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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.7530076', 'ambient_counter': 7530076, 'ambient_order': 512, 'ambient_tex': 'D_4^2:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.7530076.4.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1', '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': '128.1615', 'subgroup_hash': 1615, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '512.7530076', 'aut_centralizer_order': None, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '256.a1', 'complements': ['128.bm1', '128.bk1', '128.bu1'], 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '2.e1', '2.h1'], 'contains': ['8.h1', '8.n1', '8.be1', '8.da1', '8.dz1', '8.go1'], 'core': '4.o1', 'coset_action_label': None, 'count': 2, 'diagramx': [7393, 7407, 7391, 7414], 'generators': [2789792421136, 2789832700823, 5167, 5612462133817, 12526762740463, 5606234750016, 1313941673647], 'label': '512.7530076.4.o1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1', 'normal_contained_in': ['2.d1', '2.e1', '2.h1'], 'normal_contains': ['8.h1', '8.n1', '8.be1'], 'normalizer': '1.a1', 'old_label': '4.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1', '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': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4, 16, 32], [65, 2, 68, 16, 96], [1, 2, 92, 80, 32], [81, 82, 39, 16, 32], [65, 66, 84, 16, 32], [65, 66, 20, 80, 112], [25, 2, 94, 80, 34], [65, 82, 93, 16, 48], [81, 66, 94, 16, 48], [1, 26, 93, 80, 33], [1, 66, 68, 16, 96], [2, 1, 4, 16, 96]], 'aut_group': '8192.bab', 'aut_hash': 8201102105152535214, 'aut_nilpotency_class': 6, 'aut_nilpotent': True, 'aut_order': 8192, 'aut_permdeg': 32, 'aut_perms': [214071389779371266110473401729022751, 123837066829968803666763849291541207, 167022703835536409865752324163488387, 34977101703780578301724467373949166, 123699914447392945950283628941299366, 238970706638229113756004118114759855, 226568346338056945748941211678331494, 244272621410959074918210890938146799, 222412793517901389251770456315884727, 214139375645659212409299445591463041, 6118822555851591960150247770703128], 'aut_phi_ratio': 128.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 2, 2, 1], [2, 2, 8, 1], [2, 4, 4, 1], [4, 2, 4, 1], [4, 4, 4, 1], [4, 4, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6.C_2\\wr D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 8, 'autcentquo_group': '512.406983', 'autcentquo_hash': 7717662186163716498, 'autcentquo_nilpotent': True, 'autcentquo_order': 512, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^6:D_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 11], [2, 4, 4], [4, 2, 4], [4, 4, 20]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '64.193', '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', '2.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1615, '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, 11], [2, 4, 1, 4], [4, 2, 1, 4], [4, 4, 1, 4], [4, 4, 2, 8]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 10080, 'exponent': 4, 'exponents_of_order': [7], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[8, 1, 1]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '16.14', 'hash': 1615, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 4, 2, 2], 'inner_gens': [[1, 66, 4, 16, 32], [65, 2, 4, 16, 32], [1, 2, 4, 80, 112], [1, 2, 68, 16, 32], [1, 2, 84, 16, 32]], 'inner_hash': 193, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': False, 'inner_tex': 'C_2^4:C_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 32], [2, 8], [8, 1]], 'label': '128.1615', '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': 'C2^3.C2^4', 'ngens': 4, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 41, 'number_divisions': 33, 'number_normal_subgroups': 170, 'number_subgroup_autclasses': 72, 'number_subgroup_classes': 400, 'number_subgroups': 820, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 39], [4, 88]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 8, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 41, 8, 0, 80, 0], 'outer_gens': [[1, 10, 4, 16, 33], [10, 9, 12, 80, 43], [1, 18, 101, 80, 48], [9, 10, 4, 16, 43], [1, 82, 5, 16, 32], [81, 82, 23, 16, 32], [1, 2, 12, 80, 32]], 'outer_group': '128.928', 'outer_hash': 928, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 8, 'outer_perms': [5329, 39597, 18259, 21821, 526, 3420, 18498], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\wr D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [8, 1]], 'representations': {'PC': {'code': 4792113695780765796, 'gens': [1, 2, 3, 5, 6], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 925, 58, 718, 1195, 530, 124]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [11040833, 10024001, 17109059, 32746561, 5128257, 18848835, 6210625]}, 'Perm': {'d': 16, 'gens': [11212861322880, 5606234750016, 2789792421136, 6227383801, 5167, 40279687, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3.C_2^4', 'transitive_degree': 16, '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': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [4, 2, 2, 4, 8, 8, 2], 'aut_gens': [[11212821043200, 6920176400047, 1313941685176, 5612462133817, 2789792421136, 5606234750016, 2789832700823, 5167, 1313941673647], [14008840853062, 1313941685176, 5606234731567, 6913949034937, 4103734089616, 4103693809943, 6920176423663, 1313941668480, 1313941673647], [12520495779121, 4103693798400, 23616, 2789792426303, 5612462138742, 4103693809943, 6920176418496, 5167, 1313941673647], [14002613464336, 6920176394880, 1313941680023, 6913949034937, 2789792421136, 6920176423663, 4103693815096, 5167, 1313941673647], [15310288195342, 6920176394880, 16696, 6913949039862, 4103734089616, 6920176418496, 2789832705976, 5167, 1313941673647], [11219048427001, 5606234726400, 16696, 2789792426303, 6913949039862, 5606234750016, 2789832705976, 5167, 1313941673647], [19608848214352, 4103693803567, 1313941692096, 6913949034937, 2789792421136, 2789832705976, 6920176423663, 5167, 1313941673647], [18132997466863, 5606234726400, 1313941685176, 5612462133817, 2789792421136, 5606234750016, 4103693809943, 5167, 1313941673647]], 'aut_group': '16384.ku', 'aut_hash': 6461665870828750133, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 16384, 'aut_permdeg': 48, 'aut_perms': [2714847770522233919875424233329916378546681010225094452987058, 2036583356512394302185676913081984815675660833634498549455431, 8146712296055260091802838208642175025131798634818507680641631, 6270998563231891915627835749423032959071081572525137232621766, 374469862533098215381987692840467528090573576502118035359158, 7021758928045821651260909567162827334414278512250178829607463, 5996098752287112503955625357947504781285347271188855688828744], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 2, 4, 1], [2, 4, 1, 1], [2, 4, 2, 1], [2, 4, 4, 2], [2, 8, 1, 1], [2, 8, 2, 1], [2, 8, 4, 2], [4, 2, 2, 1], [4, 4, 1, 1], [4, 4, 2, 3], [4, 8, 1, 2], [4, 8, 2, 4], [4, 8, 4, 2], [4, 16, 8, 1], [8, 16, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^5.D_4^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '32.51', 'autcent_hash': 51, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '512.6480905', 'autcentquo_hash': 411620650426100056, 'autcentquo_nilpotent': True, 'autcentquo_order': 512, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^3:D_4^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 5], [2, 4, 11], [2, 8, 11], [4, 2, 2], [4, 4, 7], [4, 8, 18], [4, 16, 8], [8, 16, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '256.53380', 'commutator_count': 1, 'commutator_label': '16.11', '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', '2.1', '2.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 7530076, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 5], [2, 4, 1, 11], [2, 8, 1, 11], [4, 2, 1, 2], [4, 4, 1, 7], [4, 8, 1, 18], [4, 16, 1, 8], [8, 16, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': 639959040, 'exponent': 8, 'exponents_of_order': [9], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[8, 1, 4]], 'familial': False, 'frattini_label': '16.11', 'frattini_quotient': '32.51', 'hash': 7530076, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 1], 'inner_gens': [[11212821043200, 1313941697263, 4103693803567, 5612462133817, 2789792421136, 5606234750016, 2789832700823, 1313941668480, 1313941673647], [16819055793216, 6920176400047, 1313941685176, 5612462133817, 2789792421136, 5606234750016, 4103693809943, 5167, 1313941673647], [14002653744023, 6920176400047, 1313941685176, 5612462133817, 2789792421136, 5606234755183, 2789832700823, 5167, 1313941673647], [11212821043200, 6920176400047, 1313941685176, 5612462133817, 4103734094783, 5606234750016, 2789832700823, 5167, 1313941673647], [11212821043200, 6920176400047, 1313941685176, 6913949039862, 2789792421136, 5606234750016, 2789832700823, 5167, 1313941673647], [11212821043200, 6920176400047, 1313941680023, 5612462133817, 2789792421136, 5606234750016, 4103693815096, 5167, 1313941673647], [11212821043200, 5606234731567, 1313941685176, 5612462133817, 2789792421136, 6920176423663, 2789832700823, 5167, 1313941673647], [12526762716847, 6920176400047, 1313941685176, 5612462133817, 2789792421136, 5606234750016, 2789832700823, 5167, 1313941673647], [11212821043200, 6920176400047, 1313941685176, 5612462133817, 2789792421136, 5606234750016, 2789832700823, 5167, 1313941673647]], 'inner_hash': 53380, 'inner_nilpotent': True, 'inner_order': 256, 'inner_split': True, 'inner_tex': 'C_2^5:D_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 32], [2, 24], [4, 8], [8, 4]], 'label': '512.7530076', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'D4^2:C2^3', 'ngens': 9, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [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': 44, 'number_conjugacy_classes': 68, 'number_divisions': 68, 'number_normal_subgroups': 568, 'number_subgroup_autclasses': 1108, 'number_subgroup_classes': 4194, 'number_subgroups': 14530, 'old_label': None, 'order': 512, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 143], [4, 304], [8, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 8402254554953, 0, 0, 5167, 0], 'outer_gens': [[16825283177017, 4103693803567, 1313941697263, 5612462133817, 4103734089616, 2789832700823, 5606234750016, 5167, 1313941673647], [11212821043200, 6920176400047, 1313941685176, 4103734094783, 5612462133817, 5606234750016, 2789832700823, 5167, 1313941673647], [11212821043200, 6920176400047, 11543, 5612462133817, 2789792421136, 5606234750016, 2789832700823, 5167, 1313941673647], [14002613464336, 6920176400047, 1313941685176, 5612462138742, 2789792421136, 5606234750016, 2789832700823, 5167, 1313941673647], [19615075603078, 6920176400047, 1313941685176, 5612462138742, 2789792426303, 5606234750016, 2789832700823, 5167, 1313941673647], [11212821043200, 5606234726400, 11543, 5612462133817, 2789792421136, 5606234750016, 2789832700823, 5167, 1313941673647]], 'outer_group': '64.226', 'outer_hash': 226, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 16, 'outer_perms': [1328391572785, 87179097602, 4396538203938, 2966658509284, 6723108415325, 14199681472674], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 24], [4, 8], [8, 4]], 'representations': {'PC': {'code': '11237655691807102279812964071161329411556008', 'gens': [1, 2, 3, 4, 6, 8], 'pres': [9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1838, 444, 102, 2408, 365, 158, 17296, 1474, 1771, 214, 12977, 3275]}, 'Perm': {'d': 16, 'gens': [11212821043200, 6920176400047, 1313941685176, 5612462133817, 2789792421136, 5606234750016, 2789832700823, 5167, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 5, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_4^2:C_2^3', 'transitive_degree': 16, '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}
