-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2865', 'ambient_counter': 2865, 'ambient_order': 1344, 'ambient_tex': 'D_{84}.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 336, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2865.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.174', 'subgroup_hash': 174, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:Q_8', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '1344.2865', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.h1.a1', '8.k1.a1', '8.o1.a1', '12.a1.a1', '28.e1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 192, 336, 448, 4, 672], 'label': '1344.2865.4.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [6, 14, 4, 4, 2, 2], 'aut_gens': [[1, 2, 4], [1, 2, 244], [169, 242, 4], [169, 2, 5], [169, 255, 172], [1, 2, 116], [1, 3, 172]], 'aut_group': '5376.db', 'aut_hash': 1775239541180599517, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5376, 'aut_permdeg': 58, 'aut_perms': [7393939573109590491155127336672037917391407075868284315957061224957309556, 444591894541905235761393302763201808377239744059096480821420700795759284753, 222216448114387298171537055274230502607641155335704873289834091453460885, 651602099057286789374651663868020268016389432528343616055712533623122395113, 40526919504877216755680601905432322134980384796226602145184481280000000000000, 25854497265064707583953179098352044012682828800078108534467927407897095561], 'aut_phi_ratio': 56.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [4, 2, 2, 1], [4, 14, 4, 1], [6, 1, 2, 1], [6, 1, 4, 1], [7, 2, 3, 1], [12, 2, 4, 1], [12, 14, 8, 1], [14, 2, 3, 1], [14, 2, 6, 1], [21, 2, 6, 1], [28, 2, 12, 1], [42, 2, 6, 1], [42, 2, 12, 1], [84, 2, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4:D_4\\times F_7', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.202', 'autcent_hash': 202, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '84.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 84, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [4, 2, 2], [4, 14, 4], [6, 1, 6], [7, 2, 3], [12, 2, 4], [12, 14, 8], [14, 2, 9], [21, 2, 6], [28, 2, 12], [42, 2, 18], [84, 2, 24]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '28.3', 'commutator_count': 1, 'commutator_label': '14.2', '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': 174, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['56.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 2, 1, 2], [4, 14, 1, 4], [6, 1, 2, 3], [7, 2, 3, 1], [12, 2, 2, 2], [12, 14, 2, 4], [14, 2, 3, 3], [21, 2, 6, 1], [28, 2, 6, 2], [42, 2, 6, 3], [84, 2, 12, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2184, 'exponent': 84, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '168.54', 'hash': 174, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [1, 2, 14], 'inner_gens': [[1, 2, 4], [1, 2, 220], [1, 122, 4]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 28, 'inner_split': False, 'inner_tex': 'D_{14}', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 78]], 'label': '336.174', 'linC_count': 384, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 52, 'linQ_dim': 10, 'linQ_dim_count': 4, 'linR_count': 48, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C42:Q8', 'ngens': 6, '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': 18, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 102, 'number_divisions': 32, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 76, 'number_subgroups': 208, 'old_label': None, 'order': 336, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 60], [6, 6], [7, 6], [12, 120], [14, 18], [21, 12], [28, 24], [42, 36], [84, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 12], 'outer_gen_pows': [0, 0, 28, 0, 0], 'outer_gens': [[169, 2, 4], [1, 2, 284], [1, 86, 4], [1, 171, 172], [169, 2, 77]], 'outer_group': '192.1410', 'outer_hash': 1410, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 13, 'outer_perms': [83502720, 40320, 120, 1037839224, 522588268], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 2], [6, 4], [12, 6], [24, 2]], 'representations': {'PC': {'code': 118545964720661192527370279819, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -2, -3, -7, 1015, 1988, 50, 1257, 69, 3130, 118, 5195]}, 'GLZN': {'d': 2, 'p': 21, 'gens': [9325, 120406, 61776, 80557, 74096, 37048]}, 'Perm': {'d': 20, 'gens': [6423384157440504, 479001600, 487450344, 3, 12541704, 134491780578355200]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{42}:Q_8', 'transitive_degree': 336, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'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': [12, 14, 42, 6, 12, 6, 12, 84], 'aut_gens': [[1, 2, 4, 8], [117, 1314, 4, 636], [673, 962, 4, 904], [1121, 354, 4, 8], [789, 834, 676, 1160], [789, 162, 4, 1212], [1013, 722, 4, 536], [677, 866, 676, 40], [901, 34, 676, 680]], 'aut_group': None, 'aut_hash': 9161810123478319507, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 88, 'aut_perms': [4497663518367917035967062121527631786655868644586868170191506275561441713848711379023047460383762183657801713283582954183882797843, 19164484487662132746080499596134089368258438396502042434110621175188986055484617503045935183483168393304955335783592562521975876420130, 175265366735937971157797783139781127083323764043191738073170086995793293322479097136982915909655732628878546708134981128206226588915762, 134338457940878511072805539853013923087176053005956598710927633164729868509776265283792943238657214959672189958136188433524435135803757, 10659127102585799554812634293950737840532663789396979436237264085748177536327311490544469970465879738466729146041583185790385171650548, 126171815513268709493217145150297753191037228180993940096201829816618166326508410650587758271036035256963477020935124994172297094717654, 108750872539973774810077007056633931798667432258120930536294448619251221232458775986164126762278617808302744170955664486647424294521096, 95916918492181524660907997910718099659744671461188262600636421191006634696987129829331897068181116731038717675605265158237693834095940], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 24, 1, 1], [4, 56, 1, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 24, 1, 1], [8, 42, 2, 1], [8, 56, 1, 1], [8, 84, 1, 1], [12, 4, 1, 2], [12, 56, 2, 1], [14, 2, 3, 1], [14, 4, 3, 1], [21, 4, 3, 1], [24, 8, 2, 1], [24, 56, 2, 1], [28, 4, 3, 2], [28, 24, 6, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 8, 6, 1], [56, 24, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^2', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': None, 'autcentquo_hash': 6896085666905541017, 'autcentquo_nilpotent': False, 'autcentquo_order': 4032, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 84, 1], [3, 2, 1], [4, 2, 2], [4, 24, 1], [4, 56, 1], [4, 84, 1], [6, 2, 1], [6, 4, 1], [7, 2, 3], [8, 4, 2], [8, 24, 1], [8, 42, 2], [8, 56, 1], [8, 84, 1], [12, 4, 2], [12, 56, 2], [14, 2, 3], [14, 4, 3], [21, 4, 3], [24, 8, 2], [24, 56, 2], [28, 4, 6], [28, 24, 6], [42, 4, 3], [42, 8, 3], [56, 8, 6], [56, 24, 6], [84, 4, 6], [84, 8, 3], [168, 8, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '672.605', 'commutator_count': 2, 'commutator_label': '168.39', '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': 2865, '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, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 24, 1, 1], [4, 56, 1, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 24, 1, 1], [8, 42, 2, 1], [8, 56, 1, 1], [8, 84, 1, 1], [12, 4, 1, 2], [12, 56, 2, 1], [14, 2, 3, 1], [14, 4, 3, 1], [21, 4, 3, 1], [24, 8, 2, 1], [24, 56, 2, 1], [28, 4, 3, 2], [28, 24, 6, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 8, 6, 1], [56, 24, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 21504, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, 0, 6]], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '168.50', 'hash': 2865, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 4, 2, 84], 'inner_gens': [[1, 338, 4, 236], [1009, 2, 4, 328], [1, 2, 4, 680], [453, 1026, 676, 8]], 'inner_hash': 605, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': 'D_{42}:D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 38], [4, 34], [8, 10]], 'label': '1344.2865', '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.D4', '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': 52, 'number_conjugacy_classes': 90, 'number_divisions': 36, 'number_normal_subgroups': 52, 'number_subgroup_autclasses': 200, 'number_subgroup_classes': 200, 'number_subgroups': 1684, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 87], [3, 2], [4, 168], [6, 6], [7, 6], [8, 256], [12, 120], [14, 18], [21, 12], [24, 128], [28, 168], [42, 36], [56, 192], [84, 48], [168, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [0, 0, 1008, 0], 'outer_gens': [[1, 2, 4, 904], [1, 674, 4, 8], [337, 2, 4, 904], [1, 338, 676, 536]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [744, 3628800, 24, 40323], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 42, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 3], [6, 4], [8, 3], [12, 4], [24, 5], [48, 1]], 'representations': {'PC': {'code': 202797249805044787670014709171568860180977740773134860985790476770059, 'gens': [1, 2, 3, 4], 'pres': [8, -2, -2, -2, 2, -2, -2, -3, -7, 5376, 5409, 8073, 7555, 5259, 5459, 91, 45444, 13132, 116, 44549, 31501, 141, 28678, 35854, 222, 36879]}, 'Perm': {'d': 42, 'gens': [816438677858700483452020063364007257365088185692, 8701128753596821002912997869098109044, 26340670275379773640968878294828373, 3974861169727848189186688964589, 34840860416302983971454251705973597, 43337613556404296642408707668437709, 303916116658416027343136804044800000000, 35085403596887862568986022075080631753113600000000]}}, '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}.D_4', 'transitive_degree': 672, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'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}
