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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.131', 'ambient_counter': 131, 'ambient_order': 432, 'ambient_tex': 'C_{12}:C_{36}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 432, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '432.131.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.131', 'subgroup_hash': 131, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:C_{36}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '432.131', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.c1.a1', 'complements': ['432.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1', '3.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3190, 4577, 5452, 5987, 3453, 4266, 5959, 5422], 'generators': [9, 12, 216, 108, 144, 4, 18], 'label': '432.131.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '6.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '144.20', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 6, 6, 12, 12], 'aut_gens': [[1, 36], [251, 54], [19, 396], [5, 54], [317, 180], [259, 270], [355, 270]], 'aut_group': '1152.134251', 'aut_hash': 8723103591453834860, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1152, 'aut_permdeg': 30, 'aut_perms': [27146241720829671807422047066954, 57467567718460144711224256895131, 4106144990524829211987144367208, 8309060020586029516571523331984, 248607492081954995667630932949279, 38107069920652295880556023188130], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 4, 1], [4, 3, 8, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 2], [6, 2, 4, 1], [9, 1, 6, 1], [9, 2, 6, 1], [12, 1, 8, 1], [12, 2, 4, 1], [12, 2, 8, 1], [12, 3, 16, 1], [18, 1, 6, 1], [18, 1, 12, 1], [18, 2, 6, 1], [18, 2, 12, 1], [36, 1, 24, 1], [36, 2, 24, 1], [36, 3, 48, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_6^2.C_2^5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '192.1410', 'autcent_hash': 1410, 'autcent_nilpotent': True, 'autcent_order': 192, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5:C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [3, 2, 3], [4, 1, 4], [4, 3, 8], [6, 1, 6], [6, 2, 9], [9, 1, 6], [9, 2, 6], [12, 1, 8], [12, 2, 12], [12, 3, 16], [18, 1, 18], [18, 2, 18], [36, 1, 24], [36, 2, 24], [36, 3, 48]], 'center_label': '72.9', 'center_order': 72, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 131, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.1', 1], ['4.1', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 2], [4, 3, 2, 4], [6, 1, 2, 3], [6, 2, 1, 3], [6, 2, 2, 3], [9, 1, 6, 1], [9, 2, 6, 1], [12, 1, 4, 2], [12, 2, 2, 2], [12, 2, 4, 2], [12, 3, 4, 4], [18, 1, 6, 3], [18, 2, 6, 3], [36, 1, 12, 2], [36, 2, 12, 2], [36, 3, 12, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 36, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '12.5', 'frattini_quotient': '36.12', 'hash': 131, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 180], [289, 36]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 144], [2, 72]], 'label': '432.131', 'linC_count': 3456, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 32, 'linQ_dim': 12, 'linQ_dim_count': 192, 'linR_count': 2616, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C12:C36', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 216, 'number_divisions': 48, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 66, 'number_subgroup_classes': 106, 'number_subgroups': 164, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 3], [3, 8], [4, 28], [6, 24], [9, 18], [12, 80], [18, 54], [36, 216]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 12], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[19, 36], [17, 36], [19, 270], [19, 252], [133, 36]], 'outer_group': '192.1410', 'outer_hash': 1410, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 48, 'outer_perms': [11274338498281355372026976700950857762195356225426031, 2434729936807888072723479187659316925687532343564575389448960, 16894363024349085381985912479676634413252986202708811, 815465298289800461576155849980921396177544772278662484870132, 5462641175370042945215894834224821793309974228463007351751043], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:C_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [4, 4, 9], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 14], [4, 12], [6, 4], [8, 2], [12, 10], [24, 2]], 'representations': {'PC': {'code': 48463456410106137299160341401, 'gens': [1, 5], 'pres': [7, -2, -2, -3, -3, -2, -2, -3, 14, 36, 79, 6304, 102, 15125, 124, 14118]}, 'GLZN': {'d': 2, 'p': 57, 'gens': [248027, 4629850, 1296358, 3703880, 185200, 3559384, 6852178]}, 'Perm': {'d': 20, 'gens': [4032127, 17, 135184941877708800, 7983360, 7, 263631088065945600, 840]}}, 'schur_multiplier': [4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 36], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}:C_{36}', 'transitive_degree': 144, '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': '144.20', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 6, 6, 12, 12], 'aut_gens': [[1, 36], [251, 54], [19, 396], [5, 54], [317, 180], [259, 270], [355, 270]], 'aut_group': '1152.134251', 'aut_hash': 8723103591453834860, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1152, 'aut_permdeg': 30, 'aut_perms': [27146241720829671807422047066954, 57467567718460144711224256895131, 4106144990524829211987144367208, 8309060020586029516571523331984, 248607492081954995667630932949279, 38107069920652295880556023188130], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 4, 1], [4, 3, 8, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 2], [6, 2, 4, 1], [9, 1, 6, 1], [9, 2, 6, 1], [12, 1, 8, 1], [12, 2, 4, 1], [12, 2, 8, 1], [12, 3, 16, 1], [18, 1, 6, 1], [18, 1, 12, 1], [18, 2, 6, 1], [18, 2, 12, 1], [36, 1, 24, 1], [36, 2, 24, 1], [36, 3, 48, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_6^2.C_2^5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '192.1410', 'autcent_hash': 1410, 'autcent_nilpotent': True, 'autcent_order': 192, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5:C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [3, 2, 3], [4, 1, 4], [4, 3, 8], [6, 1, 6], [6, 2, 9], [9, 1, 6], [9, 2, 6], [12, 1, 8], [12, 2, 12], [12, 3, 16], [18, 1, 18], [18, 2, 18], [36, 1, 24], [36, 2, 24], [36, 3, 48]], 'center_label': '72.9', 'center_order': 72, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 131, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.1', 1], ['4.1', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 2], [4, 3, 2, 4], [6, 1, 2, 3], [6, 2, 1, 3], [6, 2, 2, 3], [9, 1, 6, 1], [9, 2, 6, 1], [12, 1, 4, 2], [12, 2, 2, 2], [12, 2, 4, 2], [12, 3, 4, 4], [18, 1, 6, 3], [18, 2, 6, 3], [36, 1, 12, 2], [36, 2, 12, 2], [36, 3, 12, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 36, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '12.5', 'frattini_quotient': '36.12', 'hash': 131, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 180], [289, 36]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 144], [2, 72]], 'label': '432.131', 'linC_count': 3456, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 32, 'linQ_dim': 12, 'linQ_dim_count': 192, 'linR_count': 2616, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C12:C36', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 216, 'number_divisions': 48, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 66, 'number_subgroup_classes': 106, 'number_subgroups': 164, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 3], [3, 8], [4, 28], [6, 24], [9, 18], [12, 80], [18, 54], [36, 216]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 12], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[19, 36], [17, 36], [19, 270], [19, 252], [133, 36]], 'outer_group': '192.1410', 'outer_hash': 1410, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 48, 'outer_perms': [11274338498281355372026976700950857762195356225426031, 2434729936807888072723479187659316925687532343564575389448960, 16894363024349085381985912479676634413252986202708811, 815465298289800461576155849980921396177544772278662484870132, 5462641175370042945215894834224821793309974228463007351751043], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:C_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [4, 4, 9], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 14], [4, 12], [6, 4], [8, 2], [12, 10], [24, 2]], 'representations': {'PC': {'code': 48463456410106137299160341401, 'gens': [1, 5], 'pres': [7, -2, -2, -3, -3, -2, -2, -3, 14, 36, 79, 6304, 102, 15125, 124, 14118]}, 'GLZN': {'d': 2, 'p': 57, 'gens': [248027, 4629850, 1296358, 3703880, 185200, 3559384, 6852178]}, 'Perm': {'d': 20, 'gens': [4032127, 17, 135184941877708800, 7983360, 7, 263631088065945600, 840]}}, 'schur_multiplier': [4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 36], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}:C_{36}', 'transitive_degree': 144, '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': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', '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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, 'wreath_data': None, 'wreath_product': False}
