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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10969', 'ambient_counter': 10969, 'ambient_order': 960, 'ambient_tex': '\\GL(2,3):D_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 480, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10969.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, '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': '480.1031', 'subgroup_hash': 1031, 'subgroup_order': 480, 'subgroup_tex': 'C_{20}.S_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.10969', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240396', 'aut_weyl_index': 4, 'centralizer': '240.a1.a1', 'complements': ['480.d1.a1', '480.d1.b1', '480.c1.a1', '480.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '6.i1.a1', '8.e1.a1', '10.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1544, 4135, 7394, 5446, 2148, 5232, 2925, 4503], 'generators': [483, 720, 484, 192, 24, 480, 12], 'label': '960.10969.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '480.1193', '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': '240.194'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [2, 2, 2, 12, 10, 2], 'aut_gens': [[1, 2, 12, 24], [377, 370, 252, 276], [241, 2, 12, 24], [1, 242, 12, 24], [377, 374, 120, 420], [49, 254, 252, 24], [121, 374, 12, 264]], 'aut_group': '1920.240396', 'aut_hash': 3782145897709286038, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1920, 'aut_permdeg': 62, 'aut_perms': [19719149786377917115412697475181527471663733669008724241993435272492855214582060732893, 22519833500647512828647123722732723093221156978705146274823077170973965038702783354824, 22519833500647515249944118558739330872334671713404447007549843592151553665177372359624, 9669020872285150773630785422458231428400076732087666735471809098276402816208470309920, 7544746977310072399906803127022092060301928621843310208407161168016048246113451281139, 18531232367438059318790114699706298248330387840847544099831202584434898450463254616289], 'aut_phi_ratio': 15.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 60, 1, 1], [3, 8, 1, 1], [4, 1, 2, 1], [4, 6, 1, 1], [4, 60, 1, 1], [5, 2, 2, 1], [6, 8, 1, 1], [8, 30, 2, 2], [10, 2, 2, 1], [10, 12, 2, 1], [12, 8, 2, 1], [15, 8, 4, 1], [20, 2, 4, 1], [20, 12, 2, 1], [30, 8, 4, 1], [60, 8, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times F_5\\times S_4', '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': 60, 'autcentquo_group': '480.1189', 'autcentquo_hash': 1189, 'autcentquo_nilpotent': False, 'autcentquo_order': 480, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 1], [2, 60, 1], [3, 8, 1], [4, 1, 2], [4, 6, 1], [4, 60, 1], [5, 2, 2], [6, 8, 1], [8, 30, 4], [10, 2, 2], [10, 12, 2], [12, 8, 2], [15, 8, 4], [20, 2, 4], [20, 12, 2], [30, 8, 4], [60, 8, 8]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '120.38', 'commutator_count': 1, 'commutator_label': '120.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1031, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 60, 1, 1], [3, 8, 1, 1], [4, 1, 2, 1], [4, 6, 1, 1], [4, 60, 1, 1], [5, 2, 2, 1], [6, 8, 1, 1], [8, 30, 2, 2], [10, 2, 2, 1], [10, 12, 2, 1], [12, 8, 2, 1], [15, 8, 4, 1], [20, 2, 4, 1], [20, 12, 2, 1], [30, 8, 4, 1], [60, 8, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 18, 'exponent': 120, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 0, 12]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '240.197', 'hash': 1031, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 3, 2, 10], 'inner_gens': [[1, 10, 372, 456], [245, 2, 360, 276], [121, 374, 12, 264], [49, 254, 252, 24]], 'inner_hash': 38, 'inner_nilpotent': False, 'inner_order': 120, 'inner_split': True, 'inner_tex': 'C_5:S_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 32, 'irrR_degree': 8, 'irrep_stats': [[1, 4], [2, 18], [3, 4], [4, 14], [6, 4]], 'label': '480.1031', 'linC_count': 60, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 4, 'linQ_dim': 12, 'linQ_dim_count': 4, 'linR_count': 24, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C20.S4', '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': 20, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 44, 'number_divisions': 20, 'number_normal_subgroups': 17, 'number_subgroup_autclasses': 76, 'number_subgroup_classes': 78, 'number_subgroups': 626, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 67], [3, 8], [4, 68], [5, 4], [6, 8], [8, 120], [10, 28], [12, 16], [15, 32], [20, 32], [30, 32], [60, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 242, 12, 24], [1, 254, 252, 24], [1, 2, 12, 312]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [120, 5040, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [3, 4], [4, 2], [8, 4], [12, 2], [16, 1], [32, 1]], 'representations': {'PC': {'code': 257533339855428660706701014925682546325348251609301251, 'gens': [1, 2, 4, 5], 'pres': [7, -2, -2, -3, -2, 2, -2, -5, 141, 36, 5210, 1276, 10419, 5050, 941, 584, 15964, 4841, 1383, 795, 102, 18149, 124, 18822]}, 'GLZN': {'d': 2, 'p': 85, 'gens': [5527161, 615571, 49744146, 31755201, 9826016, 22108559, 3721361]}, 'Perm': {'d': 21, 'gens': [2453594737116862087, 5360670404269932240, 1551016485094320, 37, 7945857101822945760, 10508816973312484560, 2453238962035062480]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{20}.S_4', 'transitive_degree': 80, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [4, 2, 2, 2, 4, 2, 2, 2, 12, 10, 10], 'aut_gens': [[1, 2, 12, 24, 48], [481, 686, 492, 24, 144], [733, 734, 492, 504, 48], [481, 770, 12, 504, 432], [253, 722, 12, 504, 528], [517, 26, 492, 24, 336], [481, 482, 12, 504, 48], [253, 254, 492, 504, 48], [253, 242, 12, 24, 528], [9, 2, 240, 276, 636], [481, 194, 12, 504, 48], [9, 202, 732, 744, 528]], 'aut_group': '7680.fo', 'aut_hash': 1388670470427655320, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7680, 'aut_permdeg': 44, 'aut_perms': [45849199590059764978117810851146844263694668329921728, 1270963925816863346973773089206560570138001365954417288, 1445826429681158197277171451747075976534679629515930294, 1270159831444055125214391620508231640765052717849772242, 2142188279195532788186578318579995232994495865620264633, 1421938870431271458434995732393201785076722058661624422, 2571300770489037885503212102434950398463455190646238546, 1301812081828473870652355824107054765764335025994390005, 546138371340363084905007413886247790254131276966341265, 1434603512868065529254058462710819377126541726998982005, 1978809818059657521915428539579886790116754543924571675], 'aut_phi_ratio': 30.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 12, 2, 1], [2, 30, 2, 1], [2, 60, 1, 1], [3, 8, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [4, 10, 2, 1], [4, 60, 1, 1], [5, 2, 2, 1], [6, 8, 1, 1], [8, 12, 2, 1], [8, 30, 2, 1], [8, 60, 1, 1], [10, 2, 2, 1], [10, 12, 2, 1], [10, 24, 4, 1], [12, 16, 1, 1], [12, 80, 2, 1], [15, 16, 2, 1], [20, 4, 2, 1], [20, 12, 2, 1], [30, 16, 2, 1], [40, 24, 4, 1], [60, 16, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_{10}.(C_2^4\\times S_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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '960.11361', 'autcentquo_hash': 11361, 'autcentquo_nilpotent': False, 'autcentquo_order': 960, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times F_5\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 1], [2, 12, 2], [2, 30, 2], [2, 60, 1], [3, 8, 1], [4, 2, 1], [4, 6, 1], [4, 10, 2], [4, 60, 1], [5, 2, 2], [6, 8, 1], [8, 12, 2], [8, 30, 2], [8, 60, 1], [10, 2, 2], [10, 12, 2], [10, 24, 4], [12, 16, 1], [12, 80, 2], [15, 16, 2], [20, 4, 2], [20, 12, 2], [30, 16, 2], [40, 24, 4], [60, 16, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '480.1193', 'commutator_count': 1, 'commutator_label': '120.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 10969, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 12, 1, 2], [2, 30, 1, 2], [2, 60, 1, 1], [3, 8, 1, 1], [4, 2, 1, 1], [4, 6, 1, 1], [4, 10, 1, 2], [4, 60, 1, 1], [5, 2, 2, 1], [6, 8, 1, 1], [8, 12, 1, 2], [8, 30, 2, 1], [8, 60, 1, 1], [10, 2, 2, 1], [10, 12, 2, 1], [10, 24, 2, 2], [12, 16, 1, 1], [12, 80, 1, 2], [15, 16, 2, 1], [20, 4, 2, 1], [20, 12, 2, 1], [30, 16, 2, 1], [40, 24, 2, 2], [60, 16, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 30240, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[8, 0, 4], [8, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '480.1193', 'hash': 10969, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 6, 2, 2, 10], 'inner_gens': [[1, 10, 720, 756, 300], [485, 2, 252, 744, 204], [733, 722, 12, 24, 528], [253, 242, 12, 24, 528], [253, 350, 492, 504, 48]], 'inner_hash': 1193, 'inner_nilpotent': False, 'inner_order': 480, 'inner_split': True, 'inner_tex': 'D_{10}\\times S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 32, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 12], [3, 8], [4, 6], [6, 8], [8, 7]], 'label': '960.10969', 'linC_count': 16, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 8, 'linQ_dim': 12, 'linQ_dim_count': 4, 'linR_count': 16, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'GL(2,3):D10', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 49, 'number_divisions': 34, 'number_normal_subgroups': 37, 'number_subgroup_autclasses': 210, 'number_subgroup_classes': 292, 'number_subgroups': 2902, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 151], [3, 8], [4, 88], [5, 4], [6, 8], [8, 144], [10, 124], [12, 176], [15, 32], [20, 32], [30, 32], [40, 96], [60, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [36, 0, 0], 'outer_gens': [[517, 518, 12, 24, 48], [1, 494, 492, 504, 528], [1, 2, 12, 24, 816]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [120, 5040, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 37, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [3, 8], [4, 4], [8, 4], [12, 4], [16, 1], [32, 1]], 'representations': {'PC': {'code': 7265015848810408650008026797965485498342460430214932831340505674789291011, 'gens': [1, 2, 4, 5, 6], 'pres': [8, -2, -2, -3, -2, 2, 2, -2, -5, 161, 41, 11714, 2898, 23043, 4043, 1939, 1307, 30244, 14892, 7580, 14405, 4909, 741, 2141, 1093, 141, 24206, 166, 24591]}, 'Perm': {'d': 37, 'gens': [425145272065065391941345777435208359779047, 806058281936123066278341462049756078884480, 1188644696803324991318135089289269398254640, 386747844520217939624359501958281680, 37, 1573687777956632438980209270414687216707760, 1956320192186697867326541100034138944190160, 2337413985317563889586958236860973808802640]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\GL(2,3):D_{10}', 'transitive_degree': 160, '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}
