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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '792.91', 'ambient_counter': 91, 'ambient_order': 792, 'ambient_tex': 'C_{12}\\times D_{33}', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 396, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '792.91.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '396.13', 'subgroup_hash': 13, 'subgroup_order': 396, 'subgroup_tex': 'C_{33}:C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '792.91', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '66.a1.a1', 'complements': ['396.b1.b1', '396.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.d1.a1', '6.f1.a1', '22.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3692, 4923, 3547, 4840, 7015, 5306, 4653, 5864], 'generators': [9, 396, 528, 2, 72], 'label': '792.91.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '132.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '66.3'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 330, 'aut_gen_orders': [22, 10, 66, 10, 30], 'aut_gens': [[1, 12], [337, 276], [217, 60], [281, 12], [217, 336], [163, 336]], 'aut_group': None, 'aut_hash': 4845733366138083661, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2640, 'aut_permdeg': 68, 'aut_perms': [772530505889175007062458301990161878204012078255023961620356884759110029168101747299504476373723, 723274219127909559564854511345364990188541912291323619294589624757674850515774594834357988343975, 1527926244055793793527311276141985196255619415236177112500786444625965912631395886176354183572519, 1370040608417716104709513521901758346096051687910612654539804896689653501800280633054286252352129, 744977310478667584551709039326899902865940871006743266460505305636491481606808489573026221275659], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 33, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [11, 2, 5, 1], [12, 33, 4, 1], [22, 2, 5, 1], [33, 2, 10, 2], [33, 2, 20, 1], [66, 2, 10, 2], [66, 2, 20, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{11}:(C_2^2\\times C_{10}\\times S_3)', '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': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 2, 3], [4, 33, 2], [6, 1, 2], [6, 2, 3], [11, 2, 5], [12, 33, 4], [22, 2, 5], [33, 2, 40], [66, 2, 40]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '66.3', 'commutator_count': 1, 'commutator_label': '33.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 13, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['132.3', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 33, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [11, 2, 5, 1], [12, 33, 4, 1], [22, 2, 5, 1], [33, 2, 10, 2], [33, 2, 20, 1], [66, 2, 10, 2], [66, 2, 20, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 132, 'exponents_of_order': [2, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 0, 20]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '198.7', 'hash': 13, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [2, 33], 'inner_gens': [[1, 384], [25, 12]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 66, 'inner_split': True, 'inner_tex': 'D_{33}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 40, 'irrQ_dim': 40, 'irrR_degree': 4, 'irrep_stats': [[1, 12], [2, 96]], 'label': '396.13', 'linC_count': 20, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 9, 'linQ_dim': 14, 'linQ_dim_count': 1, 'linR_count': 30, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C33: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': 18, 'number_conjugacy_classes': 108, 'number_divisions': 18, 'number_normal_subgroups': 18, 'number_subgroup_autclasses': 28, 'number_subgroup_classes': 28, 'number_subgroups': 120, 'old_label': None, 'order': 396, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1], [3, 8], [4, 66], [6, 8], [11, 10], [12, 132], [22, 10], [33, 80], [66, 80]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 10], 'outer_gen_pows': [264, 0, 132], 'outer_gens': [[265, 120], [7, 120], [269, 84]], 'outer_group': '40.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 40, 'outer_permdeg': 11, 'outer_perms': [720, 3628800, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{10}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 5], [4, 3], [10, 2], [20, 4], [40, 2]], 'representations': {'PC': {'code': 364749738054471500119, 'gens': [1, 4], 'pres': [5, -2, -2, -3, -3, -11, 10, 26, 7683, 78, 9004]}, 'GLFp': {'d': 2, 'p': 67, 'gens': [7035, 10225944, 11128232]}, 'Perm': {'d': 21, 'gens': [122023018301552047, 6706022400, 753220435968000, 2554547108585472000, 4364893]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [12], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{33}:C_{12}', 'transitive_degree': 132, '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': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 330, 'aut_gen_orders': [2, 30, 2, 10, 2, 22], 'aut_gens': [[1, 6], [113, 258], [65, 150], [617, 654], [149, 294], [197, 786], [301, 534]], 'aut_group': None, 'aut_hash': 6779243509808250168, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5280, 'aut_permdeg': 70, 'aut_perms': [8428614840153996575484958496152439681307945471613590021743948146296123357872376725019886569683975925, 11282106947402510156121667533199464095257078844903278488017358310084998708571240835486324187628938725, 537948926397516136649868999624307090016551909650225386939319434088946796539202421295218376523113795, 6939232002145886265047193715318810802400173687128082342742803895200807181183226037111789262166108126, 8927387706294117808281337348585688736474873829556008883979073309256164605429393624762149497483784327, 6389934303506735945118771037825153671555554353347054585103292683771593446817793797806508459204469132], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 33, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 33, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 33, 4, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 2, 4, 1], [12, 33, 4, 1], [22, 2, 5, 1], [33, 2, 10, 2], [33, 2, 20, 1], [44, 2, 10, 1], [66, 2, 10, 2], [66, 2, 20, 1], [132, 2, 20, 2], [132, 2, 40, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{33}.(C_2^4\\times C_{10})', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 33, 2], [3, 1, 2], [3, 2, 3], [4, 1, 2], [4, 33, 2], [6, 1, 2], [6, 2, 3], [6, 33, 4], [11, 2, 5], [12, 1, 4], [12, 2, 6], [12, 33, 4], [22, 2, 5], [33, 2, 40], [44, 2, 10], [66, 2, 40], [132, 2, 80]], 'center_label': '12.2', 'center_order': 12, 'central_product': True, 'central_quotient': '66.3', 'commutator_count': 1, 'commutator_label': '33.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 91, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['4.1', 1], ['66.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 33, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 33, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 33, 2, 2], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 2, 4, 1], [12, 33, 4, 1], [22, 2, 5, 1], [33, 2, 10, 2], [33, 2, 20, 1], [44, 2, 10, 1], [66, 2, 10, 2], [66, 2, 20, 1], [132, 2, 20, 2], [132, 2, 40, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 132, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 0, 40]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '396.27', 'hash': 91, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [2, 33], 'inner_gens': [[1, 390], [409, 6]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 66, 'inner_split': True, 'inner_tex': 'D_{33}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 4, 'irrep_stats': [[1, 24], [2, 192]], 'label': '792.91', 'linC_count': 40, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 56, 'linQ_dim': 16, 'linQ_dim_count': 56, 'linR_count': 100, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C12*D33', 'ngens': 6, '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': 28, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 216, 'number_divisions': 30, 'number_normal_subgroups': 34, 'number_subgroup_autclasses': 62, 'number_subgroup_classes': 70, 'number_subgroups': 516, 'old_label': None, 'order': 792, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 67], [3, 8], [4, 68], [6, 140], [11, 10], [12, 148], [22, 10], [33, 80], [44, 20], [66, 80], [132, 160]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 2, 10], 'outer_gen_pows': [726, 0, 0, 66], 'outer_gens': [[529, 654], [397, 654], [1, 258], [533, 438]], 'outer_group': '80.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 80, 'outer_permdeg': 13, 'outer_perms': [720, 479001600, 3628800, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{10}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 5], [8, 1], [10, 2], [20, 5], [40, 4], [80, 1]], 'representations': {'PC': {'code': 1850115134966174437789926365010019, 'gens': [1, 3], 'pres': [6, -2, -3, -2, -2, -3, -11, 12, 7022, 50, 18723, 69, 23044, 118, 25925]}, 'GLFp': {'d': 2, 'p': 397, 'gens': [9323045302, 8572196043, 158006]}, 'Perm': {'d': 21, 'gens': [122002101778273920, 864, 3, 1680, 403200, 2676906211693190400]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}\\times D_{33}', 'transitive_degree': 264, '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': '2.1', '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': [[1]], '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], [2, 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], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, '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'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 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': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
