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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.53749', 'ambient_counter': 53749, 'ambient_order': 256, 'ambient_tex': '(C_2^2\\times Q_{16}):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.53749.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.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': '128.2221', 'subgroup_hash': 2221, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '256.53749', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.i1.a1', '128.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '4.i1.a1', '4.j1.a1', '4.o1.a1', '4.q1.a1', '4.bl1.a1', '4.bl1.b1', '4.bm1.a1', '4.bm1.b1', '4.cb1.a1', '4.cb1.b1', '4.cc1.a1', '4.cc1.b1', '4.dw1.a1', '4.dw1.b1', '4.dy1.a1', '4.dy1.b1', '4.ea1.a1', '4.ec1.a1', '4.ee1.a1', '4.eg1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3756, 3884, 4304, 1624, 3750, 3889, 4301, 1625], 'generators': [33, 2, 4, 64, 40], 'label': '256.53749.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.i1.a1', '4.j1.a1', '4.c1.a1', '4.e1.a1', '4.o1.a1', '4.q1.a1', '4.bl1.a1', '4.bl1.b1', '4.bm1.a1', '4.bm1.b1', '4.cb1.a1', '4.cb1.b1', '4.cc1.a1', '4.cc1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', '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': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2], 'aut_gens': [[1, 2, 4, 8, 32], [1, 2, 4, 24, 32], [53, 2, 68, 124, 32], [1, 2, 20, 24, 32], [81, 2, 53, 41, 32], [81, 82, 68, 72, 112], [81, 2, 84, 24, 32], [17, 18, 20, 24, 48], [1, 2, 4, 72, 32], [1, 66, 4, 72, 32], [17, 18, 20, 40, 48], [1, 82, 4, 88, 32], [17, 2, 20, 8, 32], [1, 2, 84, 88, 32]], 'aut_group': '12288.bmj', 'aut_hash': 4169318348325865856, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12288, 'aut_permdeg': 24, 'aut_perms': [871844002020474344888, 428351629007695080442971, 6797765811451564057977, 483427703334112612192125, 480057635150294424261922, 487620374610110893823546, 161963997604457323574363, 617119167064619656328, 29323250549765954070, 162068369117645754065224, 14725837441066999830, 161963408583283772920344, 21409704995708968280211], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [2, 2, 6, 1], [2, 4, 2, 1], [2, 4, 3, 1], [4, 2, 2, 2], [4, 2, 6, 1], [4, 4, 2, 1], [4, 4, 3, 1], [4, 4, 6, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^{10}.D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '1024.djt', 'autcent_hash': 1957374279625110839, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '12.4', 'autcentquo_hash': 4, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 8], [2, 4, 5], [4, 2, 10], [4, 4, 17]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '32.51', 'commutator_count': 1, 'commutator_label': '4.2', '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': 2221, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 8], [2, 4, 1, 5], [4, 2, 1, 8], [4, 2, 2, 1], [4, 4, 1, 17]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 833280, 'exponent': 4, 'exponents_of_order': [7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '32.51', 'hash': 2221, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 2, 2], 'inner_gens': [[1, 2, 68, 8, 32], [1, 2, 4, 88, 32], [65, 2, 4, 8, 32], [1, 82, 4, 8, 96], [1, 2, 4, 72, 32]], 'inner_hash': 51, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': False, 'inner_tex': 'C_2^5', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 4]], 'label': '128.2221', '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': 'C4^2.C2^3', 'ngens': 5, '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': 15, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 44, 'number_divisions': 43, 'number_normal_subgroups': 430, 'number_subgroup_autclasses': 156, 'number_subgroup_classes': 761, 'number_subgroups': 1156, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 39], [4, 88]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 6, 2, 2], 'outer_gen_pows': [0, 32, 36, 0, 0, 0, 0], 'outer_gens': [[1, 18, 4, 8, 32], [1, 18, 4, 40, 32], [37, 82, 4, 44, 32], [1, 66, 4, 8, 32], [53, 82, 81, 121, 112], [81, 2, 84, 8, 32], [81, 2, 4, 8, 32]], 'outer_group': '384.20162', 'outer_hash': 20162, 'outer_nilpotent': False, 'outer_order': 384, 'outer_permdeg': 12, 'outer_perms': [16680, 11520, 3628807, 11527, 7257623, 40279680, 127370880], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^4\\times S_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 20, '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, 8], [4, 2], [8, 1]], 'representations': {'PC': {'code': 37438388646715560, 'gens': [1, 2, 3, 4, 6], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 1430, 1242, 80, 530, 124]}, 'Perm': {'d': 20, 'gens': [136678212202579927, 269033106288214936, 399446573840497565, 2512404627915736, 528012191831243176, 399446573840497560, 16]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2], '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_4^2.C_2^3', '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': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 2, 4, 4, 2, 4, 4, 4, 2, 2, 4], 'aut_gens': [[1, 2, 4, 8, 32], [21, 18, 132, 200, 112], [145, 18, 148, 24, 160], [65, 130, 132, 216, 160], [5, 18, 132, 88, 160], [209, 18, 148, 216, 240], [213, 2, 20, 136, 48], [65, 146, 132, 88, 32], [197, 130, 20, 136, 176], [1, 18, 4, 8, 176], [213, 2, 4, 136, 224], [149, 146, 4, 72, 48]], 'aut_group': None, 'aut_hash': 8629282911301114921, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 8192, 'aut_permdeg': 28, 'aut_perms': [248638250421474546823895775601, 248460045245644351189664872086, 11001224886865369066507237624, 248668570399735886284966285462, 248475718949595084990392932087, 208686737960993012784754609, 259348915333739139932897248463, 11163944115524780502473673768, 248556728148371045548672285462, 305664396501701497824643255, 259526875856685374974794747263], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [2, 4, 1, 2], [2, 4, 2, 2], [2, 8, 1, 1], [2, 8, 2, 1], [4, 2, 1, 2], [4, 2, 2, 2], [4, 4, 1, 1], [4, 4, 2, 2], [4, 8, 1, 7], [4, 8, 2, 3], [8, 4, 2, 2], [8, 8, 1, 2], [8, 8, 2, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^9.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '1024.djt', 'autcent_hash': 1957374279625110839, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{10}', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '8.5', 'autcentquo_hash': 5, 'autcentquo_nilpotent': True, 'autcentquo_order': 8, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 4, 6], [2, 8, 3], [4, 2, 6], [4, 4, 5], [4, 8, 13], [8, 4, 4], [8, 8, 6]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '64.261', 'commutator_count': 1, 'commutator_label': '8.2', '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': 53749, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 6], [2, 8, 1, 3], [4, 2, 1, 4], [4, 2, 2, 1], [4, 4, 1, 5], [4, 8, 1, 13], [8, 4, 2, 2], [8, 8, 1, 6]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 39997440, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '32.51', 'hash': 53749, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 2, 2, 4], 'inner_gens': [[1, 2, 4, 24, 96], [1, 2, 4, 8, 48], [1, 2, 4, 136, 32], [17, 2, 132, 8, 224], [193, 18, 4, 72, 32]], 'inner_hash': 261, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': None, 'inner_tex': 'D_4\\times C_2^3', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 8], [8, 1]], 'label': '256.53749', 'linC_count': 16, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 4, 'linQ_dim': 20, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C2^2*Q16):C2^2', 'ngens': 5, 'nilpotency_class': 3, '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': 34, 'number_characteristic_subgroups': 143, 'number_conjugacy_classes': 49, 'number_divisions': 46, 'number_normal_subgroups': 439, 'number_subgroup_autclasses': 645, 'number_subgroup_classes': 1070, 'number_subgroups': 2327, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 55], [4, 136], [8, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2], 'outer_gen_pows': [68, 0, 64, 64, 0, 0, 64, 0, 0, 0, 4], 'outer_gens': [[21, 18, 132, 200, 112], [145, 18, 148, 24, 160], [65, 130, 132, 216, 160], [5, 18, 132, 88, 160], [209, 18, 148, 216, 240], [213, 2, 20, 136, 48], [65, 146, 132, 88, 32], [197, 130, 20, 136, 176], [1, 18, 4, 8, 176], [213, 2, 4, 136, 224], [149, 146, 4, 72, 48]], 'outer_group': '128.2320', 'outer_hash': 2320, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 64, 'outer_perms': [283749061951112193612594678567346247498491635559170014225324220483866926341970380785904, 1985297254507505202162796209691256798456656110511084605274184550327606627106972341385087, 4154163391483527056151441641965388860244296619076007206214858607087418786953719079993496, 6270649498318461300830028943900115598152572600654107976982343377010312722731295084425336, 8285389982623824126568266836364616660846066374317455438105280091665544008645238805548894, 10296942319699901002124459571010452117333888836051420352390245461553696275255986729195263, 12308491105588624329503823445264439882843540022872349133050568368813804252855121323734857, 14319532436287009162361425485029432482096567781131610466929023786479606204832591547439424, 16020949697518372636605940928986626761273191631518419887235354550572002861060082382005295, 18324864805747833567120494516429497853984754275623181498464534443512966442028445852596373, 12402901645936465564124374904212131930130519805284799525257971169096804146823148343253897], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times C_2^4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 40, '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, 8], [4, 4], [8, 1], [16, 1]], 'representations': {'PC': {'code': 42025806340855149392502271771810410, 'gens': [1, 2, 3, 4, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 1033, 771, 1107, 91, 4613, 1165, 1373, 141, 10758, 1374, 166]}, 'Perm': {'d': 40, 'gens': [23139166798519167515266622599498716762693375055, 124301967064081413751500352732757239911170, 43937345016978311650973367324437365312585222650, 64994415757547951935256504242989117870126854789, 85931578110564935723575677752634250030362624000, 17764, 105788341790010778502039012734232017833824102400, 127261645935628125597286544799316239805306980480]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2], '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_2^2\\times Q_{16}):C_2^2', '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}
