [4, 193, 2], [6, 193, 8], [12, 193, 16], [193, 12, 16], [579, 12, 32]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '2316.b', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '193.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2316.b', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 193, 1, 1], [3, 1, 2, 1], [3, 193, 2, 3], [4, 193, 2, 1], [6, 193, 2, 4], [12, 193, 4, 4], [193, 12, 16, 1], [579, 12, 32, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 96, 'exponent': 2316, 'exponents_of_order': [2, 2, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': [[12, 0, 32]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '6948.a', 'hash': 163829408175284635, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 2316, 'inner_gen_orders': [12, 193], 'inner_gens': [[1, 1560], [5401, 12]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 2316, 'inner_split': False, 'inner_tex': 'C_{193}:C_{12}', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 384, 'irrQ_dim': 384, 'irrR_degree': 24, 'irrep_stats': [[1, 36], [12, 48]], 'label': '6948.a', 'linC_count': 32, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 194, 'linQ_degree_count': 6, 'linQ_dim': 194, 'linQ_dim_count': 6, 'linR_count': 192, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C579:C12', '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': 18, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 84, 'number_divisions': 17, 'number_normal_subgroups': 20, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 36, 'number_subgroups': 3108, 'old_label': None, 'order': 6948, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 193], [3, 1160], [4, 386], [6, 1544], [12, 3088], [193, 192], [579, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 48, 'outer_gen_orders': [2, 48], 'outer_gen_pows': [0, 3], 'outer_gens': [[2317, 6936], [4633, 5124]], 'outer_group': '96.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 96, 'outer_permdeg': 19, 'outer_perms': [6423384156578665, 13560771052696588], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3\\times C_{16}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 196, 'pgroup': 0, 'primary_abelian_invariants': [4, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9], [4, 4], [192, 1], [384, 1]], 'representations': {'PC': {'code': '2484544393403494715474679500204522112733094646143', 'gens': [1, 4], 'pres': [5, -2, -2, -3, -3, -193, 10, 26, 31203, 13088, 18073, 78, 117004, 49059, 24314]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 7189106, 776418240]}, 'Perm': {'d': 196, 'gens': [26997883370683755077834348632583544075689123646545924239333415195270970618446762803151534820839084168332574930202330878136717844416248344506188842014859582665659028857979420994463281937424786636465603603264193802991238759711988872255230924689688520127256054785069161550511582761091078406738638113786583221698027154119610457882727594361829212191882754524688969640, 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'tex_name': 'C_{579}:C_{12}', 'transitive_degree': 579, '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': '576.182', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [64, 192, 96], 'aut_gens': [[1, 192], [97153, 39552], [105793, 64320], [47809, 18816]], 'aut_group': None, 'aut_hash': 9034218873832238734, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 222336, 'aut_permdeg': 579, 'aut_perms': 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'aut_phi_ratio': 6.03125, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 193, 1, 1], [3, 1, 2, 1], [3, 193, 3, 2], [4, 193, 1, 2], [6, 193, 2, 1], [6, 193, 3, 2], [8, 193, 1, 4], [12, 193, 2, 2], [12, 193, 3, 4], [16, 193, 1, 8], [24, 193, 2, 4], [24, 193, 3, 8], [32, 193, 1, 16], [48, 193, 2, 8], [48, 193, 3, 16], [64, 193, 1, 32], [96, 193, 2, 16], [96, 193, 3, 32], [192, 193, 2, 32], [192, 193, 3, 64], [193, 192, 1, 1], [579, 192, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{579}.C_{96}.C_2^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [2, 193, 1], [3, 1, 2], [3, 193, 6], [4, 193, 2], [6, 193, 8], [8, 193, 4], [12, 193, 16], [16, 193, 8], [24, 193, 32], [32, 193, 16], [48, 193, 64], [64, 193, 32], [96, 193, 128], [192, 193, 256], [193, 192, 1], [579, 192, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '37056.a', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '193.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['37056.a', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 193, 1, 1], [3, 1, 2, 1], [3, 193, 2, 3], [4, 193, 2, 1], [6, 193, 2, 4], [8, 193, 4, 1], [12, 193, 4, 4], [16, 193, 8, 1], [24, 193, 8, 4], [32, 193, 16, 1], [48, 193, 16, 4], [64, 193, 32, 1], [96, 193, 32, 4], [192, 193, 64, 4], [193, 192, 1, 1], [579, 192, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24576, 'exponent': 37056, 'exponents_of_order': [6, 2, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': [[192, 0, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '111168.a', 'hash': 2544430592072231885, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 37056, 'inner_gen_orders': [192, 193], 'inner_gens': [[1, 28416], [82945, 192]], 'inner_hash': 1432757702296672986, 'inner_nilpotent': False, 'inner_order': 37056, 'inner_split': True, 'inner_tex': 'F_{193}', 'inner_used': [1, 2], 'irrC_degree': 192, 'irrQ_degree': 384, 'irrQ_dim': 384, 'irrR_degree': None, 'irrep_stats': [[1, 576], [192, 3]], 'label': '111168.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': True, 'monomial': True, 'name': 'C3*F193', 'ngens': 9, '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, 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': 258, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 579, 'number_divisions': 37, 'number_normal_subgroups': 44, 'number_subgroup_autclasses': 56, 'number_subgroup_classes': 84, 'number_subgroups': 7764, 'old_label': None, 'order': 111168, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 193], [3, 1160], [4, 386], [6, 1544], [8, 772], [12, 3088], [16, 1544], [24, 6176], [32, 3088], [48, 12352], [64, 6176], [96, 24704], [192, 49408], [193, 192], [579, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[37057, 110976], [74113, 192]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 196, 'pgroup': 0, 'primary_abelian_invariants': [64, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9], [4, 5], [8, 5], [16, 5], [32, 5], [64, 4], [192, 1], [384, 1]], 'representations': {'PC': {'code': '43023836931081284013122713998333971413484062145605317493274726077956947008935476624168211114647392625691859060173537147616629038650528127', 'gens': [1, 8], 'pres': [9, -2, -2, -2, -2, -2, -2, -3, -3, -193, 18, 46, 74, 102, 130, 158, 2045959, 3324688, 1175065, 654946, 42379, 36772, 59893, 286, 6905096, 2216177, 1714634, 1084787, 142928, 123983, 61298]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [201293672, 7189251, 776418240]}, 'Perm': {'d': 196, 'gens': [26998242104082005447251696691331464774121971917348421755781267835361429941668435221333290080630207260549917888723056059763539993175776658074908879762949012617169070415501257720842862810632964336955359428101490488135920181880491972015344559396903845870899558118113549760267322033639158277229321994017930485074559887727912882386576752937183479668551985879937835304, 2631778338730623662950964945824670653980764756662906445448946890283312750222914027144913759101874195455749646321665281014480436912763364625294578572203894275170402936839769371092982389742011367078542571256093075126368574007362860032302134699363967331838336966533207438392507094484694472919274785125127394266993739467967407942441269210233369459195139463953392461104, 53651049977427163004782649094143068173087154853604693633795859769783469643879806996027569149175074794409538134264301490310872601961150471788286697107340058590630568151646039445332768032894779979465847323816958134956968491642077503940495849602428272197081574774182305031506649821005649262198902553255728399362769286478552688840974860927203438716481864507921529723]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 192], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times F_{193}', 'transitive_degree': 579, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '16.1', '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], [15], [3]], 'aut_group': '8.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 8, 'aut_permdeg': 6, 'aut_perms': [120, 130], '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], [16, 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], [4, 1, 2], [8, 1, 4], [16, 1, 8]], 'center_label': '16.1', 'center_order': 16, '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': ['2.1', '2.1', '2.1', '2.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [8, 1, 4, 1], [16, 1, 8, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 16, 'exponents_of_order': [4], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[1, 0, 8]], 'familial': True, 'frattini_label': '8.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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, 16]], 'label': '16.1', 'linC_count': 8, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 1, 'linQ_dim': 8, 'linQ_dim_count': 1, 'linR_count': 4, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C16', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 16, 'number_divisions': 5, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 5, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 16, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 1], [4, 2], [8, 4], [16, 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': [[15], [3]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 130], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [16], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 1], [8, 1]], 'representations': {'PC': {'code': 149511, 'gens': [1], 'pres': [4, -2, -2, -2, -2, 8, 21, 34]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [1860]}, 'Perm': {'d': 16, 'gens': [20916435456000, 9703614452976, 4097506710982, 1313941673647]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [16], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{16}', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
