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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.8738', 'ambient_counter': 8738, 'ambient_order': 1344, 'ambient_tex': 'D_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 336, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.8738.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.197', 'subgroup_hash': 197, 'subgroup_order': 336, 'subgroup_tex': 'D_{84}:C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.8738', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.c1', 'complements': ['336.g1', '336.l1'], 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '2.f1'], 'contains': ['8.d1', '8.g1', '8.h1', '8.o1', '8.r1', '12.l1', '28.m1'], 'core': '4.g1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [673, 32, 168, 112, 6, 448], 'label': '1344.8738.4.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1', 'normal_contained_in': ['2.b1', '2.f1'], 'normal_contains': ['8.d1', '8.g1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [14, 2, 6, 12, 6, 2], 'aut_gens': [[7386641556, 12859645009, 113906], [5511276542, 38273089, 21292671], [8687915124, 12859645009, 9325127], [344454852, 12859645009, 9652017], [11481826155, 12859645009, 37338926], [1416091943, 38273089, 2113664], [5511276542, 12859645009, 21514417]], 'aut_group': None, 'aut_hash': 866793471638122205, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4032, 'aut_permdeg': 86, 'aut_perms': [8495802875864850104285657904682950617464512894530941764777743202679831836535736305393543976953274297543577298326249050622985910618, 6395642569540508394650599292308404958268704024161427900318425876772479597066786154161473925694125232627263040809590950920739683343, 18902413586893750685388336824536102085575033056915203149267387476019234304844914748169870228450324430577358995962311566392271683068, 5631657261707649810524061415616708534997512610519767885426972573357450461259928679211746823346013191607838203082772588570066295407, 11249818465513292779155627410509123844104493694920572355605831344161678361142262776800079997334395966931469430630898454801752674296, 11703107976481570399217670507534298911126295624242869341333474013391937561792656511481488740029527394920767114222093445402416789725], 'aut_phi_ratio': 42.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 42, 2, 1], [3, 2, 1, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 42, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [7, 2, 3, 1], [12, 2, 2, 2], [14, 2, 3, 1], [14, 2, 6, 1], [21, 2, 6, 1], [28, 2, 6, 2], [42, 2, 6, 1], [42, 2, 12, 1], [84, 2, 12, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^4\\times C_6)', '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': 42, 'autcentquo_group': '504.162', 'autcentquo_hash': 162, 'autcentquo_nilpotent': False, 'autcentquo_order': 504, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 42, 2], [3, 2, 1], [4, 1, 2], [4, 2, 1], [4, 42, 2], [6, 2, 3], [7, 2, 3], [12, 2, 4], [14, 2, 9], [21, 2, 6], [28, 2, 12], [42, 2, 18], [84, 2, 24]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '84.14', 'commutator_count': 1, 'commutator_label': '42.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 197, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 42, 1, 2], [3, 2, 1, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 42, 1, 2], [6, 2, 1, 1], [6, 2, 2, 1], [7, 2, 3, 1], [12, 2, 2, 2], [14, 2, 3, 1], [14, 2, 6, 1], [21, 2, 6, 1], [28, 2, 6, 2], [42, 2, 6, 1], [42, 2, 12, 1], [84, 2, 12, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 2688, 'exponent': 84, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[2, 0, 24]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '168.56', 'hash': 197, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [42, 2, 2], 'inner_gens': [[7386641556, 12859645009, 34698868], [7386641556, 12859645009, 38272416], [8687915124, 38273089, 113906]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 84, 'inner_split': True, 'inner_tex': 'D_{42}', 'inner_used': [1, 3], 'irrC_degree': 2, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 4, 'irrep_stats': [[1, 8], [2, 82]], 'label': '336.197', 'linC_count': 24, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 16, 'linQ_dim': 12, 'linQ_dim_count': 16, 'linR_count': 12, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D84:C2', 'ngens': 3, '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': 22, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 90, 'number_divisions': 24, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': 60, 'number_subgroup_classes': 80, 'number_subgroups': 512, 'old_label': None, 'order': 336, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 87], [3, 2], [4, 88], [6, 6], [7, 6], [12, 8], [14, 18], [21, 12], [28, 24], [42, 36], [84, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [38272754, 38272754, 38272754, 12859645009], 'outer_gens': [[10065734335, 12859645009, 113906], [1569182947, 12859645009, 113906], [5511276542, 12859645009, 113906], [3138365783, 12859645009, 16871905]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [24, 3628800, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [4, 1], [6, 4], [8, 1], [12, 4], [24, 1], [48, 1]], 'representations': {'PC': {'code': 1055768785629518800904843, 'gens': [1, 2, 4], 'pres': [6, -2, -2, -2, 2, -3, -7, 31, 7971, 69, 9604, 118, 10373]}, 'GLFp': {'d': 2, 'p': 337, 'gens': [7386641556, 12859645009, 113906]}, 'Perm': {'d': 18, 'gens': [21010447548856, 11845, 18498, 24338, 3991680, 397707843456000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{84}:C_2', 'transitive_degree': 168, '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [14, 14, 6, 2, 2, 4, 6, 84, 12], 'aut_gens': [[1, 2, 4, 224], [1, 130, 4, 1232], [113, 803, 677, 1232], [785, 162, 1076, 224], [113, 2, 620, 1120], [785, 818, 612, 1120], [785, 787, 845, 1232], [113, 890, 44, 1120], [785, 186, 1180, 336], [785, 171, 1213, 1120]], 'aut_group': None, 'aut_hash': 2121436511852193631, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 258048, 'aut_permdeg': 160, 'aut_perms': [342906011369171562033954521938554985601957975504566000030952712549335734636881129851699990485637663445406151759108607235042485605874408943587900661240488275285008461927875433067481064427132138370375749114588227935183564555141272175457433493437365070305453225678268417016079132300134704, 77184662643784264146680829086333738935263263516654173511419733749619874700005739528167835446192067243048102228327192499971715801808787512994699311027798682914135255822844630012040060743064076216072745673597035828342677215189182529617208507257763387612219081204287230551592751125672132, 307536620730170784668664970864475533989642929602135953778519726972538165559157603096316485339070691186583462374948046646250555889882076611364253916816378452026811203832000666824668239007562720264460169419440968406500097845241567658756871148426067902765415254137846167398935067726515979, 356576634353358844403558877012815321726948323161621339512391538448979103878467868821545328175017596280833597448684787691008872309055550164961574033125591028682121026261370131120652244613024315377172108100991704889060818801482085649393071527693951641717951992920725630257580986287804074, 31410878843918519229828966039509603343960339192054635050243389839815251710393614533199967684187466032337740785569515203019655554706066784460396789631004166418178245687343759961221242907145532786969629100790879871338590351146348185685664841788513131553852918181803893821671844554218788, 411248652971741614041229440511284063069642116983738788651132432382316829957293135250450210733058214437590179611004117330643485899862704156486288223018586348928952649798500088108458314375006624463115788640332284244086733873110100019147612455610608352793142736519036841100955620227320036, 385766418702965439033848357895949741145834412302490890055706474471479349345304505093574000534531587997807857458166673290483470881708251189095232400691078404264002282384238745851374883637945195477305884873158665843528211703624737558213223534607336211305966004684405096510497725410263781, 404558514328673547242357920838390694774218535540688956694336210776084906251313672576296778404564855881859471791780476369464869824349656606224897914649513254246459369539512986839639280154946415443991915327227626035556403961009226887890122853337962681523019349358682313131364511091652236, 462991360470428782189704369597715627528693309313673919846844428519275361150502528697624740378077822094384891257729406248290679013081334226767671830182124227501683235690902178502972916852824314317529731416371307788549306560906510418424364468476847716596447121480409459568368416333605751], 'aut_phi_ratio': 672.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 28, 4, 1], [2, 84, 2, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 84, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 2, 4, 1], [6, 28, 8, 1], [7, 2, 3, 1], [8, 12, 4, 1], [12, 4, 1, 2], [12, 4, 2, 1], [14, 2, 3, 1], [14, 2, 6, 1], [14, 4, 6, 1], [21, 4, 3, 1], [28, 2, 6, 2], [28, 4, 6, 1], [42, 4, 3, 1], [42, 4, 6, 1], [42, 4, 12, 1], [56, 12, 24, 1], [84, 4, 6, 2], [84, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1578', 'autcent_hash': 1578, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': None, 'autcentquo_hash': 5451351369529179689, 'autcentquo_nilpotent': False, 'autcentquo_order': 2016, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^3\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 28, 4], [2, 84, 2], [3, 2, 1], [4, 2, 4], [4, 84, 2], [6, 2, 7], [6, 28, 8], [7, 2, 3], [8, 12, 4], [12, 4, 4], [14, 2, 9], [14, 4, 6], [21, 4, 3], [28, 2, 12], [28, 4, 6], [42, 4, 21], [56, 12, 24], [84, 4, 24]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '336.158', 'commutator_count': 1, 'commutator_label': '84.6', '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', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 8738, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['672.456', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 28, 1, 4], [2, 84, 1, 2], [3, 2, 1, 1], [4, 2, 1, 4], [4, 84, 1, 2], [6, 2, 1, 3], [6, 2, 2, 2], [6, 28, 2, 4], [7, 2, 3, 1], [8, 12, 1, 4], [12, 4, 1, 4], [14, 2, 3, 3], [14, 4, 3, 2], [21, 4, 3, 1], [28, 2, 6, 2], [28, 4, 3, 2], [42, 4, 3, 3], [42, 4, 6, 2], [56, 12, 6, 4], [84, 4, 6, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3734640, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '336.219', 'hash': 8738, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 28, 3], 'inner_gens': [[1, 2, 116, 224], [1, 2, 220, 224], [113, 10, 4, 1120], [1, 2, 452, 224]], 'inner_hash': 158, 'inner_nilpotent': False, 'inner_order': 336, 'inner_split': False, 'inner_tex': 'C_6:D_{28}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 68], [4, 66]], 'label': '1344.8738', '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': 'D84:C2^3', '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': 34, 'number_characteristic_subgroups': 44, 'number_conjugacy_classes': 150, 'number_divisions': 60, 'number_normal_subgroups': 160, 'number_subgroup_autclasses': 244, 'number_subgroup_classes': 596, 'number_subgroups': 5364, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 287], [3, 2], [4, 176], [6, 238], [7, 6], [8, 48], [12, 16], [14, 42], [21, 12], [28, 48], [42, 84], [56, 288], [84, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 4, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 56, 0, 0, 0, 0], 'outer_gens': [[673, 674, 860, 224], [673, 674, 676, 336], [1, 842, 676, 224], [1, 2, 60, 224], [1, 674, 676, 224], [1, 2, 676, 224], [1, 675, 789, 224]], 'outer_group': '768.55643', 'outer_hash': 55643, 'outer_nilpotent': True, 'outer_order': 768, 'outer_permdeg': 17, 'outer_perms': [21204442869868, 23819871398424, 24, 131760, 47089213920000, 90720, 5324585414400], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^7:C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 6], [6, 8], [8, 2], [12, 12], [24, 2], [48, 2]], 'representations': {'PC': {'code': 1111489944815756596009013726469293393134705106101, 'gens': [1, 2, 3, 7], 'pres': [8, -2, -2, -2, -2, -2, -7, -2, -3, 2786, 2650, 66, 3467, 91, 4172, 116, 4621, 15702, 166, 14359]}, 'Perm': {'d': 20, 'gens': [6423383674049808, 40331670, 1, 167407, 859248, 1270440, 518918400, 134491780578355200]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{84}:C_2^3', 'transitive_degree': 336, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
