-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.29080', 'ambient_counter': 29080, 'ambient_order': 256, 'ambient_tex': 'C_2^2:D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.29080.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '256.29080', 'aut_centralizer_order': 1024, 'aut_label': '8.l1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '384.20100', 'aut_weyl_index': 1024, 'centralizer': '2.i1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.s1', '4.t1', '4.u1', '4.v1', '4.w1'], 'contains': ['16.f1', '16.s1', '16.ba1', '16.ce1'], 'core': '8.l1', 'coset_action_label': None, 'count': 1, 'diagramx': [1540, 8938, 1534, 8871], 'generators': [19013, 2671, 1801, 12103, 8645], 'label': '256.29080.8.l1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.l1', 'normal_contained_in': ['4.s1', '4.t1', '4.u1', '4.v1', '4.w1'], 'normal_contains': ['16.f1', '16.s1'], 'normalizer': '1.a1', 'old_label': '8.l1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 26040, 'aut_gen_orders': [2, 5], 'aut_gens': [[1, 2, 4, 8, 16], [5, 2, 4, 12, 16], [11, 8, 27, 26, 13]], 'aut_group': '9999360.a', 'aut_hash': 2505043529366670169, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 9999360, 'aut_permdeg': 31, 'aut_perms': [2450617681096434660778009755366, 945758899833610526331495647332850], 'aut_phi_ratio': 624960.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 31, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(5,2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 26040, 'autcent_group': '9999360.a', 'autcent_hash': 2505043529366670169, 'autcent_nilpotent': False, 'autcent_order': 9999360, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(5,2)', '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, 31]], 'center_label': '32.51', 'center_order': 32, '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', '2.1', '2.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 51, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 5]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 31]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3, 5, 7, 31], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '32.51', 'hash': 51, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 8, 16], [1, 2, 4, 8, 16], [1, 2, 4, 8, 16], [1, 2, 4, 8, 16], [1, 2, 4, 8, 16]], '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, 32]], 'label': '32.51', 'linC_count': None, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, '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': 'C2^5', 'ngens': 5, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 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': 32, 'number_divisions': 32, 'number_normal_subgroups': 374, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 374, 'number_subgroups': 374, 'old_label': None, 'order': 32, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 31]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 26040, 'outer_gen_orders': [2, 5], 'outer_gen_pows': [0, 0], 'outer_gens': [[5, 2, 4, 12, 16], [11, 8, 27, 26, 13]], 'outer_group': '9999360.a', 'outer_hash': 2505043529366670169, 'outer_nilpotent': False, 'outer_order': 9999360, 'outer_permdeg': 31, 'outer_perms': [2450617681096434660778009755366, 945758899833610526331495647332850], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\GL(5,2)', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 10, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 32]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3, 4, 5], 'pres': [5, -2, 2, 2, 2, 2]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [141602720900, 705686952884, 706461793860, 706460730980, 706461792404]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [5226561, 7292993, 5128257, 20225089, 6210625]}, 'Perm': {'d': 10, 'gens': [362880, 5040, 120, 6, 1]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2], 'aut_gens': [[5811, 19013, 2671, 1801, 5859, 13069], [5811, 19013, 2671, 1801, 5859, 2635], [5811, 19013, 2671, 1801, 6387, 13069], [5811, 12097, 2671, 1801, 6387, 2635], [6435, 19013, 2671, 1801, 6387, 13069], [5811, 8651, 2671, 1801, 5859, 13069], [6435, 12097, 9587, 1801, 6387, 9623], [8641, 19013, 2671, 1801, 6387, 2635], [16185, 1735, 2671, 1801, 16233, 2635], [5811, 19013, 2671, 1801, 5859, 2707], [5811, 1807, 19877, 1801, 16161, 19985], [5811, 19013, 2671, 1801, 5859, 19985], [5811, 1735, 13033, 1801, 16233, 13069], [5811, 8723, 2671, 1801, 5859, 13069], [5883, 19085, 2593, 1801, 5859, 2629], [5811, 19085, 13033, 1801, 5859, 2635], [5811, 19949, 12169, 12103, 5859, 12139], [16257, 1807, 9587, 1801, 16161, 9623], [5811, 8723, 12961, 1801, 5859, 2707]], 'aut_group': '393216.ks', 'aut_hash': 7890213455797903960, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 393216, 'aut_permdeg': 40, 'aut_perms': [20411667091058432246505316974235419004352681647, 418701021943486378894063690223238345484897536000, 438858229938491675237970216785258431074201269167, 418700856482971009531605346437095251117680230976, 13764352240142053955379472772441330119761846, 648208745794919218780374952124341409714126437927, 439112823478928711743650417625886008937371791359, 296526531828236851992724973553229781941560654, 648463189230341654295629756429838108595720822567, 229635224798537815669272152616698775295422242503, 418701021943588235992231571803850064660413491200, 20680624202330070381620508949360292828021643175, 437866293355082858762297168507970490041298134, 455697469238640341352176912786102682742905676453, 20835748079319736019560405948599118956142832208, 559672839034284208695586761897044022158424729120, 418856255721551573564769923910645976870709150766, 648053324681678279296018200946777890931830518694], 'aut_phi_ratio': 3072.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 3, 2], [2, 2, 8, 1], [2, 2, 12, 1], [2, 4, 2, 1], [2, 4, 12, 1], [2, 8, 2, 1], [4, 2, 4, 1], [4, 4, 6, 2], [4, 8, 1, 1], [4, 8, 3, 1], [4, 8, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^{12}.(C_2^2\\times S_4)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': None, 'autcent_hash': 3946057693156513511, 'autcent_nilpotent': True, 'autcent_order': 32768, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{15}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '12.4', 'autcentquo_hash': 4, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 20], [2, 4, 14], [2, 8, 2], [4, 2, 4], [4, 4, 12], [4, 8, 10]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '32.51', 'commutator_count': 1, 'commutator_label': '8.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 29080, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['32.27', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 20], [2, 4, 1, 14], [2, 8, 1, 2], [4, 2, 1, 4], [4, 4, 1, 12], [4, 8, 1, 10]], 'element_repr_type': 'GLZN', 'elementary': 2, 'eulerian_function': 833280, 'exponent': 4, 'exponents_of_order': [8], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '32.51', 'hash': 29080, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 1, 2, 2], 'inner_gens': [[5811, 19013, 2671, 1801, 6387, 13069], [5811, 19013, 2671, 1801, 5859, 12997], [5811, 19013, 2671, 1801, 5859, 2635], [5811, 19013, 2671, 1801, 5859, 13069], [6435, 19013, 2671, 1801, 5859, 13069], [5811, 19085, 13033, 1801, 5859, 13069]], 'inner_hash': 51, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': False, 'inner_tex': 'C_2^5', 'inner_used': [1, 2, 3, 5, 6], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 32], [4, 6]], 'label': '256.29080', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, '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': 'C2^2:D4^2', 'ngens': 5, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 70, 'number_divisions': 70, 'number_normal_subgroups': 635, 'number_subgroup_autclasses': 297, 'number_subgroup_classes': 4309, 'number_subgroups': 10903, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 119], [4, 136]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [4, 2, 4, 2, 4], 'outer_gen_pows': [1729, 15969, 1729, 1729, 1729], 'outer_gens': [[16185, 2593, 12961, 12175, 16161, 13069], [8713, 2599, 8651, 12103, 16161, 1837], [16185, 13039, 19949, 12175, 16233, 13069], [16185, 8651, 19949, 1801, 16161, 13069], [8713, 19949, 12097, 12103, 5859, 8681]], 'outer_group': None, 'outer_hash': 8137149755355345617, 'outer_nilpotent': False, 'outer_order': 12288, 'outer_permdeg': 20, 'outer_perms': [628940458926327985, 39147941002006447, 136315986362063670, 275345396997114366, 396990329238262446], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^8.D_6.C_2^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 12, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 32], [4, 6]], 'representations': {'PC': {'code': 156806340759326557264, 'gens': [1, 2, 3, 4, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 1924, 116, 2030, 2710, 166]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [91793140190669372, 125101729084386182, 25038659807093174, 125101729084381808, 125101736038820194]}, 'GLZN': {'d': 2, 'p': 12, 'gens': [1765, 16233, 8645, 2665, 19019, 1733, 1801, 9587]}, 'Perm': {'d': 12, 'gens': [40723320, 11291166, 14933656, 90842401, 135732256, 90842400, 135732240, 7]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2:D_4^2', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 84, 'aut_gen_orders': [3, 3], 'aut_gens': [[1, 2, 4], [4, 5, 3], [2, 4, 1]], 'aut_group': '168.42', 'aut_hash': 42, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 168, 'aut_permdeg': 7, 'aut_perms': [4361, 244], 'aut_phi_ratio': 42.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 7, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PSL(2,7)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 84, 'autcent_group': '168.42', 'autcent_hash': 42, 'autcent_nilpotent': False, 'autcent_order': 168, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\PSL(2,7)', '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, 7]], 'center_label': '8.5', 'center_order': 8, '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'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [3], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '8.5', 'hash': 5, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 4], [1, 2, 4], [1, 2, 4]], '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, 8]], 'label': '8.5', 'linC_count': 28, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 28, 'linQ_dim': 3, 'linQ_dim_count': 28, 'linR_count': 28, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^3', 'ngens': 3, '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': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 8, 'number_divisions': 8, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 16, 'number_subgroups': 16, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 7]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 84, 'outer_gen_orders': [3, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[4, 5, 3], [2, 4, 1]], 'outer_group': '168.42', 'outer_hash': 42, 'outer_nilpotent': False, 'outer_order': 168, 'outer_permdeg': 7, 'outer_perms': [4361, 244], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\PSL(2,7)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 6, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3], 'pres': [3, -2, 2, 2]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [16482, 16322, 3362]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [8156, 13286, 13933]}, 'Perm': {'d': 6, 'gens': [120, 6, 1]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3', 'transitive_degree': 8, 'wreath_data': None, 'wreath_product': False}
