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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1824.368', 'ambient_counter': 368, 'ambient_order': 1824, 'ambient_tex': 'C_{38}.(C_6\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 456, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1824.368.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '456.21', 'subgroup_hash': 21, 'subgroup_order': 456, 'subgroup_tex': 'C_{76}.C_6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1824.368', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2736.be', 'aut_weyl_index': 4, 'centralizer': '456.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.c1.a1', '8.f1.a1', '12.d1.a1', '76.h1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5357, 6644, 6548, 6799, 5250, 5344, 4789, 6192], 'generators': [24, 96, 16, 36, 913], 'label': '1824.368.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.c1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '912.129', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '456.11'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 684, 'aut_gen_orders': [18, 6, 2, 38], 'aut_gens': [[1, 6], [343, 378], [343, 339], [229, 6], [49, 234]], 'aut_group': '8208.e', 'aut_hash': 5451499820202377276, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 8208, 'aut_permdeg': 25, 'aut_perms': [9831165572869381011082685, 13568775956992080963877948, 29439511, 12301064573735015361158401], 'aut_phi_ratio': 57.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 19, 1, 2], [4, 2, 3, 1], [6, 19, 1, 2], [12, 38, 3, 2], [19, 3, 6, 1], [38, 3, 6, 1], [76, 6, 18, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4\\times F_{19}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 342, 'autcentquo_group': '2052.s', 'autcentquo_hash': 8582295013454683600, 'autcentquo_nilpotent': False, 'autcentquo_order': 2052, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{19}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 19, 2], [4, 2, 3], [6, 19, 2], [12, 38, 6], [19, 3, 6], [38, 3, 6], [76, 6, 18]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '228.9', 'commutator_count': 1, 'commutator_label': '38.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '19.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 21, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['57.1', 1], ['8.4', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 19, 2, 1], [4, 2, 1, 3], [6, 19, 2, 1], [12, 38, 2, 3], [19, 3, 6, 1], [38, 3, 6, 1], [76, 6, 6, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8, 'exponent': 228, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3, 19], 'factors_of_order': [2, 3, 19], 'faithful_reps': [[6, 0, 6]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '228.9', 'hash': 21, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 114, 'inner_gen_orders': [6, 38], 'inner_gens': [[1, 42], [421, 6]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 228, 'inner_split': False, 'inner_tex': 'C_{38}:C_6', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 36, 'irrQ_dim': 36, 'irrR_degree': 12, 'irrep_stats': [[1, 12], [2, 3], [3, 24], [6, 6]], 'label': '456.21', 'linC_count': 72, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 4, 'linQ_dim': 22, 'linQ_dim_count': 8, 'linR_count': 24, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C76.C6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 12, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 45, 'number_divisions': 15, 'number_normal_subgroups': 18, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 24, 'number_subgroups': 132, 'old_label': None, 'order': 456, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1], [3, 38], [4, 6], [6, 38], [12, 228], [19, 18], [38, 18], [76, 108]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6, 6], 'outer_gen_pows': [116, 0], 'outer_gens': [[343, 78], [115, 111]], 'outer_group': '36.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 36, 'outer_permdeg': 8, 'outer_perms': [750, 5761], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [4, 1], [18, 4], [36, 1]], 'representations': {'PC': {'code': 264207106169181347364458666875875257, 'gens': [1, 3], 'pres': [5, -2, -3, -2, -2, -19, 10, 1146, 632, 2212, 42, 1683, 1328, 58, 4204, 3309]}, 'GLZN': {'d': 2, 'p': 57, 'gens': [248027, 1296400, 185365, 3703880, 10433659]}, 'Perm': {'d': 27, 'gens': [7039, 12593, 16829872126675744847961600, 18619, 436283398747903846884958080]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{76}.C_6', 'transitive_degree': 152, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 684, 'aut_gen_orders': [4, 9, 36, 18, 18, 36], 'aut_gens': [[1, 2, 48], [37, 1658, 1776], [1, 386, 1680], [13, 866, 1200], [25, 218, 816], [37, 902, 240], [13, 482, 456]], 'aut_group': None, 'aut_hash': 8769557382641253795, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10944, 'aut_permdeg': 101, 'aut_perms': [7726635786047239960242434028895676676842018636408952972604583320176112362244445163037171856353098846218733759355450648164654640670392939777969974694934613074450, 6786830678249063999050191721087306092144697682042737844966062405372105850309192687737049991342897203798688049360847706609821119300079792856608937881401299661970, 6032876663550780704987800771095318904447420178974563991118495962380243230762678089028630001240402334377751342946624108398599323459474420051542786693058017392504, 372343407136136480967850354158037048588871037762169148643597079368109645104728675889106906064542075108365162253489659661336453659365425844606022927565658652056, 7257289306431930893537863853711061351536336560773537193238232065947857131736230591632699271746342187052518542339975184303390998179642386303378359437898603353408, 471439423621655823196036787237116203302445763253003335209190991161455606415454985189294117777937510988827743535058464734780646028089459397881769328755998259198], 'aut_phi_ratio': 19.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 76, 1, 1], [3, 19, 1, 2], [4, 1, 2, 1], [4, 2, 1, 1], [4, 4, 1, 1], [4, 76, 1, 1], [6, 19, 1, 2], [6, 38, 1, 2], [6, 76, 1, 4], [8, 38, 2, 2], [12, 19, 2, 2], [12, 38, 1, 2], [12, 76, 1, 4], [19, 6, 3, 1], [24, 38, 2, 4], [38, 6, 3, 1], [38, 12, 3, 1], [38, 12, 6, 1], [76, 6, 6, 1], [76, 12, 3, 1], [76, 12, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{38}.C_{18}.C_2^4', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 342, 'autcentquo_group': '1368.165', 'autcentquo_hash': 165, 'autcentquo_nilpotent': False, 'autcentquo_order': 1368, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times F_{19}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 76, 1], [3, 19, 2], [4, 1, 2], [4, 2, 1], [4, 4, 1], [4, 76, 1], [6, 19, 2], [6, 38, 2], [6, 76, 4], [8, 38, 4], [12, 19, 4], [12, 38, 2], [12, 76, 4], [19, 6, 3], [24, 38, 8], [38, 6, 3], [38, 12, 9], [76, 6, 6], [76, 12, 9]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '456.11', 'commutator_count': 1, 'commutator_label': '76.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '19.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 368, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 76, 1, 1], [3, 19, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 4, 1, 1], [4, 76, 1, 1], [6, 19, 2, 1], [6, 38, 2, 1], [6, 76, 2, 2], [8, 38, 2, 2], [12, 19, 4, 1], [12, 38, 2, 1], [12, 76, 2, 2], [19, 6, 3, 1], [24, 38, 4, 2], [38, 6, 3, 1], [38, 12, 3, 1], [38, 12, 6, 1], [76, 6, 6, 1], [76, 12, 3, 1], [76, 12, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 174720, 'exponent': 456, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 19], 'factors_of_order': [2, 3, 19], 'faithful_reps': [[12, 0, 6]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '456.44', 'hash': 368, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 228, 'inner_gen_orders': [2, 12, 38], 'inner_gens': [[1, 14, 72], [37, 2, 1488], [25, 386, 48]], 'inner_hash': 11, 'inner_nilpotent': False, 'inner_order': 456, 'inner_split': False, 'inner_tex': 'D_{38}:C_6', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 72, 'irrQ_dim': 72, 'irrR_degree': 24, 'irrep_stats': [[1, 24], [2, 18], [6, 24], [12, 6]], 'label': '1824.368', 'linC_count': 288, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 26, 'linQ_degree_count': 4, 'linQ_dim': 26, 'linQ_dim_count': 4, 'linR_count': 72, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C38.(C6*D4)', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 40, 'number_characteristic_subgroups': 49, 'number_conjugacy_classes': 72, 'number_divisions': 29, 'number_normal_subgroups': 49, 'number_subgroup_autclasses': 124, 'number_subgroup_classes': 124, 'number_subgroups': 1426, 'old_label': None, 'order': 1824, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 83], [3, 38], [4, 84], [6, 418], [8, 152], [12, 456], [19, 18], [24, 304], [38, 126], [76, 144]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 16], 'outer_gens': [[25, 2, 1776], [1, 26, 1776], [25, 2, 744]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [24, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 2], [8, 1], [16, 1], [18, 4], [36, 2], [72, 1]], 'representations': {'PC': {'code': 3708379798458057232578081547606565180675068355598908789272035413, 'gens': [1, 2, 6], 'pres': [7, 2, 2, 2, 2, 3, 2, 19, 197, 36, 590, 58, 80, 3029, 31260, 5563, 1790, 1419, 124, 28237, 12956, 4143, 3268]}, 'Perm': {'d': 35, 'gens': [8700824928274815125551995560585433676, 3079030941673, 4490069588562, 18182049055650231038417582272364544000, 5669587549392, 7177442312043, 321317014377178472917828585806360576000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{38}.(C_6\\times D_4)', 'transitive_degree': 304, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', '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': 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, 3]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], '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': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
