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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '48400.j', 'ambient_counter': 10, 'ambient_order': 48400, 'ambient_tex': 'C_{55}:(Q_8\\times F_{11})', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 24200, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '48400.j.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', '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': '24200.k', 'subgroup_hash': 2991584039182823895, 'subgroup_order': 24200, 'subgroup_tex': 'C_{11}^2:(Q_8\\times C_5^2)', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '48400.j', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1', 'complements': ['24200.b1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '10.g1', '10.h1', '22.f1'], 'core': '2.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [1871, 5422, 6993, 4291], 'generators': [1105, 43580, 2, 9680, 9790, 4400, 24200], 'label': '48400.j.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1', '10.g1', '10.h1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '4840.y', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '4840.y'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '100.16', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [110, 10, 20, 10, 4], 'aut_gens': [[1, 10, 2200], [24001, 10510, 2200], [8021, 2690, 17600], [15781, 3695, 800], [4701, 19390, 4400], [2661, 1475, 200]], 'aut_group': None, 'aut_hash': 410256423351182531, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1936000, 'aut_permdeg': 649, 'aut_perms': 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'aut_phi_ratio': 220.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 22, 2, 1], [4, 242, 1, 1], [5, 1, 4, 1], [5, 121, 5, 4], [10, 1, 4, 1], [10, 121, 5, 4], [11, 10, 2, 1], [11, 20, 5, 1], [20, 22, 8, 1], [20, 242, 4, 1], [20, 242, 5, 4], [20, 242, 10, 4], [22, 10, 2, 1], [22, 20, 5, 1], [44, 110, 4, 1], [55, 10, 8, 1], [55, 20, 20, 1], [110, 10, 8, 1], [110, 20, 20, 1], [220, 110, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{10}^2.C_{10}.C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '80.50', 'autcent_hash': 50, 'autcent_nilpotent': False, 'autcent_order': 80, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': '24200.bg', 'autcentquo_hash': 3957277396302200749, 'autcentquo_nilpotent': False, 'autcentquo_order': 24200, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{11}\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [4, 22, 2], [4, 242, 1], [5, 1, 4], [5, 121, 20], [10, 1, 4], [10, 121, 20], [11, 10, 2], [11, 20, 5], [20, 22, 8], [20, 242, 64], [22, 10, 2], [22, 20, 5], [44, 110, 4], [55, 10, 8], [55, 20, 20], [110, 10, 8], [110, 20, 20], [220, 110, 16]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '2420.x', 'commutator_count': 1, 'commutator_label': '242.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '5.1', '11.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 11, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['4840.bc', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 22, 1, 2], [4, 242, 1, 1], [5, 1, 4, 1], [5, 121, 4, 5], [10, 1, 4, 1], [10, 121, 4, 5], [11, 10, 1, 2], [11, 20, 1, 5], [20, 22, 4, 2], [20, 242, 4, 16], [22, 10, 1, 2], [22, 20, 1, 5], [44, 110, 2, 2], [55, 10, 4, 2], [55, 20, 4, 5], [110, 10, 4, 2], [110, 20, 4, 5], [220, 110, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 220, 'exponents_of_order': [3, 2, 2], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[20, 0, 20]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '12100.t', 'hash': 2991584039182823895, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 22, 11], 'inner_gens': [[1, 18110, 15400], [8301, 10, 22000], [11001, 4410, 2200]], 'inner_hash': 3244222575460283753, 'inner_nilpotent': False, 'inner_order': 2420, 'inner_split': True, 'inner_tex': 'D_{11}:F_{11}', 'inner_used': [1, 2], 'irrC_degree': 20, 'irrQ_degree': 80, 'irrQ_dim': 160, 'irrR_degree': 40, 'irrep_stats': [[1, 100], [2, 25], [10, 40], [20, 50]], 'label': '24200.k', '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': 'C11^2:(Q8*C5^2)', '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, 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': 34, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 215, 'number_divisions': 67, 'number_normal_subgroups': 64, 'number_subgroup_autclasses': 76, 'number_subgroup_classes': 312, 'number_subgroups': 8112, 'old_label': None, 'order': 24200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1], [4, 286], [5, 2424], [10, 2424], [11, 120], [20, 15664], [22, 120], [44, 440], [55, 480], [110, 480], [220, 1760]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 20, 'outer_gen_orders': [2, 4, 10, 10], 'outer_gen_pows': [1108, 0, 0, 0], 'outer_gens': [[1101, 12315, 2000], [1541, 1530, 2200], [1101, 2710, 22000], [1761, 10710, 8800]], 'outer_group': '800.1009', 'outer_hash': 1009, 'outer_nilpotent': False, 'outer_order': 800, 'outer_permdeg': 14, 'outer_perms': [1037963520, 9, 13974549840, 131868], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_5:D_4\\times F_5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 24], [8, 6], [10, 4], [20, 12], [40, 4], [80, 12]], 'representations': {'PC': {'code': '6907022355318770949422698690502715118376963184795841757444945477054875565110300399', 'gens': [1, 3, 7], 'pres': [7, -2, -5, -2, -2, -5, -11, -11, 14, 7708, 380312, 226914, 58, 28563, 19890, 80, 71404, 11211, 207, 58805, 21012, 754606, 269513, 107820]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 19172920764866308, 32892940274777495, 6475832249954295, 33418192856010432, 23726635956891084, 41628676495383410]}, 'Perm': {'d': 35, 'gens': [313414318502940782496203121422782181705, 2622054758400, 25959064785554231654400, 625504449028695221150699832410112000000, 9736645905249681951158078338870063012, 921756376070079426563308108148533446818, 1224916221458541781210785220292666450301]}}, 'schur_multiplier': [5], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^2:(Q_8\\times C_5^2)', 'transitive_degree': 440, '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': '200.52', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [20, 10, 44, 110, 20, 20, 10], 'aut_gens': [[1, 10, 220], [34021, 16250, 47740], [37121, 43410, 8580], [40941, 31655, 12220], [43681, 12770, 12980], [17301, 6530, 23980], [28261, 43675, 21980], [18541, 23050, 6820]], 'aut_group': None, 'aut_hash': 9002056612195110899, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7744000, 'aut_permdeg': 693, 'aut_perms': 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'aut_phi_ratio': 440.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 2, 1], [4, 2, 1, 1], [4, 22, 4, 1], [4, 242, 1, 1], [5, 1, 4, 1], [5, 121, 5, 4], [10, 1, 4, 1], [10, 121, 5, 4], [10, 121, 8, 1], [10, 121, 10, 4], [11, 10, 2, 1], [11, 20, 5, 1], [20, 2, 4, 1], [20, 22, 16, 1], [20, 242, 4, 1], [20, 242, 5, 8], [20, 242, 20, 4], [22, 10, 2, 1], [22, 20, 5, 1], [44, 20, 2, 1], [44, 20, 10, 1], [44, 220, 4, 1], [55, 10, 8, 1], [55, 20, 20, 1], [110, 10, 8, 1], [110, 20, 20, 1], [220, 20, 8, 1], [220, 20, 40, 1], [220, 220, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{10}^2.C_{10}.C_2^6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '160.236', 'autcent_hash': 236, 'autcent_nilpotent': False, 'autcent_order': 160, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': '48400.l', 'autcentquo_hash': 3341594860267235989, 'autcentquo_nilpotent': False, 'autcentquo_order': 48400, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{11}^2:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 121, 2], [4, 2, 1], [4, 22, 4], [4, 242, 1], [5, 1, 4], [5, 121, 20], [10, 1, 4], [10, 121, 68], [11, 10, 2], [11, 20, 5], [20, 2, 4], [20, 22, 16], [20, 242, 124], [22, 10, 2], [22, 20, 5], [44, 20, 12], [44, 220, 4], [55, 10, 8], [55, 20, 20], [110, 10, 8], [110, 20, 20], [220, 20, 48], [220, 220, 16]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '4840.y', 'commutator_count': 1, 'commutator_label': '242.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '11.1', '11.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 10, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['5.1', 1], ['9680.p', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 1, 2], [4, 2, 1, 1], [4, 22, 1, 4], [4, 242, 1, 1], [5, 1, 4, 1], [5, 121, 4, 5], [10, 1, 4, 1], [10, 121, 4, 17], [11, 10, 1, 2], [11, 20, 1, 5], [20, 2, 4, 1], [20, 22, 4, 4], [20, 242, 4, 31], [22, 10, 1, 2], [22, 20, 1, 5], [44, 20, 1, 2], [44, 20, 2, 5], [44, 220, 1, 4], [55, 10, 4, 2], [55, 20, 4, 5], [110, 10, 4, 2], [110, 20, 4, 5], [220, 20, 4, 2], [220, 20, 8, 5], [220, 220, 4, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4499712, 'exponent': 220, 'exponents_of_order': [4, 2, 2], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[20, 0, 40]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '24200.bb', 'hash': 4834653770333006103, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 22, 22], 'inner_gens': [[1, 41490, 22220], [2301, 10, 28820], [26401, 19810, 220]], 'inner_hash': 4409101876861599779, 'inner_nilpotent': False, 'inner_order': 4840, 'inner_split': False, 'inner_tex': 'D_{22}:F_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 20, 'irrQ_degree': 160, 'irrQ_dim': 160, 'irrR_degree': 40, 'irrep_stats': [[1, 200], [2, 50], [10, 40], [20, 110]], 'label': '48400.j', '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': 'C55:(Q8*F11)', 'ngens': 8, '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, 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': 50, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 400, 'number_divisions': 120, 'number_normal_subgroups': 182, 'number_subgroup_autclasses': 180, 'number_subgroup_classes': 928, 'number_subgroups': 26048, 'old_label': None, 'order': 48400, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 243], [4, 332], [5, 2424], [10, 8232], [11, 120], [20, 30368], [22, 120], [44, 1120], [55, 480], [110, 480], [220, 4480]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 20, 'outer_gen_orders': [2, 2, 4, 10, 10], 'outer_gen_pows': [8, 31463, 8, 0, 31460], 'outer_gens': [[24201, 23050, 37620], [24201, 375, 41180], [4841, 41870, 8140], [24201, 950, 15620], [43561, 37770, 35420]], 'outer_group': '1600.10270', 'outer_hash': 10270, 'outer_nilpotent': False, 'outer_order': 1600, 'outer_permdeg': 16, 'outer_perms': [720, 87657292800, 7983370, 2622058427520, 11652576], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_{10}^2:C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 48], [8, 12], [10, 8], [20, 12], [40, 13], [80, 12], [160, 5]], 'representations': {'PC': {'code': '7448159017964649280210462135800156879979719781823346485195202299980745229619171587194770804638552974022515084503090039', 'gens': [1, 3, 5], 'pres': [8, -2, -5, -2, -11, -2, -2, -5, -11, 16, 995762, 387250, 66, 1395203, 543371, 7771, 888804, 356412, 115300, 116, 2133125, 855373, 44373, 141, 2266886, 640654, 103510, 334, 563207, 563215, 281623]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 19172920764866308, 32892940274777495, 10886754631083510, 6475832249954295, 33418192856010432, 41628676495383410, 23726635956891084]}, 'Perm': {'d': 35, 'gens': [33, 44241577878396196997079087499778684913, 486985713, 313134520945894831102656125649599539200, 618129183500240293440253351151599104064, 938653834500120482147476612647429084000, 1243367581730349012014431516879132416000, 1547820794698224140158192228323836874993]}}, 'schur_multiplier': [2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{55}:(Q_8\\times F_{11})', 'transitive_degree': 440, 'wreath_data': None, 'wreath_product': False}
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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}
