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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1088.249', 'ambient_counter': 249, 'ambient_order': 1088, 'ambient_tex': 'C_{136}.C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 136, 'characteristic': False, 'core_order': 544, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1088.249.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '544.193', 'subgroup_hash': 193, 'subgroup_order': 544, 'subgroup_tex': '\\OD_{16}:C_{34}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1088.249', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '1536.408624996', 'aut_weyl_index': 16, 'centralizer': '8.g1', 'complements': ['544.b1', '544.c1'], 'conjugacy_class_count': 8, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.a2', '4.c1', '34.b1'], 'core': '2.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [2797, 8453, 6522, 6317], 'generators': [64, 8, 16, 4, 546, 1], 'label': '1088.249.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.a2', '4.c1', '34.b1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '16.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '272.46', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 48, 'aut_gen_orders': [16, 12, 48, 12, 4], 'aut_gens': [[18906, 95140161, 7714062], [18906, 37401, 290563002], [708153, 1890600, 205708320], [2571489, 2552721, 249421338], [349704009, 37401, 205708320], [2571489, 1890600, 321419250]], 'aut_group': '1536.408624996', 'aut_hash': 737399360701677454, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536, 'aut_permdeg': 26, 'aut_perms': [75905091810364813774283196, 209222309660816803931434716, 327878235575797253536381603, 203622538035030082598810676, 233544056780311854686787440], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 3, 1], [4, 1, 2, 1], [4, 2, 3, 1], [8, 1, 4, 1], [8, 2, 6, 1], [17, 1, 16, 1], [34, 1, 16, 1], [34, 2, 48, 1], [68, 1, 32, 1], [68, 2, 48, 1], [136, 1, 64, 1], [136, 2, 96, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_{16}\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 16, 'autcent_group': '256.55608', 'autcent_hash': 55608, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\times C_{16}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [4, 1, 2], [4, 2, 3], [8, 1, 4], [8, 2, 6], [17, 1, 16], [34, 1, 16], [34, 2, 48], [68, 1, 32], [68, 2, 48], [136, 1, 64], [136, 2, 96]], 'center_label': '136.2', 'center_order': 136, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '17.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 193, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['17.1', 1], ['32.38', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [4, 1, 2, 1], [4, 2, 1, 3], [8, 1, 4, 1], [8, 2, 2, 3], [17, 1, 16, 1], [34, 1, 16, 1], [34, 2, 16, 3], [68, 1, 32, 1], [68, 2, 16, 3], [136, 1, 64, 1], [136, 2, 32, 3]], 'element_repr_type': 'GLFp', 'elementary': 2, 'eulerian_function': 34384, 'exponent': 136, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 17], 'faithful_reps': [[2, 0, 64]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '136.15', 'hash': 193, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 1], 'inner_gens': [[18906, 257135337, 7714062], [2571216, 95140161, 7714062], [18906, 95140161, 7714062]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 128, 'irrQ_dim': 128, 'irrR_degree': 4, 'irrep_stats': [[1, 272], [2, 68]], 'label': '544.193', 'linC_count': 64, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 24, 'linQ_degree_count': 8, 'linQ_dim': 24, 'linQ_dim_count': 8, 'linR_count': 32, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'OD16:C34', 'ngens': 3, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 14, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 340, 'number_divisions': 26, 'number_normal_subgroups': 56, 'number_subgroup_autclasses': 30, 'number_subgroup_classes': 62, 'number_subgroups': 68, 'old_label': None, 'order': 544, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [4, 8], [8, 16], [17, 16], [34, 112], [68, 128], [136, 256]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 48, 'outer_gen_orders': [2, 2, 2, 48], 'outer_gen_pows': [2571354, 18906, 2571354, 2571354], 'outer_gens': [[18906, 257135337, 233993214], [18906, 37401, 7714062], [18906, 95140161, 344561436], [349704009, 37401, 210851028]], 'outer_group': '384.14574', 'outer_hash': 14574, 'outer_nilpotent': False, 'outer_order': 384, 'outer_permdeg': 192, 'outer_perms': [5595583159870777171214009893842698048600257745175452484407649725872711984453196564574776563124882393507372551987995960665667704360311368365758732898861093646989103991232035076823858401801213924423424939137815477103623423147338777486537521476562085064063638839490323793573369549153409602142848382880614362230511696665958671511284082298294968173109623606178, 11478850970224075363249399217047056215505552606381871510622231916906567392983943323458853144925052141072681935599971295523181274430572586259794024110698545102348418732313351889087327683533640783733243738039206081701843255478559430947820430404889330858043490753982456080005395759663810350221842705289824149854024217946790760014876096300709223796040, 1849095291190910202026690308931268032397199826603479882553246239609040457656946999269211814162635650898686870673303244132021579681207428838124886451122471435496786720716550300142673265586292908645836845827983769996629277450165916460250061700678876144119901263298957347209983141177648133879346847201932368001677596413891871771152961624143346365692200337641, 107900871624413825386521991183812980497021937679906691453128154508395622636638941500014548712589317938675114915483795411145112546934103068007744609681815047348402985001097467132442122428342262924388356194363538707086705860133345346551822662536256534739020076351307994377050150595125474880760714552424130376410130088233479919257326913315483318728584963815604], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{48}:C_2^3', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 33, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 17], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [8, 1], [16, 8], [32, 4], [128, 1]], 'representations': {'PC': {'code': 2837377259010847080448, 'gens': [1, 3, 4], 'pres': [6, -2, -17, -2, -2, -2, -2, 12, 5510, 69, 88]}, 'GLFp': {'d': 2, 'p': 137, 'gens': [18906, 95140161, 7714062]}, 'Perm': {'d': 33, 'gens': [2978863815797762108496860676096000000, 1629484621320921002409183539871744000, 1086511080841299437022706003476480000, 334764638208000, 805839124554122228896064701906944000, 263396395085763368908085856657408000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 68], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '\\OD_{16}:C_{34}', 'transitive_degree': 272, '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': '544.236', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 48, 'aut_gen_orders': [6, 8, 12, 8, 16, 8], 'aut_gens': [[1, 2, 4, 32], [553, 18, 20, 529], [562, 2, 7, 257], [560, 18, 572, 699], [17, 18, 31, 315], [555, 18, 23, 354], [546, 2, 559, 1043]], 'aut_group': None, 'aut_hash': 6306246606448742379, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24576, 'aut_permdeg': 48, 'aut_perms': [1401423918603526781708878879690622930390886290589287895459279, 7720998095425615319389095538849411036558948148677370853443267, 10177138249631839376325185525782984439149908104973286721060659, 6757714605381399248147291098706570610601047939798000784059303, 4420765124806686761619122241243761305858297108146910569995596, 1989159365628520395910710857646195223394970852272762363581186], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 2, 6, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 2, 6, 1], [8, 2, 16, 1], [17, 1, 16, 1], [34, 1, 16, 1], [34, 2, 16, 1], [34, 2, 96, 1], [68, 1, 32, 1], [68, 2, 16, 1], [68, 2, 96, 1], [136, 2, 256, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^3:A_4.C_8.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 16, 'autcent_group': '512.10493039', 'autcent_hash': 3046548263559564634, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5\times C_{16}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '48.48', 'autcentquo_hash': 48, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 7], [4, 1, 2], [4, 2, 7], [8, 2, 16], [17, 1, 16], [34, 1, 16], [34, 2, 112], [68, 1, 32], [68, 2, 112], [136, 2, 256]], 'center_label': '68.2', 'center_order': 68, 'central_product': True, 'central_quotient': '16.14', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '17.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 249, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['17.1', 1], ['64.249', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 7], [4, 1, 2, 1], [4, 2, 1, 7], [8, 2, 2, 8], [17, 1, 16, 1], [34, 1, 16, 1], [34, 2, 16, 7], [68, 1, 32, 1], [68, 2, 16, 7], [136, 2, 32, 8]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 17539200, 'exponent': 136, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 17], 'faithful_reps': [[4, 0, 32]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '272.54', 'hash': 249, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 2], 'inner_gens': [[1, 2, 4, 48], [1, 2, 20, 32], [1, 18, 4, 32], [17, 2, 4, 32]], 'inner_hash': 14, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': False, 'inner_tex': 'C_2^4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 128, 'irrQ_dim': 128, 'irrR_degree': None, 'irrep_stats': [[1, 544], [4, 34]], 'label': '1088.249', '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': 'C136.C2^3', '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': 16, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 578, 'number_divisions': 50, 'number_normal_subgroups': 238, 'number_subgroup_autclasses': 60, 'number_subgroup_classes': 258, 'number_subgroups': 290, 'old_label': None, 'order': 1088, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 15], [4, 16], [8, 32], [17, 16], [34, 240], [68, 256], [136, 512]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 48, 'outer_gen_orders': [16, 2, 48, 16, 16], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[19, 18, 548, 955], [19, 2, 564, 32], [569, 2, 4, 897], [544, 18, 556, 659], [19, 18, 549, 242]], 'outer_group': '1536.408624996', 'outer_hash': 737399360701677454, 'outer_nilpotent': False, 'outer_order': 1536, 'outer_permdeg': 256, 'outer_perms': [320588277017030241875377189371827021335378065347747118427541898109826226879083677509979173794467888413559246296811832851759610972183089246694025086835199359032081304412804086855082786302662879456601941701266096888592092173277650978346401250980181948520602218511893252718331449647071144018616744999638904856183081798425554676555693087184058062677620352315172150326951218134998045590528948363693881265488779318071642495664232876199448797265801553542006920245106696219068900189061046431542102355217061075934500, 570626669551108362237118123399363955884083879897961777300947493436397015817658689286024707600626621220257054818061365503650769254140665570961333416319292171700185310115398036100990832928449728274398779980439102294898330810224460758848265071518797762733415851493797512669994966663493205662689464511343937251420653484174287951403011364887936711375270192970051238962267644086993573507086353262113255804343185062414961222980549862798763562688875474219283256046265556084761635098903712264225056452575862418916272, 464955177905136544195249485532663935400403647437572724265596875114578730769903825933834107968150281893621229206233821745197510578919916658555587100732237839595728924714125093868031567551797549221519228235403999854005031056087348679994570166545146352757506188464774256279742033168781293413626837928003947369510318158902208172059190228207948828988707266027414685500338967336859088550002788851946225663478505023561235967457089941573864635030466753916265446343575832183293258806627234491299738628448113859051053, 354399540338758438869937382169532986790683317434601996123495116500082886889871915704239812446415436747088155763661771684108054771692063735113476027669283732744438785621461700496057040464980559079031007792708555135384208843936536361203842985718257504377996935106502504058192598779926759833507591763110627714567704138654307750672463582405000930011514733049841244891695650995044364023822651501336118210697900299464624157265238810661445491379643980503010090509987486717176900036144214695284084679118153056775912, 833884545798533961374863910864888460209376527429201348080119171426396252110685335440926211597278174088582997363265736725583153852181794774646216083370471243344187317432692770123913528506259758338326206053335927766592048528136868123278914955960690466449984412796100983277253179352718902937991410126586956283270740082573190404122043404812522479449204995624607185577972680970081315479967569470300467097842059552059043979360010588624117316109128944008435510893508734580946262429603764422817634217658452667086092], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^2\\times C_{16}\\times S_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 33, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4, 17], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [8, 1], [16, 16], [32, 8], [128, 1]], 'representations': {'PC': {'code': 1718079498528731075987848036367, 'gens': [1, 2, 3, 6], 'pres': [7, -2, -2, -2, -2, -2, 2, -17, 219, 58, 80, 2021, 124]}, 'Perm': {'d': 33, 'gens': [2978863815797762108496860676096000000, 1629484621320921002409183539871744000, 1086511080841299437022706003476480000, 621574841765398929408000, 805839124554122228896064701906944000, 263396395085763368908085856657408000, 334764638208000]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 68], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{136}.C_2^3', 'transitive_degree': 272, '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}
