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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.4021', 'ambient_counter': 4021, 'ambient_order': 960, 'ambient_tex': '(C_2\\times C_{60}):Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 480, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.4021.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', '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': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '480.919', 'subgroup_hash': 919, 'subgroup_order': 480, 'subgroup_tex': 'C_2\\times C_4\\times C_{60}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.4021', 'aut_centralizer_order': 80, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 80, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.h1', '6.a1', '10.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5549, 4447, 4726, 3633], 'generators': [2, 4, 240, 16, 24, 480, 192], 'label': '960.4021.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '6.a1', '10.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '40.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '480.919', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 4, 4, 6], 'aut_gens': [[1, 2, 8], [245, 247, 13], [1, 242, 475], [1, 7, 111], [1, 121, 90]], 'aut_group': None, 'aut_hash': 8596656399186838937, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12288, 'aut_permdeg': 30, 'aut_perms': [159163210500281568292638327290412, 155759454552747412435426033126130, 8848246704567947517120964212813, 63984318851403707379571767564554], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 1, 4, 1], [3, 1, 2, 1], [4, 1, 24, 1], [5, 1, 4, 1], [6, 1, 6, 1], [6, 1, 8, 1], [10, 1, 12, 1], [10, 1, 16, 1], [12, 1, 48, 1], [15, 1, 8, 1], [20, 1, 96, 1], [30, 1, 24, 1], [30, 1, 32, 1], [60, 1, 192, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_4\\times C_2^6.S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': None, 'autcent_hash': 8596656399186838937, 'autcent_nilpotent': False, 'autcent_order': 12288, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2\\times C_4\\times C_2^6.S_4', '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, 7], [3, 1, 2], [4, 1, 24], [5, 1, 4], [6, 1, 14], [10, 1, 28], [12, 1, 48], [15, 1, 8], [20, 1, 96], [30, 1, 56], [60, 1, 192]], 'center_label': '480.919', 'center_order': 480, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', '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': 919, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['4.1', 2], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 1, 2, 12], [5, 1, 4, 1], [6, 1, 2, 7], [10, 1, 4, 7], [12, 1, 4, 12], [15, 1, 8, 1], [20, 1, 8, 12], [30, 1, 8, 7], [60, 1, 16, 12]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 2821, 'exponent': 60, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '120.47', 'hash': 919, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 8], [1, 2, 8], [1, 2, 8]], '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, 480]], 'label': '480.919', 'linC_count': None, 'linC_degree': 3, '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': 'C2*C4*C60', 'ngens': 7, 'nilpotency_class': 1, 'nilpotent': True, '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': 16, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 480, 'number_divisions': 80, 'number_normal_subgroups': 216, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 216, 'number_subgroups': 216, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 24], [5, 4], [6, 14], [10, 28], [12, 48], [15, 8], [20, 96], [30, 56], [60, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [4, 4, 3, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[5, 124, 134], [1, 363, 380], [241, 360, 254], [245, 120, 227]], 'outer_group': None, 'outer_hash': 8596656399186838937, 'outer_nilpotent': False, 'outer_order': 12288, 'outer_permdeg': 30, 'outer_perms': [118014485420116202904712819931342, 219182020528196612718537792691205, 72890964295058794160865053486462, 73811293597240036471345672796639], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times C_4\\times C_2^6.S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 4, 3, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 20], [4, 20], [8, 20], [16, 12]], 'representations': {'PC': {'code': 245743619577238945799, 'gens': [1, 2, 4], 'pres': [7, -2, -2, -2, -2, -2, -3, -5, 36, 80, 102, 166]}, 'GLZN': {'d': 2, 'p': 40, 'gens': [1088017, 2513229, 576009, 2312611, 1344021, 192003, 64321]}, 'Perm': {'d': 18, 'gens': [4097379686400, 127008000, 355687428096000, 10080, 96, 1313901388800, 40279680]}}, 'schur_multiplier': [2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 60], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_4\\times C_{60}', 'transitive_degree': 480, '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': '48.44', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20, 'aut_gen_orders': [4, 2, 4, 4, 10, 20, 20, 10], 'aut_gens': [[1, 2, 8, 48], [289, 510, 40, 648], [413, 506, 40, 460], [625, 722, 488, 172], [749, 510, 40, 148], [121, 482, 40, 528], [49, 242, 520, 532], [869, 726, 488, 52], [193, 482, 8, 532]], 'aut_group': None, 'aut_hash': 2768082913228380694, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 81920, 'aut_permdeg': 98, 'aut_perms': [7796416536062497040202642552835058992676476677875947673209760488467086383103900743085763401083311788583856003623077591843947114128370473823006222717288719, 1603707290244832767116671517911169266793689392049664404894146230302979307600674869341548812491884375237904773134316346030752017286608609268199001335836746, 3525812682528624784686527070175583110686825937655397821885406955645460876075216101871200863150268804707753580387127998733039370408649311351593750247448784, 4469951256667325799977599134413458903486639539045438217735517113202730371443671737492690458289903903343386142950914215248331837700094119812769999957186123, 8473794322180497059594775184822237086171855821473333210306528073610968536710500452854360073026256297794220800126617142561138966272177325441338729846187763, 4762332833861594527366594098520930207998442086164566017327137955513214575765629309197450295324191948464231721274945146473749781154470411370221151652851280, 8651573561503310686458480517998950394869493503062389452642723325346671078920428840519769577791687465336382645737672812232323769822056912186739068420301146, 9136310243127957335319286937937927020001833001885530155425878218340043616923917337795610409402640580410800980324025279029757921780138125796735759286260400], 'aut_phi_ratio': 320.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 2, 2], [3, 1, 2, 1], [4, 2, 4, 1], [4, 2, 8, 1], [4, 20, 4, 2], [5, 2, 2, 1], [6, 1, 2, 3], [6, 1, 4, 2], [10, 2, 2, 3], [10, 2, 4, 2], [12, 2, 8, 1], [12, 2, 16, 1], [12, 20, 8, 2], [15, 2, 4, 1], [20, 2, 16, 1], [20, 2, 32, 1], [30, 2, 4, 3], [30, 2, 8, 2], [60, 2, 32, 1], [60, 2, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_5:(C_2^9.C_2^5)', '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': 20, 'autcentquo_group': '80.50', 'autcentquo_hash': 50, 'autcentquo_nilpotent': False, 'autcentquo_order': 80, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 7], [3, 1, 2], [4, 2, 12], [4, 20, 8], [5, 2, 2], [6, 1, 14], [10, 2, 14], [12, 2, 24], [12, 20, 16], [15, 2, 4], [20, 2, 48], [30, 2, 28], [60, 2, 96]], 'center_label': '24.15', 'center_order': 24, 'central_product': True, 'central_quotient': '40.13', 'commutator_count': 1, 'commutator_label': '20.5', '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': 4021, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['320.556', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 2, 1, 4], [4, 2, 2, 4], [4, 20, 1, 4], [4, 20, 2, 2], [5, 2, 2, 1], [6, 1, 2, 7], [10, 2, 2, 7], [12, 2, 2, 4], [12, 2, 4, 4], [12, 20, 2, 4], [12, 20, 4, 2], [15, 2, 4, 1], [20, 2, 4, 4], [20, 2, 8, 4], [30, 2, 4, 7], [60, 2, 8, 4], [60, 2, 16, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3276, 'exponent': 60, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '120.44', 'hash': 4021, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 10, 'inner_gen_orders': [2, 2, 1, 10], 'inner_gens': [[1, 26, 8, 912], [25, 2, 8, 48], [1, 2, 8, 48], [97, 2, 8, 48]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 40, 'inner_split': False, 'inner_tex': 'C_2\\times D_{10}', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [2, 228]], 'label': '960.4021', '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': '(C2*C60):Q8', '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': 36, 'number_characteristic_subgroups': 46, 'number_conjugacy_classes': 276, 'number_divisions': 76, 'number_normal_subgroups': 174, 'number_subgroup_autclasses': 168, 'number_subgroup_classes': 372, 'number_subgroups': 1212, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 184], [5, 4], [6, 14], [10, 28], [12, 368], [15, 8], [20, 96], [30, 56], [60, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 2, 4, 4, 2, 4, 4, 2], 'outer_gen_pows': [0, 0, 0, 0, 576, 576, 768, 192], 'outer_gens': [[289, 510, 40, 648], [413, 506, 40, 460], [625, 722, 488, 172], [749, 510, 40, 148], [121, 482, 40, 528], [49, 242, 520, 532], [869, 726, 488, 52], [193, 482, 8, 532]], 'outer_group': None, 'outer_hash': 6517064034494676899, 'outer_nilpotent': True, 'outer_order': 2048, 'outer_permdeg': 256, 'outer_perms': [3417020494250011024970649401185112497064907162077114355427264017602908657923464014650505422426381951416030000752957414552864599601154012171576594055537494854574829802325496928761155939641694908728401441252734005135224848286051356264917044394757352408780436267242863550281250965161167550948824211802957209868093693820976553733314877361601030015568430889721412756748643439988140981701997142521474932513222048570605511206728267293599357714716930865258035922213264520734449759081147666673903574418808455557470, 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16873298872188133195871665451798460376863221009681259636754985851777264462647007606345251763561875999761777873372792178028571170658143025938926269779782900835725500567337203075325742544602185181268979292391167225324607996117921777095908397762296893419027494422452177186334521011068999721909729380854294440034597345161151776419446364790258080832300482858495762272642491036494902380835118585877518024606652965622847479528529552985567256742175533750816768774236590975496813467213146949067050613268757293149321, 831046717168036182294698979837167108970963751895047392275763608826284095249607905029388802363904709737797011889803867853648458097162478986172035274882175041907577408456800722857292735091366397573594023709493306590076563766475492946977796669744848325300432084111427358721658179448090914962457769475296035449414774079054011973355830826837813072770577346529939179172997461976505128760934871358368858564460041151271948047507537360342501502783503341612002127299531251517420902036446380041428774612159316849], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^7.C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 20], [4, 18], [8, 16], [16, 12], [32, 2]], 'representations': {'PC': {'code': 4880059206226635434594337879587077947459, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -2, -2, -3, -2, -2, -5, 3840, 417, 41, 91, 43781, 141, 48390, 166, 49159]}, 'GLZN': {'d': 2, 'p': 76, 'gens': [17120103, 19919065, 16242149, 21509873, 26132617, 5776633, 441865, 20021699]}, 'Perm': {'d': 24, 'gens': [25903107702066694545919, 25903107681056686092593, 54003125878199405125819, 128047474114560000, 25903107681056686080000, 18619, 44460928512000, 559198080]}}, 'schur_multiplier': [2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 12], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_{60}):Q_8', 'transitive_degree': 960, '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}
