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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2165', 'ambient_counter': 2165, 'ambient_order': 1344, 'ambient_tex': '(C_3\\times D_{14}):Q_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 336, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2165.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.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': '336.79', 'subgroup_hash': 79, 'subgroup_order': 336, 'subgroup_tex': 'C_6:C_{56}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.2165', 'aut_centralizer_order': 224, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.1043', 'aut_weyl_index': 224, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.o1.a1', '12.h1.a1', '28.c1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7329, 4794, 2401, 4662, 8844, 7707, 7848, 7038], 'generators': [30, 448, 16, 392, 336, 672], 'label': '1344.2165.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '28.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '336.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '112.22', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 6, 12], 'aut_gens': [[1, 8], [1, 12], [3, 8], [1, 104], [1, 188], [285, 12]], 'aut_group': '576.8609', 'aut_hash': 8609, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 576, 'aut_permdeg': 30, 'aut_perms': [156300105817084637646720, 206059428920218920081815554659722, 47179930664085823330681113, 239044856576796031712299656609907, 214233335393502171072736350493970], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 2, 1, 1], [4, 1, 2, 2], [6, 2, 1, 1], [6, 2, 2, 1], [7, 1, 6, 1], [8, 3, 8, 1], [12, 2, 2, 2], [14, 1, 6, 1], [14, 1, 12, 1], [21, 2, 6, 1], [28, 1, 12, 2], [42, 2, 6, 1], [42, 2, 12, 1], [56, 3, 48, 1], [84, 2, 12, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_6^2:C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '96.221', 'autcent_hash': 221, 'autcent_nilpotent': True, 'autcent_order': 96, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_{12}:C_2^3', '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, 3], [3, 2, 1], [4, 1, 4], [6, 2, 3], [7, 1, 6], [8, 3, 8], [12, 2, 4], [14, 1, 18], [21, 2, 6], [28, 1, 24], [42, 2, 18], [56, 3, 48], [84, 2, 24]], 'center_label': '56.8', 'center_order': 56, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', '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': 79, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['24.1', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 1, 2, 2], [6, 2, 1, 3], [7, 1, 6, 1], [8, 3, 4, 2], [12, 2, 2, 2], [14, 1, 6, 3], [21, 2, 6, 1], [28, 1, 12, 2], [42, 2, 6, 3], [56, 3, 24, 2], [84, 2, 12, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 168, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '84.13', 'hash': 79, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 232], [113, 8]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 112], [2, 56]], 'label': '336.79', 'linC_count': 2304, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 4, 'linQ_dim': 10, 'linQ_dim_count': 4, 'linR_count': 24, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C6:C56', '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': 22, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 168, 'number_divisions': 28, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 44, 'number_subgroups': 56, 'old_label': None, 'order': 336, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 4], [6, 6], [7, 6], [8, 24], [12, 8], [14, 18], [21, 12], [28, 24], [42, 36], [56, 144], [84, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 12], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[3, 8], [5, 104], [169, 8], [169, 204]], 'outer_group': '96.221', 'outer_hash': 221, 'outer_nilpotent': True, 'outer_order': 96, 'outer_permdeg': 11, 'outer_perms': [1680, 744, 7983360, 8025364], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{12}:C_2^3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 8, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 4], [6, 4], [12, 6], [24, 4]], 'representations': {'PC': {'code': 1896811477055165373389003, 'gens': [1, 4], 'pres': [6, -2, -2, -2, -2, -3, -7, 12, 31, 5571, 69, 3844, 118]}, 'GLZN': {'d': 2, 'p': 35, 'gens': [377791, 43051, 343008, 1243404, 257256, 661270]}, 'Perm': {'d': 20, 'gens': [128802095633836801, 1, 46230, 263274254866022400, 391971468784896000, 43545600]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 56], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6:C_{56}', 'transitive_degree': 336, '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': '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, 4, 6, 2, 6, 6, 6, 12, 6, 6], 'aut_gens': [[1, 2, 4, 112], [769, 898, 4, 560], [49, 394, 444, 560], [73, 674, 1084, 1232], [1, 674, 60, 560], [753, 730, 76, 112], [761, 1122, 92, 112], [65, 506, 1116, 784], [745, 842, 1044, 560], [73, 226, 108, 112], [57, 2, 692, 112]], 'aut_group': None, 'aut_hash': 5255589997166976132, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 64512, 'aut_permdeg': 60, 'aut_perms': [3481345598680320743205567088267747195390132581035671849442241936273537736471362481, 983193935591746716395516966089427984723906875293937510897441048183764412485773495, 4642441846498161948341309726450030698044964925155750836104896257854842732002379682, 2350549340482266388867840700949018630947784882504026391714297210954475504702055, 3088224361369779878478063814617735392240818516773882112722606142433993210198018541, 5756442930539542752068858202038953913839349129175241356987041901812168361140475574, 1543824512205155113013652228402508954980762401020459820350050560242801583567696884, 5369505639443773423823728487729812822403478811361328285103406967861742251625449355, 4649369780277017300659646481884202692804317386049742507137781887266979664975400930, 4221690659734860627552080825677064539176224270763857825453723798441851117868505624], 'aut_phi_ratio': 168.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 14, 2, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 8, 1, 1], [4, 12, 2, 1], [4, 28, 1, 1], [4, 56, 1, 1], [4, 84, 2, 1], [6, 2, 1, 3], [6, 28, 2, 1], [7, 2, 3, 1], [8, 12, 2, 1], [8, 84, 2, 1], [12, 4, 1, 2], [12, 8, 2, 1], [12, 28, 2, 1], [12, 56, 2, 1], [14, 2, 3, 3], [21, 4, 3, 1], [28, 4, 3, 2], [28, 8, 6, 1], [28, 24, 6, 1], [42, 4, 3, 3], [56, 12, 12, 1], [84, 8, 3, 2], [84, 8, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '1008.906', 'autcentquo_hash': 906, 'autcentquo_nilpotent': False, 'autcentquo_order': 1008, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 14, 2], [3, 2, 1], [4, 2, 2], [4, 8, 1], [4, 12, 2], [4, 28, 1], [4, 56, 1], [4, 84, 2], [6, 2, 3], [6, 28, 2], [7, 2, 3], [8, 12, 2], [8, 84, 2], [12, 4, 2], [12, 8, 2], [12, 28, 2], [12, 56, 2], [14, 2, 9], [21, 4, 3], [28, 4, 6], [28, 8, 6], [28, 24, 6], [42, 4, 9], [56, 12, 12], [84, 8, 18]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '336.161', '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': 2165, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 14, 1, 2], [3, 2, 1, 1], [4, 2, 1, 2], [4, 8, 1, 1], [4, 12, 1, 2], [4, 28, 1, 1], [4, 56, 1, 1], [4, 84, 1, 2], [6, 2, 1, 3], [6, 28, 1, 2], [7, 2, 3, 1], [8, 12, 2, 1], [8, 84, 2, 1], [12, 4, 1, 2], [12, 8, 2, 1], [12, 28, 2, 1], [12, 56, 2, 1], [14, 2, 3, 3], [21, 4, 3, 1], [28, 4, 3, 2], [28, 8, 6, 1], [28, 24, 3, 2], [42, 4, 3, 3], [56, 12, 12, 1], [84, 8, 3, 2], [84, 8, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 10752, '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': '8.2', 'frattini_quotient': '168.50', 'hash': 2165, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 14, 6], 'inner_gens': [[1, 2, 780, 112], [1, 2, 340, 1232], [681, 1010, 4, 784], [1, 226, 676, 112]], 'inner_hash': 161, 'inner_nilpotent': False, 'inner_order': 336, 'inner_split': True, 'inner_tex': 'D_6:D_{14}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 42], [4, 49], [8, 6]], 'label': '1344.2165', 'linC_count': 480, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 32, 'linQ_dim': 16, 'linQ_dim_count': 32, 'linR_count': 216, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C3*D14):Q16', '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': 40, 'number_characteristic_subgroups': 60, 'number_conjugacy_classes': 105, 'number_divisions': 45, 'number_normal_subgroups': 70, 'number_subgroup_autclasses': 232, 'number_subgroup_classes': 296, 'number_subgroups': 2532, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 31], [3, 2], [4, 288], [6, 62], [7, 6], [8, 192], [12, 192], [14, 18], [21, 12], [28, 216], [42, 36], [56, 144], [84, 144]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 4, 560], [673, 2, 4, 112], [1, 674, 4, 112], [729, 2, 4, 112], [1, 730, 4, 112], [1, 2, 20, 112]], 'outer_group': '192.1543', 'outer_hash': 1543, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 15, 'outer_perms': [720, 87178291200, 479001600, 3628800, 40320, 27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 9], [6, 4], [8, 1], [12, 6], [24, 7]], 'representations': {'PC': {'code': 8020324943753808311688609599756703628070262008569279033, 'gens': [1, 2, 3, 6], 'pres': [8, -2, -2, -2, -2, -7, -2, -2, -3, 5385, 18722, 4090, 66, 3331, 91, 3844, 29581, 9429, 141, 31374, 166, 28687]}, 'Perm': {'d': 30, 'gens': [305292256625856985728122880000, 7605914577989905, 1177538874631854665880, 21136758688690584, 2350183339898634240000, 27924137878061520, 3, 9452345886333784620057231360000]}}, 'schur_multiplier': [2, 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': '(C_3\\times D_{14}):Q_{16}', 'transitive_degree': 672, '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}
