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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.1100', 'ambient_counter': 1100, 'ambient_order': 1296, 'ambient_tex': '(C_4\\times \\He_3).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 648, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.1100.2.b1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.c1', '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': '648.137', 'subgroup_hash': 137, 'subgroup_order': 648, 'subgroup_tex': '\\He_3.D_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1296.1100', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '648.a1.a1', 'complements': ['648.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.a1.c1', '4.b1.b1', '6.b1.c1', '6.f1.c1'], 'core': '2.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5205, 5485, 3424, 5704, 4155, 4901, 2100, 4463], 'generators': [3, 1008, 660, 324, 432, 2, 648], 'label': '1296.1100.2.b1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.a1.c1', '4.b1.b1', '6.b1.c1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.c1', 'projective_image': '648.331', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.c1', 'subgroup_fusion': None, 'weyl_group': '648.331'}
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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': [6, 9, 6, 12, 2], 'aut_gens': [[1, 6, 54], [31, 444, 306], [241, 222, 72], [257, 240, 288], [499, 12, 270], [313, 48, 594]], 'aut_group': None, 'aut_hash': 4735543535497533725, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7776, 'aut_permdeg': 126, 'aut_perms': [23556938726458671729695465635301336909978308546957092377047726005266534128077899405021662133911324819820370963213307720337784745121430213709613818602342688609454278372612133572584081457194460610422467156520695912, 3401733268231137296774330323619233507744232189014478661301530278217691925610590819324806301815168875518168243441265347145423015449624748490740486091771106874787486454951721583063303111361685918005607699774278363, 20308273185893233588153042694535120395309082589896843296998209709092044603629494768407958078225874699277187544547694254494039612758983055488823529070354755296050267206083465787944066523323315489140826634369312326, 19965385556237310372121147734632002935761256009659010869308540478495790584002752145913808029979915620615597598553565435642016440678094709071167961922976447810521534943987119620560101569156862414334113943574447714, 11719012565483112907150885801722352243425640147036935145073634983574856959901688718531929498689242837970331421392795909615317523320558915257861623241453234498168455573097817757556123594088995693053336343096827825], 'aut_phi_ratio': 36.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 54, 2, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 9, 2, 1], [4, 2, 1, 1], [6, 2, 1, 1], [6, 6, 1, 1], [6, 9, 2, 1], [6, 54, 4, 1], [9, 6, 3, 1], [9, 18, 2, 1], [12, 2, 2, 1], [12, 6, 2, 1], [12, 18, 2, 1], [18, 6, 3, 1], [18, 18, 2, 1], [36, 6, 6, 1], [36, 18, 4, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_3\\times C_9).C_6^2.C_2^3', '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': 18, 'autcentquo_group': '1944.2701', 'autcentquo_hash': 2701, 'autcentquo_nilpotent': False, 'autcentquo_order': 1944, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times C_3^3.S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 54, 2], [3, 2, 1], [3, 6, 1], [3, 9, 2], [4, 2, 1], [6, 2, 1], [6, 6, 1], [6, 9, 2], [6, 54, 4], [9, 6, 3], [9, 18, 2], [12, 2, 2], [12, 6, 2], [12, 18, 2], [18, 6, 3], [18, 18, 2], [36, 6, 6], [36, 18, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '324.71', 'commutator_count': 1, 'commutator_label': '54.9', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 137, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 54, 1, 2], [3, 2, 1, 1], [3, 6, 1, 1], [3, 9, 2, 1], [4, 2, 1, 1], [6, 2, 1, 1], [6, 6, 1, 1], [6, 9, 2, 1], [6, 54, 2, 2], [9, 6, 3, 1], [9, 18, 2, 1], [12, 2, 2, 1], [12, 6, 2, 1], [12, 18, 2, 1], [18, 6, 3, 1], [18, 18, 2, 1], [36, 6, 6, 1], [36, 18, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 36, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 1, 6]], 'familial': False, 'frattini_label': '18.5', 'frattini_quotient': '36.12', 'hash': 137, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [6, 9, 6], 'inner_gens': [[1, 264, 612], [445, 6, 54], [145, 6, 54]], 'inner_hash': 71, 'inner_nilpotent': False, 'inner_order': 324, 'inner_split': True, 'inner_tex': '\\He_3.D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 36, 'irrQ_dim': 36, 'irrR_degree': 6, 'irrep_stats': [[1, 12], [2, 15], [6, 16]], 'label': '648.137', 'linC_count': 6, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 2, 'linQ_dim': 20, 'linQ_dim_count': 2, 'linR_count': 6, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'He3.D12', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 43, 'number_divisions': 22, 'number_normal_subgroups': 24, 'number_subgroup_autclasses': 66, 'number_subgroup_classes': 86, 'number_subgroups': 908, 'old_label': None, 'order': 648, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 109], [3, 26], [4, 2], [6, 242], [9, 54], [12, 52], [18, 54], [36, 108]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [2, 0, 162], 'outer_gens': [[1, 438, 414], [5, 6, 630], [487, 480, 306]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [40344, 720, 27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 31, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 7], [4, 4], [6, 2], [8, 1], [12, 1], [18, 2], [36, 1]], 'representations': {'PC': {'code': 1133549664296503921315150624709767741219789497, 'gens': [1, 3, 5], 'pres': [7, 2, 3, 3, 3, 2, 2, 3, 14, 5546, 2529, 79, 1011, 21424, 1271, 102, 24197, 3036, 124, 22056, 5746]}, 'Perm': {'d': 31, 'gens': [1928294147530790381803769966887, 13, 293966987486427855952663559955960, 23, 568402805697432198691723641446400, 44528699517480273266550271480440, 851655381616696566355724311015800]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '\\He_3.D_{12}', 'transitive_degree': 108, '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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [12, 6, 18, 6, 6], 'aut_gens': [[1, 6, 36], [967, 894, 1074], [1103, 1086, 642], [377, 1110, 480], [133, 1200, 642], [913, 984, 1278]], 'aut_group': None, 'aut_hash': 1838672884737504050, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 46656, 'aut_permdeg': 78, 'aut_perms': [5954743240085317299937054338758427868062332607539381831307319501340574374613904510696120861356109539468203165911264, 575423252843039141818671419456976107218874999619179482137587523708092083783208247502052585813638896902380825687243, 9286334320605566428197091585278665112150524648448094275315611938834018480036176238977988691916739270560138884520810, 4521779838149786347594639797874771276009523063915971421844827312056524730162382802576571151003630487470753463347011, 9876589071682584030232333466409476726277685435938508042751526293447777236658809723432262761446854021834145691965955], 'aut_phi_ratio': 108.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 54, 3, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 9, 2, 1], [4, 2, 3, 1], [4, 27, 2, 1], [6, 2, 1, 1], [6, 6, 1, 1], [6, 9, 2, 1], [6, 54, 6, 1], [9, 6, 3, 1], [9, 18, 2, 1], [12, 4, 3, 1], [12, 12, 3, 1], [12, 18, 6, 1], [12, 27, 4, 1], [18, 6, 3, 1], [18, 18, 2, 1], [36, 12, 9, 1], [36, 36, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2.C_3^4.C_2^4', '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': 18, 'autcentquo_group': None, 'autcentquo_hash': 140594708777273934, 'autcentquo_nilpotent': False, 'autcentquo_order': 5832, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': '\\He_3.C_3^3.C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 54, 3], [3, 2, 1], [3, 6, 1], [3, 9, 2], [4, 2, 3], [4, 27, 2], [6, 2, 1], [6, 6, 1], [6, 9, 2], [6, 54, 6], [9, 6, 3], [9, 18, 2], [12, 4, 3], [12, 12, 3], [12, 18, 6], [12, 27, 4], [18, 6, 3], [18, 18, 2], [36, 12, 9], [36, 36, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '648.331', 'commutator_count': 1, 'commutator_label': '54.9', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 1100, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 54, 1, 3], [3, 2, 1, 1], [3, 6, 1, 1], [3, 9, 2, 1], [4, 2, 1, 3], [4, 27, 2, 1], [6, 2, 1, 1], [6, 6, 1, 1], [6, 9, 2, 1], [6, 54, 2, 3], [9, 6, 3, 1], [9, 18, 2, 1], [12, 4, 1, 3], [12, 12, 1, 3], [12, 18, 2, 3], [12, 27, 4, 1], [18, 6, 3, 1], [18, 18, 2, 1], [36, 12, 3, 3], [36, 36, 2, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 13104, 'exponent': 36, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 3]], 'familial': False, 'frattini_label': '18.5', 'frattini_quotient': '72.48', 'hash': 1100, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [6, 6, 18], 'inner_gens': [[1, 246, 1056], [445, 6, 684], [961, 654, 36]], 'inner_hash': 331, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': True, 'inner_tex': '(C_6\\times C_{18}):C_6', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 36, 'irrQ_dim': 72, 'irrR_degree': 12, 'irrep_stats': [[1, 24], [2, 18], [4, 3], [6, 16], [12, 4]], 'label': '1296.1100', 'linC_count': 72, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 22, 'linQ_degree_count': 8, 'linQ_dim': 22, 'linQ_dim_count': 4, 'linR_count': 48, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C4*He3).D6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 22, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 65, 'number_divisions': 38, 'number_normal_subgroups': 58, 'number_subgroup_autclasses': 108, 'number_subgroup_classes': 212, 'number_subgroups': 2164, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 163], [3, 26], [4, 60], [6, 350], [9, 54], [12, 264], [18, 54], [36, 324]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6, 6], 'outer_gen_pows': [2, 324, 0], 'outer_gens': [[649, 894, 408], [325, 1194, 696], [329, 996, 630]], 'outer_group': '72.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 10, 'outer_perms': [720, 40351, 403201], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 6], [6, 4], [8, 2], [12, 1], [18, 4], [36, 1]], 'representations': {'PC': {'code': 9413588015059812473848462537421030908571996932448110627387636415827, 'gens': [1, 3, 5], 'pres': [8, 2, 3, 2, 3, 2, 2, 3, 3, 16, 5906, 10450, 66, 35331, 7115, 1755, 42244, 5292, 4580, 116, 39173, 12685, 141, 53094, 10430, 222, 55303]}, 'Perm': {'d': 35, 'gens': [27686354283797883291941464322875416655, 13438, 15531, 36593563287800401209726360489108806400, 22828, 339734881850783218036900685384364576000, 626829203890670055273168769991459692800, 939699206173250580561474763802475607680]}}, 'schur_multiplier': [2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_4\\times \\He_3).D_6', 'transitive_degree': 216, '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}
