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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30638', 'ambient_counter': 30638, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30638.2.l1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.l1', 'outer_equivalence': True, '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': '128.1410', 'subgroup_hash': 1410, 'subgroup_order': 128, 'subgroup_tex': 'C_2.D_4^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '256.30638', 'aut_centralizer_order': None, 'aut_label': '2.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1', 'complements': ['128.n1', '128.h1', '128.j1', '128.k1', '128.o1', '128.m1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.x1', '4.z1', '4.ba1', '4.be1', '4.bf1', '4.bi1', '4.bl1', '4.bv1', '4.bw1', '4.ca1', '4.ce1', '4.cy1', '4.dc1', '4.di1', '4.dp1'], 'core': '2.l1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [3560440, 4887236, 3118060, 3715041], 'label': '256.30638.2.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.l1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.x1', '4.z1', '4.ba1', '4.be1', '4.bf1', '4.bi1', '4.bl1', '4.bv1', '4.bw1', '4.ca1', '4.ce1', '4.cy1', '4.dc1', '4.di1', '4.dp1'], 'normalizer': '1.a1', 'old_label': '2.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.l1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1034121, 111751, 774151, 1330548, 4458688], [1069449, 111751, 774151, 1366644, 919760], [1678863, 2598929, 774151, 1330548, 4458688], [1697679, 111751, 774151, 3998268, 4445152], [1034121, 1935383, 774151, 4020828, 3573944], [1088265, 111751, 774151, 3984732, 1804504], [1034121, 165895, 774151, 3984732, 1804504], [1034121, 111751, 774151, 3984732, 4458688], [1034121, 111751, 774151, 1330548, 1804504], [1697679, 111751, 774151, 1330548, 4458688], [1034121, 111751, 774151, 3998268, 4458688], [1034121, 1935383, 774151, 1330548, 3573944], [1034121, 111751, 774151, 1330548, 3573944]], 'aut_group': '4096.bri', 'aut_hash': 3677823439335518020, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 32, 'aut_perms': [40319, 5413204723901, 12316, 1321086775680, 34990, 4296764102400, 50965158269615912011351298108137390, 25959064782932176896000, 16976205612407767746763948129344000, 16976205612302050842642213751884316, 8231691320552322981363253248005329, 187973685953487802368000], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 4, 2, 4], [2, 8, 1, 1], [4, 4, 2, 5], [4, 8, 1, 5]], 'aut_supersolvable': True, 'aut_tex': 'C_2^{12}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4096.bri', 'autcent_hash': 3677823439335518020, 'autcent_nilpotent': True, 'autcent_order': 4096, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{12}', '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], [2, 4, 8], [2, 8, 1], [4, 4, 10], [4, 8, 5]], 'center_label': '8.5', 'center_order': 8, 'central_product': False, 'central_quotient': '16.14', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1410, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 4, 1, 8], [2, 8, 1, 1], [4, 4, 1, 6], [4, 4, 2, 2], [4, 8, 1, 5]], 'element_repr_type': 'GLZN', 'elementary': 2, 'eulerian_function': 20160, 'exponent': 4, 'exponents_of_order': [7], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '16.14', 'hash': 1410, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 1, 2, 2], 'inner_gens': [[1034121, 111751, 774151, 4020828, 1804504], [1034121, 111751, 774151, 3998268, 1790968], [1034121, 111751, 774151, 1330548, 4458688], [1015305, 775297, 774151, 1330548, 4458688], [1088265, 829441, 774151, 1330548, 4458688]], 'inner_hash': 14, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': None, 'inner_tex': 'C_2^4', 'inner_used': [1, 2, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12], [4, 4]], 'label': '128.1410', 'linC_count': 64, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 80, 'linQ_dim': 8, 'linQ_dim_count': 80, 'linR_count': 80, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2.D4^2', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 82, 'number_conjugacy_classes': 32, 'number_divisions': 30, 'number_normal_subgroups': 104, 'number_subgroup_autclasses': 270, 'number_subgroup_classes': 401, 'number_subgroups': 980, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 47], [4, 80]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [110593, 110593, 110593, 110593, 110593, 110593, 110593, 110593, 110593, 110593, 110593, 110593], 'outer_gens': [[1069449, 111751, 774151, 1366644, 919760], [1678863, 2598929, 774151, 1330548, 4458688], [1697679, 111751, 774151, 3998268, 4445152], [1034121, 1935383, 774151, 4020828, 3573944], [1088265, 111751, 774151, 3984732, 1804504], [1034121, 165895, 774151, 3984732, 1804504], [1034121, 111751, 774151, 3984732, 4458688], [1034121, 111751, 774151, 1330548, 1804504], [1697679, 111751, 774151, 1330548, 4458688], [1034121, 111751, 774151, 3998268, 4458688], [1034121, 1935383, 774151, 1330548, 3573944], [1034121, 111751, 774151, 1330548, 3573944]], 'outer_group': '256.56092', 'outer_hash': 56092, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 256, 'outer_perms': [3351473963843899643211864737955490014426261046274035196226361864013187540172794645695578349969881491860447568940900871254781535370059986857505868405814437629263505181499269547768149605660826924407096122519829953840893449652968960137873301883774082840916488222544716576680199697704721647236436086278049197189726019720930350642019099282658975969256580669256648081249441280809338437804870085481598838694744264211367903046058310741254743263462032356811956571343776169434439454768355087526670553339301809491200, 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48, 'gens': [1936529, 111751, 1880081, 774151, 3560408, 1006665, 2376]}, 'Perm': {'d': 16, 'gens': [287404588809, 1339815014040, 5165, 2965618656005, 4209473318400, 16, 11520]}}, 'schur_multiplier': [2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [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.D_4^2', 'transitive_degree': 32, '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': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[2821289, 4887236, 962672, 3715041, 4562537], [2821289, 4887236, 463828, 3715041, 4562537], [2821289, 4887236, 962672, 3715041, 5226095], [2821289, 4887236, 962672, 4378599, 4562537], [3428399, 4887236, 962672, 3715041, 4562537], [2821289, 4887236, 962672, 3715041, 2793049], [2821289, 4887236, 4501600, 3715041, 4562537], [2821289, 3117748, 962672, 3715041, 4562537], [2821289, 4887236, 962672, 3715041, 4618985], [2821289, 4887236, 962672, 3660897, 4562537], [2821289, 2233052, 962672, 3715041, 4562537], [2764841, 4887236, 962672, 3715041, 4562537], [2821289, 4887236, 962672, 3751137, 4562537], [2821289, 4887236, 3630392, 3660897, 4562537], [2821289, 4901348, 962672, 3715041, 4618985], [2821289, 4887236, 3616856, 3715041, 4562537], [4590745, 2233052, 962672, 3715041, 4562537]], 'aut_group': '1024.djl', 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 65536, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 512.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 4, 1], [2, 4, 2, 3], [2, 4, 4, 1], [2, 8, 1, 1], [2, 8, 2, 2], [4, 2, 4, 1], [4, 4, 2, 6], [4, 4, 4, 1], [4, 8, 1, 3], [4, 8, 2, 4]], 'aut_supersolvable': None, 'aut_tex': 'C_2^9.C_2', 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [2, 4, 10], [2, 8, 5], [4, 2, 4], [4, 4, 16], [4, 8, 11]], 'center_label': '8.5', 'center_order': 8, 'central_product': False, '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': 30638, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [2, 4, 1, 10], [2, 8, 1, 5], [4, 2, 1, 4], [4, 4, 1, 14], [4, 4, 2, 1], [4, 8, 1, 11]], 'element_repr_type': 'GLZN', 'elementary': 2, 'eulerian_function': 4999680, 'exponent': 4, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '32.51', 'hash': 30638, 'hyperelementary': 2, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [2, 2, 2, 2, 2], 'inner_gens': [[2821289, 4887236, 962672, 3751137, 4562537], [2821289, 4887236, 3630392, 3660897, 4562537], [2821289, 4901348, 962672, 3715041, 4618985], [4590745, 2233052, 962672, 3715041, 4562537], [2821289, 4887236, 3616856, 3715041, 4562537]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 32, 'inner_split': None, 'inner_tex': 'C_2^5', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 16], [4, 10]], 'label': '256.30638', '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': False, 'monomial': True, 'name': 'C4.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': 31, 'number_characteristic_subgroups': 133, 'number_conjugacy_classes': 58, 'number_divisions': 57, 'number_normal_subgroups': 505, 'number_subgroup_autclasses': 752, 'number_subgroup_classes': 1973, 'number_subgroups': 5191, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 95], [4, 160]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': True, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 2048, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': 5, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 16], [4, 8], [8, 1]], 'representations': {'PC': {'code': 9711549556612720849142868, 'gens': [1, 2, 3, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 154, 66, 7044, 2892, 116, 2710, 166]}, 'GLZN': {'d': 2, 'p': 48, 'gens': [774151, 1014537, 1936529, 110599, 2352, 1880081, 2793049, 3630392]}, 'Perm': {'d': 16, 'gens': [1334142836767, 1495562745601, 1321086780856, 2891341111680, 4302991486103, 4302991486080, 11520, 4302991486087]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 4], '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_4.D_4^2', 'transitive_degree': 64, '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}
