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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9834', 'ambient_counter': 9834, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 672, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9834.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, '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': '672.1215', 'subgroup_hash': 1215, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.C_2^3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.9834', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': ['672.d1.a1', '672.d1.b1', '672.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '4.i1.a1', '4.i1.b1', '4.q1.a1', '4.q1.b1', '4.x1.a1', '4.x1.b1', '4.z1.a1', '4.ba1.a1', '6.a1.a1', '14.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 16, 8, 672, 6, 192, 448], 'label': '1344.9834.2.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '4.i1.a1', '4.i1.b1', '4.q1.a1', '4.q1.b1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', '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': '48.52', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 84, 'aut_gen_orders': [6, 12, 2, 6, 2, 6], 'aut_gens': [[1, 2, 4, 16], [348, 10, 12, 657], [349, 494, 4, 312], [341, 98, 12, 208], [9, 298, 12, 80], [9, 14, 12, 665], [1, 198, 12, 184]], 'aut_group': None, 'aut_hash': 2639570833013882725, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 16128, 'aut_permdeg': 36, 'aut_perms': [21898299595417832621596138263151642502355, 97498758074452295674365658086203575723318, 25988775979939096185887008558969085194666, 1247715535307867939411743865666788575939, 371784803809302685409513940618358218347399, 2668088748022536706176133242491507710404], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 3, 1], [2, 14, 2, 1], [3, 1, 2, 1], [4, 2, 1, 1], [4, 2, 3, 1], [4, 14, 6, 1], [6, 1, 2, 1], [6, 2, 6, 1], [6, 14, 4, 1], [7, 2, 3, 1], [12, 2, 2, 1], [12, 2, 6, 1], [12, 14, 12, 1], [14, 2, 3, 1], [14, 4, 9, 1], [21, 2, 6, 1], [28, 2, 6, 1], [28, 4, 9, 1], [42, 2, 6, 1], [42, 4, 18, 1], [84, 2, 12, 1], [84, 4, 18, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_{14}\\times A_4).C_6.C_2^4', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', '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, 3], [2, 14, 2], [3, 1, 2], [4, 2, 4], [4, 14, 6], [6, 1, 2], [6, 2, 6], [6, 14, 4], [7, 2, 3], [12, 2, 8], [12, 14, 12], [14, 2, 3], [14, 4, 9], [21, 2, 6], [28, 2, 6], [28, 4, 9], [42, 2, 6], [42, 4, 18], [84, 2, 12], [84, 4, 18]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '112.42', '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', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1215, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['224.186', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 14, 1, 2], [3, 1, 2, 1], [4, 2, 1, 4], [4, 14, 1, 6], [6, 1, 2, 1], [6, 2, 2, 3], [6, 14, 2, 2], [7, 2, 3, 1], [12, 2, 2, 4], [12, 14, 2, 6], [14, 2, 3, 1], [14, 4, 3, 3], [21, 2, 6, 1], [28, 2, 6, 1], [28, 4, 3, 3], [42, 2, 6, 1], [42, 4, 6, 3], [84, 2, 12, 1], [84, 4, 6, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3830400, 'exponent': 84, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[4, 0, 12]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '336.225', 'hash': 1215, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [2, 2, 2, 14], 'inner_gens': [[1, 2, 4, 24], [1, 2, 12, 216], [1, 10, 4, 16], [9, 490, 4, 16]], 'inner_hash': 42, 'inner_nilpotent': False, 'inner_order': 112, 'inner_split': True, 'inner_tex': 'C_2^2\\times D_{14}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 8, 'irrep_stats': [[1, 48], [2, 72], [4, 21]], 'label': '672.1215', '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': 'C84.C2^3', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 24, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 141, 'number_divisions': 52, 'number_normal_subgroups': 170, 'number_subgroup_autclasses': 96, 'number_subgroup_classes': 292, 'number_subgroups': 972, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 35], [3, 2], [4, 92], [6, 70], [7, 6], [12, 184], [14, 42], [21, 12], [28, 48], [42, 84], [84, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6, 6], 'outer_gen_pows': [0, 1, 0, 4], 'outer_gens': [[1, 2, 12, 16], [1, 2, 4, 25], [1, 2, 12, 80], [349, 6, 4, 357]], 'outer_group': '144.195', 'outer_hash': 195, 'outer_nilpotent': False, 'outer_order': 144, 'outer_permdeg': 12, 'outer_perms': [40279680, 127370887, 87096960, 127370911], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6^2:C_2^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 1], [6, 8], [8, 1], [12, 8], [24, 1], [48, 1]], 'representations': {'PC': {'code': 7822003376286584312205625916716835723, 'gens': [1, 2, 3, 5], 'pres': [7, -2, -2, -2, -2, 2, -3, -7, 56, 135, 58, 844, 3791, 102, 8748, 166, 14125]}, 'Perm': {'d': 26, 'gens': [621574835364360055995696, 3079509941209, 4491862056263, 5670066675292, 6758061133824000, 7177442311085, 16754357281155028254720000]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 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_{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': 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': [6, 4, 4, 12, 12, 12, 6, 12], 'aut_gens': [[1, 2, 4, 32], [1, 458, 476, 560], [9, 242, 516, 1312], [9, 242, 900, 1328], [9, 474, 1028, 1200], [9, 458, 68, 560], [25, 474, 644, 352], [17, 1122, 268, 160], [25, 1122, 260, 432]], 'aut_group': None, 'aut_hash': 9161810123478319507, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 56, 'aut_perms': [89810872213606762117365272867348572512157497834381399459355532142405605718, 372254684319407971836790018876340646582214019761936564649069116184909427403, 323546515334243260976775213733672479115712761479533025035221376031536097695, 673281220056274444325228798697418385483598201836680998549407257275865248928, 116016215965649334438800311819861836910309507331874828948055606111881244293, 675825101311722674341103579674463029738171735147586108786355634144159252235, 373780661166987304513180025551648524986108247801935218751018924635170526508, 310627653538743378348213779985157173839753234600474227557884817586972338308], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 12, 2, 1], [2, 14, 2, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 14, 2, 1], [4, 28, 2, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 4, 2, 1], [6, 28, 2, 1], [7, 2, 3, 1], [8, 12, 2, 1], [8, 42, 2, 1], [8, 84, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 28, 2, 1], [12, 28, 4, 1], [14, 2, 3, 1], [14, 4, 3, 1], [14, 8, 3, 1], [14, 24, 6, 1], [21, 4, 3, 1], [28, 4, 3, 2], [28, 8, 3, 1], [42, 4, 3, 1], [42, 8, 3, 1], [42, 8, 6, 1], [56, 24, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [84, 8, 6, 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': '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': 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, 1], [2, 2, 1], [2, 4, 1], [2, 12, 2], [2, 14, 2], [2, 84, 1], [3, 2, 1], [4, 2, 2], [4, 4, 1], [4, 14, 2], [4, 28, 2], [4, 84, 1], [6, 2, 1], [6, 4, 3], [6, 28, 2], [7, 2, 3], [8, 12, 2], [8, 42, 2], [8, 84, 1], [12, 4, 4], [12, 28, 6], [14, 2, 3], [14, 4, 3], [14, 8, 3], [14, 24, 6], [21, 4, 3], [28, 4, 6], [28, 8, 3], [42, 4, 3], [42, 8, 9], [56, 24, 6], [84, 4, 6], [84, 8, 9]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '672.1175', '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': 9834, '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, 4, 1, 1], [2, 12, 1, 2], [2, 14, 1, 2], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 14, 1, 2], [4, 28, 1, 2], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 4, 2, 1], [6, 28, 1, 2], [7, 2, 3, 1], [8, 12, 1, 2], [8, 42, 2, 1], [8, 84, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 28, 1, 2], [12, 28, 2, 2], [14, 2, 3, 1], [14, 4, 3, 1], [14, 8, 3, 1], [14, 24, 3, 2], [21, 4, 3, 1], [28, 4, 3, 2], [28, 8, 3, 1], [42, 4, 3, 1], [42, 8, 3, 1], [42, 8, 6, 1], [56, 24, 3, 2], [84, 4, 6, 1], [84, 8, 3, 1], [84, 8, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 29877120, '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': '4.1', 'frattini_quotient': '336.219', 'hash': 9834, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 4, 42], 'inner_gens': [[1, 10, 12, 48], [25, 2, 12, 928], [25, 26, 4, 1312], [17, 450, 68, 32]], 'inner_hash': 1175, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': 'D_{42}:C_2^3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 44], [4, 32], [8, 10]], 'label': '1344.9834', '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': 'C84.C2^4', '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': 42, 'number_characteristic_subgroups': 68, 'number_conjugacy_classes': 102, 'number_divisions': 52, 'number_normal_subgroups': 136, 'number_subgroup_autclasses': 364, 'number_subgroup_classes': 516, 'number_subgroups': 4196, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 143], [3, 2], [4, 176], [6, 70], [7, 6], [8, 192], [12, 184], [14, 186], [21, 12], [28, 48], [42, 84], [56, 144], [84, 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, 0, 8], 'outer_gens': [[1, 2, 4, 928], [1, 2, 20, 32], [1, 2, 4, 48], [9, 674, 4, 624]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [40320, 3628800, 24, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 26, '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, 4], [6, 8], [8, 2], [12, 6], [24, 3], [48, 1]], 'representations': {'PC': {'code': 24381430790660818386564592430868461474929566034941825689221139723, 'gens': [1, 2, 3, 6], 'pres': [8, -2, -2, -2, -2, -2, 2, -3, -7, 128, 161, 290, 154, 66, 771, 395, 91, 2309, 22285, 15765, 141, 14350, 17942, 222, 18455]}, 'Perm': {'d': 26, 'gens': [621574835364347280437578, 358566246951916, 3055293852620, 4492032974581, 5446858053712, 7203427058947, 6758061133824000, 16754357281155028254720000]}}, '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': 'C_{84}.C_2^4', 'transitive_degree': 336, '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}
