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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.2088', 'ambient_counter': 2088, 'ambient_order': 384, 'ambient_tex': '(C_2^2\\times C_6).D_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 192, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.2088.2.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', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '192.813', 'subgroup_hash': 813, 'subgroup_order': 192, 'subgroup_tex': '(C_2^2\\times C_{12}):C_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '384.2088', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.g1', '4.i1', '6.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 32, 4, 2, 192, 240, 128], 'label': '384.2088.2.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.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': '48.44', '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, 2, 4, 2, 2, 4, 4], 'aut_gens': [[1, 2, 8, 32], [21, 15, 120, 160], [97, 114, 120, 32], [17, 18, 8, 160], [21, 107, 28, 32], [117, 22, 124, 32], [97, 102, 124, 160], [17, 23, 8, 160], [113, 111, 28, 160]], 'aut_group': '1024.dia', 'aut_hash': 6505043324181827086, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 34, 'aut_perms': [193354953562244722300048279639145817970, 4237689370025564742589440665086901212, 191839101444875871503434784571632132480, 1498841799394868902357652935745721970, 4846839508157665447505839140724431074, 198540079813447806557032806576737310368, 196423082320630333930728662564421233565, 196918215478983186110308793257683901635], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 2, 2], [2, 2, 4, 1], [3, 1, 2, 1], [4, 2, 4, 2], [4, 4, 8, 1], [6, 1, 2, 3], [6, 1, 4, 2], [6, 2, 8, 1], [12, 2, 8, 2], [12, 4, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^7:D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': None, 'autcent_hash': 1957374279625110839, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{10}', 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': 4, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [3, 1, 2], [4, 2, 8], [4, 4, 8], [6, 1, 14], [6, 2, 8], [12, 2, 16], [12, 4, 16]], 'center_label': '24.15', 'center_order': 24, 'central_product': True, 'central_quotient': '8.5', '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', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 813, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['64.61', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [3, 1, 2, 1], [4, 2, 1, 4], [4, 2, 2, 2], [4, 4, 2, 4], [6, 1, 2, 7], [6, 2, 2, 4], [12, 2, 2, 4], [12, 2, 4, 2], [12, 4, 4, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 546, 'exponent': 12, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '24.15', 'hash': 813, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 1], 'inner_gens': [[1, 114, 8, 32], [113, 2, 104, 32], [1, 98, 8, 32], [1, 2, 8, 32]], 'inner_hash': 5, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': None, 'inner_tex': 'C_2^3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [2, 36]], 'label': '192.813', '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': '(C2^2*C12):C4', 'ngens': 7, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 26, 'number_conjugacy_classes': 84, 'number_divisions': 44, 'number_normal_subgroups': 114, 'number_subgroup_autclasses': 94, 'number_subgroup_classes': 234, 'number_subgroups': 370, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 48], [6, 30], [12, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 1, 0], 'outer_gens': [[117, 102, 124, 160], [97, 6, 108, 160], [1, 19, 24, 160], [1, 19, 124, 32], [1, 23, 120, 32], [1, 111, 108, 160]], 'outer_group': '512.7535005', 'outer_hash': 8294356380739340268, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 128, 'outer_perms': [322113446363221191402663975915476055661052838323124931661584420310959352730624303782596305879926519748285224935794271617435293997240174325348791362064418433703690068364487786970953368927707596657253103065841778068101, 361324676086353547485366340928759196692867864966506016947465270359873641476662661660462136100154782306192709942729325436199501875365891729954491021396261452330080100398866948976745372687358341172037873898427176692819, 102859983805486842719951735199963510012333625069646694718048985165154881063537470917839215097018157700212753020308544804473702835851277605179775042095444585125327041890442154256807725537266174379967437322427744433806, 30226995076664306316119363002726274723765016192540607273156458758753443134147517654487970019658900661584180949872247791018873016149128846604035072452757209170597907896418065276977213232630911753085354368827021539819, 33263566866726739400443047744215680672520370110130373696266931779820179288343064434319799629859491852448625499593495481082656548256084328857090634925767953799730463698198222651141320949838545961458990445335831465070, 155382372525833013456504755948816951348460931355870129668871036623701252644223843176214878942794246740301112460355784232062403613953196156581914027119307760348510992536344629972379192645753910169726016536395544370715], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3.C_2^6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 15, '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, 14], [8, 2]], 'representations': {'PC': {'code': 94603267294769460481, 'gens': [1, 2, 4, 6], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 1597, 36, 1466, 80, 124]}, 'GLZN': {'d': 2, 'p': 24, 'gens': [14113, 17791, 179725, 96775, 21037, 155741, 14017]}, 'Perm': {'d': 15, 'gens': [87661325064, 174835584000, 274467917544, 4, 274467916800, 1680, 7983360]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 12], '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 C_{12}):C_4', 'transitive_degree': 96, '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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 12, 4, 2, 6, 12, 12, 6, 6, 4], 'aut_gens': [[1, 2, 8, 64], [225, 226, 12, 64], [37, 215, 328, 64], [1, 199, 40, 320], [33, 54, 156, 320], [197, 214, 92, 64], [197, 211, 124, 64], [1, 18, 296, 64], [229, 34, 284, 64], [225, 55, 360, 64], [33, 247, 28, 64]], 'aut_group': None, 'aut_hash': 3386124555295775868, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24576, 'aut_permdeg': 80, 'aut_perms': [203822524674470814250720874586669264048519357004329297435795799395555673815595311360616496886646574589083788399371093, 51483497994287835986721233923599058083776825841974548070722883543326597881516552922763661563294309723173127148497927409, 49675313759217988170764122962050339656046876854722516136703066517721837204030516992313888220599240941305626825874708870, 55810042337718404364985467485248283606935057494957831401755083410478767721519788057567408466686836035481643897170904639, 47462976219825574272840010497120284724432831879247510173559215905118710412974602019310707752306415338715100708383167762, 55049070941016669037999828223784028476854256450338824619184363440764126099253734789909236635922031413408348812070866851, 47615295735600564058351191491562343367660303271383998844749965337589171187290661089962798491703764774010664883146003766, 52052926622022639366067405829238767999623095548910212356749907158522043844647029247584972366234178533879202712986492542, 24498459644810803868295158469439630544667174474172588088245843819799976658364091001892350307491636639213236317968870953, 25035561541359491667653059837070988771496773356655158413274139028854146530371442052749630464710788612609364319588892416], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 2, 2], [2, 2, 4, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 2, 4, 1], [4, 8, 4, 1], [4, 24, 4, 1], [6, 2, 1, 3], [6, 2, 2, 2], [6, 4, 4, 1], [8, 6, 8, 2], [12, 4, 1, 2], [12, 4, 2, 1], [12, 4, 4, 1], [12, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^7.C_2^6)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '512.10494213', 'autcent_hash': 1718285292446712970, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^9', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '48.51', 'autcentquo_hash': 51, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [3, 2, 1], [4, 2, 8], [4, 8, 4], [4, 24, 4], [6, 2, 7], [6, 4, 4], [8, 6, 16], [12, 4, 8], [12, 8, 8]], 'center_label': '8.5', 'center_order': 8, 'central_product': False, 'central_quotient': '48.43', 'commutator_count': 1, 'commutator_label': '24.9', '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', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2088, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [3, 2, 1, 1], [4, 2, 1, 4], [4, 2, 2, 2], [4, 8, 2, 2], [4, 24, 2, 2], [6, 2, 1, 7], [6, 4, 1, 4], [8, 6, 2, 4], [8, 6, 4, 2], [12, 4, 1, 4], [12, 4, 2, 2], [12, 8, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 672, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '24.14', 'hash': 2088, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 4, 3], 'inner_gens': [[1, 194, 8, 64], [193, 2, 248, 64], [1, 210, 8, 320], [1, 2, 136, 64]], 'inner_hash': 43, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': False, 'inner_tex': 'C_6:D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 44], [4, 12]], 'label': '384.2088', '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': '(C2^2*C6).D8', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 39, 'number_conjugacy_classes': 72, 'number_divisions': 48, 'number_normal_subgroups': 125, 'number_subgroup_autclasses': 168, 'number_subgroup_classes': 336, 'number_subgroups': 894, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 144], [6, 30], [8, 96], [12, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 4, 2, 2, 4, 4, 2], 'outer_gen_pows': [273, 0, 16, 0, 0, 128, 16], 'outer_gens': [[193, 211, 72, 64], [225, 51, 316, 320], [33, 195, 56, 320], [229, 6, 40, 64], [37, 23, 56, 64], [197, 39, 72, 64], [5, 54, 72, 320]], 'outer_group': '512.10493082', 'outer_hash': 7367214181469736260, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 128, 'outer_perms': [382582214846963831172641076849797072064525715062251103108853209350661423724718894764958249956927770503238060275999509805023618750095130294866874852717828951134903574461006888591339391706040041860775760028236555759902, 76563215997124184075323185930912358975941604532537134700526591683602916658502348306319726858262822358025174413537262817356462372547992178096690016108425941719790733126528657661258397946179104792693788559242941954633, 124837372576427774555106056843252683648927643557018598854295029748856252553707517570180384295935674532188044470704101617020355468535501093853738446645441263514828542206175548786099764312017564636758715116010777023024, 318898775168715381720681964360581225703658251705042836489710001663859678290269521792305299788851174587243640535235907700513496073318320615762191093727036541857305451544206133598974473611573166913172113982128406454428, 296773514969019566701504223065060553820720138468962908960592330251400826551239608518746486214790227824379791836609376645569110675704878698896858691308707889013726334218530870624373919528394648139746896092388461681802, 46602019000395481666226718460980535001443931155818281052482354850624647265856687776908671747754121902797352847012967632342242215561445578771522034819703470566152227031212368586344120410255975662961332275280745844808, 201251436988026490032716809825698861012223682601935468514410872627212570749188743254604920984874381974967976312132757788133647601699334192868069506277664168167880156760826341737693396024663379594229380587029651941184], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 20], [8, 4]], 'representations': {'PC': {'code': 4180357620400050555757528206072321, 'gens': [1, 2, 4, 7], 'pres': [8, -2, -2, -2, -2, -2, -2, -2, -3, 3105, 41, 3979, 91, 972, 116, 2270, 166, 2079]}, 'GLZN': {'d': 2, 'p': 48, 'gens': [111169, 2764825, 111361, 111745, 1315165, 774151, 2171965, 2821273]}, 'Perm': {'d': 19, 'gens': [6446835113247651, 12914592058743196, 20713823523996643, 27414266513356800, 18498, 12316, 20713823523993600, 3991680]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2^2\\times C_6).D_8', 'transitive_degree': 192, '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}
