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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.fl', 'ambient_counter': 142, 'ambient_order': 3888, 'ambient_tex': 'C_3^3.(C_6\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 1944, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.fl.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': '1944.2484', 'subgroup_hash': 2484, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4.S_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '3888.fl', 'aut_centralizer_order': 3, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1296.2922', 'aut_weyl_index': 3, 'centralizer': '1296.b1.a1', 'complements': ['1944.b1.a1', '1944.c1.a1', '1944.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.e1.a1', '6.n1.a1', '6.o1.a1', '6.p1.a1', '8.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3701, 4697, 1521, 5123, 8670, 5802, 1430, 5802], 'generators': [489, 36, 216, 1946, 1296, 1944, 2268, 2316], 'label': '3888.fl.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.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '3888.fl', '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': '1296.2922'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [3, 3, 3, 3, 9, 3, 6, 2, 2, 2], 'aut_gens': [[1, 6, 54, 324], [19, 6, 54, 324], [217, 6, 54, 324], [1, 24, 54, 324], [1, 6, 54, 360], [7, 6, 1188, 594], [649, 114, 54, 324], [1, 12, 270, 486], [1, 870, 270, 1620], [163, 168, 54, 324], [1, 978, 54, 324]], 'aut_group': None, 'aut_hash': 6451522700406010028, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 34992, 'aut_permdeg': 63, 'aut_perms': [127944062145233580733393835736853932226068170195791533288609653344487730537891116858307, 122277332712344255245326379921770077628939178292092955959296000000, 2063887036297145566040684578929517335616476200606736186516360730145160934460649815044, 2064721526807899924312507623468109944270492355076528167448261303920779542609206794387, 1258422480895320471212124435809119026825679668586926427725450583191370325746641190722240, 1563696652367773382195662260813257549226411477826237295563088111176618250276727877390080, 605013200596273407326152532565423896853459164440193481687013682096607406193017791118556, 15483423702006862147092099566211864632022723065690951832388133869149882088389010525440, 598955375800379038137440830192301316090181201714244683986547178229936363330457479774720, 507580254404148578590542501772305770638711828627813127621579202663803135778531928770], 'aut_phi_ratio': 54.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 54, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 3, 3, 2], [3, 6, 3, 3], [4, 54, 1, 1], [6, 3, 2, 1], [6, 3, 3, 2], [6, 6, 1, 1], [6, 6, 2, 1], [6, 6, 3, 3], [6, 6, 6, 1], [6, 6, 9, 2], [6, 54, 2, 1], [6, 54, 3, 2], [9, 72, 3, 3], [12, 54, 2, 1], [12, 54, 3, 2]], 'aut_supersolvable': False, 'aut_tex': '(C_3\\times C_6^2).C_3^3.D_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 3, 'autcent_group': '3.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 3, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '11664.lj', 'autcentquo_hash': 6127128702050713443, 'autcentquo_nilpotent': False, 'autcentquo_order': 11664, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4.(S_3\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 54, 1], [3, 1, 2], [3, 2, 3], [3, 3, 6], [3, 6, 9], [4, 54, 1], [6, 3, 8], [6, 6, 36], [6, 54, 8], [9, 72, 9], [12, 54, 8]], 'center_label': '3.1', 'center_order': 3, 'central_product': False, 'central_quotient': '648.570', 'commutator_count': 2, 'commutator_label': '324.59', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2484, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 54, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 3, 2, 3], [3, 6, 1, 3], [3, 6, 2, 3], [4, 54, 1, 1], [6, 3, 2, 4], [6, 6, 1, 4], [6, 6, 2, 16], [6, 54, 2, 4], [9, 72, 1, 3], [9, 72, 2, 3], [12, 54, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 98280, 'exponent': 36, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 18]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '216.164', 'hash': 2484, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [6, 9, 2, 6], 'inner_gens': [[1, 30, 54, 1782], [31, 6, 1026, 1350], [1, 978, 54, 324], [811, 1248, 54, 324]], 'inner_hash': 570, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': False, 'inner_tex': 'C_3^3.S_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 6], [2, 12], [3, 30], [6, 45]], 'label': '1944.2484', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^4.S4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 32, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 93, 'number_divisions': 54, 'number_normal_subgroups': 36, 'number_subgroup_autclasses': 186, 'number_subgroup_classes': 490, 'number_subgroups': 3700, 'old_label': None, 'order': 1944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 57], [3, 80], [4, 54], [6, 672], [9, 648], [12, 432]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 3, 3, 3], 'outer_gen_pows': [4, 3, 0, 0], 'outer_gens': [[1, 12, 270, 486], [217, 804, 54, 1818], [217, 6, 54, 360], [217, 6, 54, 324]], 'outer_group': '54.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 54, 'outer_permdeg': 9, 'outer_perms': [5065, 45360, 45507, 3], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^2:S_3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 6], [3, 2], [4, 4], [6, 21], [12, 19]], 'representations': {'PC': {'code': 79235240161038238717356082701617420059755018409333, 'gens': [1, 3, 5, 7], 'pres': [8, 2, 3, 3, 3, 2, 3, 2, 3, 16, 722, 514, 90, 1155, 6860, 116, 99798, 12622, 166, 82951, 8087]}, 'Perm': {'d': 22, 'gens': [5353514248726033282, 7447406994790963200, 61188555270497373113, 109987863495961703132, 98499, 109987863495961651200, 482630400, 1037836800]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4.S_4', 'transitive_degree': 36, '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': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [12, 18, 6, 6], 'aut_gens': [[1, 6, 108, 648], [217, 1254, 2484, 648], [3409, 6, 2160, 3348], [2377, 114, 108, 648], [1, 3354, 108, 648]], 'aut_group': '3888.fl', 'aut_hash': 3044566718417071494, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3888, 'aut_permdeg': 63, 'aut_perms': [830612640461771533641624694756461587350547575226542480167034786097010318810260779134817, 6443743887424598440296883830308049795495716909882723373512772025823720668335943936908, 767497761907956226711626478826200381700896597963076445576997636140190632484461809939178, 32593332953609159815276087395728358370211284550998388407040484609979940713583098625603], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 9, 1, 1], [2, 27, 1, 1], [2, 54, 1, 2], [3, 2, 1, 2], [3, 3, 1, 2], [3, 4, 1, 1], [3, 6, 1, 5], [3, 12, 1, 3], [4, 54, 1, 2], [6, 3, 1, 2], [6, 6, 1, 9], [6, 12, 1, 15], [6, 18, 1, 1], [6, 27, 1, 4], [6, 54, 1, 7], [6, 108, 1, 6], [9, 72, 1, 3], [9, 144, 1, 3], [12, 54, 1, 4], [12, 108, 1, 6], [18, 216, 1, 3]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.(C_6\\times S_4)', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '3888.fl', 'autcentquo_hash': 3044566718417071494, 'autcentquo_nilpotent': False, 'autcentquo_order': 3888, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3.(C_6\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 9, 1], [2, 27, 1], [2, 54, 2], [3, 2, 2], [3, 3, 2], [3, 4, 1], [3, 6, 5], [3, 12, 3], [4, 54, 2], [6, 3, 2], [6, 6, 9], [6, 12, 15], [6, 18, 1], [6, 27, 4], [6, 54, 7], [6, 108, 6], [9, 72, 3], [9, 144, 3], [12, 54, 4], [12, 108, 6], [18, 216, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '3888.fl', 'commutator_count': 1, 'commutator_label': '324.59', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 142, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 9, 1, 1], [2, 27, 1, 1], [2, 54, 1, 2], [3, 2, 1, 2], [3, 3, 2, 1], [3, 4, 1, 1], [3, 6, 1, 1], [3, 6, 2, 2], [3, 12, 1, 1], [3, 12, 2, 1], [4, 54, 1, 2], [6, 3, 2, 1], [6, 6, 1, 3], [6, 6, 2, 3], [6, 12, 1, 3], [6, 12, 2, 6], [6, 18, 1, 1], [6, 27, 2, 2], [6, 54, 1, 1], [6, 54, 2, 3], [6, 108, 1, 2], [6, 108, 2, 2], [9, 72, 1, 1], [9, 72, 2, 1], [9, 144, 1, 1], [9, 144, 2, 1], [12, 54, 2, 2], [12, 108, 1, 2], [12, 108, 2, 2], [18, 216, 1, 1], [18, 216, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 432, 'exponent': 36, 'exponents_of_order': [5, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 8], [12, 1, 1]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '432.745', 'hash': 3044566718417071494, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [12, 18, 6, 6], 'inner_gens': [[1, 714, 2484, 648], [3397, 6, 2484, 1836], [2161, 2166, 108, 648], [1, 3354, 108, 648]], 'inner_hash': 3044566718417071494, 'inner_nilpotent': False, 'inner_order': 3888, 'inner_split': True, 'inner_tex': 'C_3^3.(C_6\\times S_4)', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 12], [2, 12], [3, 12], [4, 3], [6, 26], [12, 19]], 'label': '3888.fl', 'linC_count': 93, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 13, 'linQ_dim': 12, 'linQ_dim_count': 13, 'linR_count': 13, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^3.(C6*S4)', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 84, 'number_characteristic_subgroups': 38, 'number_conjugacy_classes': 84, 'number_divisions': 56, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 710, 'number_subgroup_classes': 710, 'number_subgroups': 11098, 'old_label': None, 'order': 3888, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 147], [3, 80], [4, 108], [6, 1392], [9, 648], [12, 864], [18, 648]], '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': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [3, 4], [4, 5], [6, 14], [8, 1], [12, 13], [24, 7]], 'representations': {'PC': {'code': '17332017364350600297170854971909930236157727789920379073816802666887113347888075071157', 'gens': [1, 3, 6, 8], 'pres': [9, 2, 3, 2, 3, 3, 2, 3, 2, 3, 18, 17506, 19280, 46262, 74, 4755, 2820, 138, 3244, 134141, 22379, 10724, 158, 27222, 4560, 22057, 7162, 214, 40850, 11699]}, 'Perm': {'d': 22, 'gens': [53787474035045498409, 5257481346106226372]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3.(C_6\\times S_4)', 'transitive_degree': 36, '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}
