-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.7275', 'ambient_counter': 7275, 'ambient_order': 1344, 'ambient_tex': '(C_4\\times C_{12}):D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.7275.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '672.618', 'subgroup_hash': 618, 'subgroup_order': 672, 'subgroup_tex': 'D_6:D_{28}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '1344.7275', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1', '4.h1.a1', '4.l1.a1', '4.n1.a1', '4.u1.a1', '6.b1.a1', '14.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 448, 336, 8, 2, 192, 672], 'label': '1344.7275.2.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.e1.a1', '4.h1.a1', '4.l1.a1', '4.n1.a1', '4.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
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': 42, 'aut_gen_orders': [6, 6, 14, 6, 6, 6, 6, 6, 6], 'aut_gens': [[1, 2, 4, 8], [193, 230, 4, 140], [5, 230, 4, 188], [49, 562, 4, 236], [481, 454, 4, 492], [53, 226, 4, 140], [97, 338, 4, 376], [101, 454, 4, 296], [293, 2, 4, 380], [293, 114, 4, 424]], 'aut_group': None, 'aut_hash': 6441793362254340223, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 16128, 'aut_permdeg': 44, 'aut_perms': [60783079811553384806627579338456935816877052721722865, 60783059411330235134485962755766911690893919538279231, 727829478267204612023151655513487386545128225012100181, 118419356647870992605865956731218197341724381095821855, 240423864235401180701157773296178262102724441045831401, 1701304772742060474852916143709644339293477197570935142, 118419091462670006990535249137215472456675650439886969, 2539383123234995847356505533139817910275415275500512264, 325949507434847946953045452864660909642935107282897687], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 2, 1], [2, 14, 2, 1], [2, 28, 1, 1], [2, 42, 2, 1], [3, 2, 1, 1], [4, 4, 1, 1], [4, 12, 1, 1], [4, 84, 1, 1], [6, 2, 1, 3], [6, 28, 2, 2], [7, 2, 3, 1], [12, 4, 2, 1], [14, 2, 3, 3], [14, 12, 6, 1], [21, 4, 3, 1], [28, 4, 6, 1], [28, 12, 6, 1], [42, 4, 3, 3], [84, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6\\times S_3\\times F_7', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '252.26', 'autcentquo_hash': 26, 'autcentquo_nilpotent': False, 'autcentquo_order': 252, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 2], [2, 14, 2], [2, 28, 1], [2, 42, 2], [3, 2, 1], [4, 4, 1], [4, 12, 1], [4, 84, 1], [6, 2, 3], [6, 28, 4], [7, 2, 3], [12, 4, 2], [14, 2, 9], [14, 12, 6], [21, 4, 3], [28, 4, 6], [28, 12, 6], [42, 4, 9], [84, 4, 12]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '168.50', 'commutator_count': 1, 'commutator_label': '84.15', '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': 618, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 2], [2, 14, 1, 2], [2, 28, 1, 1], [2, 42, 1, 2], [3, 2, 1, 1], [4, 4, 1, 1], [4, 12, 1, 1], [4, 84, 1, 1], [6, 2, 1, 3], [6, 28, 1, 2], [6, 28, 2, 1], [7, 2, 3, 1], [12, 4, 2, 1], [14, 2, 3, 3], [14, 12, 3, 2], [21, 4, 3, 1], [28, 4, 6, 1], [28, 12, 6, 1], [42, 4, 3, 3], [84, 4, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 5376, 'exponent': 84, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '168.50', 'hash': 618, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [2, 2, 1, 42], 'inner_gens': [[1, 2, 4, 440], [1, 2, 4, 236], [1, 2, 4, 8], [241, 454, 4, 8]], 'inner_hash': 50, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': True, 'inner_tex': 'S_3\\times D_{14}', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 38], [4, 32]], 'label': '672.618', 'linC_count': 48, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 256, 'linQ_dim': 12, 'linQ_dim_count': 256, 'linR_count': 252, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D6:D28', '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': 30, 'number_characteristic_subgroups': 44, 'number_conjugacy_classes': 78, 'number_divisions': 35, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 184, 'number_subgroup_classes': 260, 'number_subgroups': 2376, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 155], [3, 2], [4, 100], [6, 118], [7, 6], [12, 8], [14, 90], [21, 12], [28, 96], [42, 36], [84, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 4, 232], [5, 2, 4, 8], [337, 2, 4, 8], [1, 338, 4, 8], [1, 2, 4, 488]], 'outer_group': '96.231', 'outer_hash': 231, 'outer_nilpotent': True, 'outer_order': 96, 'outer_permdeg': 13, 'outer_perms': [720, 479001600, 3628800, 40320, 27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_6', 'pc_rank': 4, '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, 10], [4, 4], [6, 4], [12, 6], [24, 3]], 'representations': {'PC': {'code': 9478402235132424014463575342871288591371, 'gens': [1, 2, 3, 4], 'pres': [7, -2, -2, -2, 2, -2, -3, -7, 12323, 3314, 80, 7284, 8131, 102, 17477, 5388, 166, 28230]}, 'GLZN': {'d': 2, 'p': 84, 'gens': [17188445, 1042546, 36897650, 41391699, 24300865, 16498173, 593713]}, 'Perm': {'d': 18, 'gens': [21010447947624, 1681, 4032024, 7983360, 744, 3, 397707843456000]}}, 'schur_multiplier': [2, 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': 'D_6:D_{28}', 'transitive_degree': 168, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[1, 2, 4, 16], [449, 2, 4, 208], [1, 2, 4, 656], [9, 2, 4, 656], [673, 2, 4, 656], [1, 10, 4, 656], [1, 674, 4, 656], [1, 2, 12, 656], [1, 2, 676, 656], [1, 2, 4, 664], [1, 2, 4, 1328], [1, 2, 4, 1168], [1, 194, 4, 16]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 64512, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 2, 1], [2, 14, 2, 1], [2, 28, 1, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 2, 2], [4, 4, 1, 1], [4, 6, 2, 1], [4, 12, 1, 2], [4, 14, 2, 1], [4, 28, 1, 1], [4, 84, 1, 3], [6, 2, 1, 3], [6, 28, 2, 2], [7, 2, 3, 1], [12, 2, 4, 1], [12, 4, 2, 2], [12, 28, 2, 2], [14, 2, 3, 3], [14, 12, 6, 1], [21, 4, 3, 1], [28, 2, 12, 1], [28, 4, 6, 2], [28, 12, 6, 3], [42, 4, 3, 3], [84, 4, 12, 3]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 2], [2, 14, 2], [2, 28, 1], [2, 84, 1], [3, 2, 1], [4, 2, 4], [4, 4, 1], [4, 6, 2], [4, 12, 2], [4, 14, 2], [4, 28, 1], [4, 84, 3], [6, 2, 3], [6, 28, 4], [7, 2, 3], [12, 2, 4], [12, 4, 4], [12, 28, 4], [14, 2, 9], [14, 12, 6], [21, 4, 3], [28, 2, 12], [28, 4, 12], [28, 12, 18], [42, 4, 9], [84, 4, 36]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '336.219', 'commutator_count': 1, 'commutator_label': '84.15', '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': 7275, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 2], [2, 14, 1, 2], [2, 28, 1, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 2, 2], [4, 4, 1, 1], [4, 6, 2, 1], [4, 12, 1, 2], [4, 14, 2, 1], [4, 28, 1, 1], [4, 84, 1, 3], [6, 2, 1, 3], [6, 28, 1, 2], [6, 28, 2, 1], [7, 2, 3, 1], [12, 2, 4, 1], [12, 4, 2, 2], [12, 28, 2, 2], [14, 2, 3, 3], [14, 12, 3, 2], [21, 4, 3, 1], [28, 2, 12, 1], [28, 4, 6, 2], [28, 12, 6, 3], [42, 4, 3, 3], [84, 4, 12, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 14938560, 'exponent': 84, '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': '4.2', 'frattini_quotient': '336.219', 'hash': 7275, 'hyperelementary': 2, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 336, 'inner_split': None, 'inner_tex': 'D_6\\times D_{14}', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 72], [4, 65]], 'label': '1344.7275', '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': '(C4*C12):D14', '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': 48, 'number_characteristic_subgroups': 120, 'number_conjugacy_classes': 153, 'number_divisions': 52, 'number_normal_subgroups': 128, 'number_subgroup_autclasses': 444, 'number_subgroup_classes': 496, 'number_subgroups': 4388, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 155], [3, 2], [4, 356], [6, 118], [7, 6], [12, 136], [14, 90], [21, 12], [28, 288], [42, 36], [84, 144]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '192.1543', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 192, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^5\\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, 8], [4, 5], [6, 8], [8, 4], [12, 4], [24, 4], [48, 3]], 'representations': {'PC': {'code': 7462431205876332509775184325050745651100910951658507, 'gens': [1, 2, 3, 5], 'pres': [8, -2, -2, -2, -2, 2, -2, -3, -7, 8122, 66, 18884, 17612, 116, 44549, 9997, 141, 28678, 23310, 222, 36879]}, 'Perm': {'d': 26, 'gens': [621574835364355253080369, 358654206316541, 4397057132443, 5801296304836, 1327912197889, 2966658145996, 6758061133824000, 16754357281155028254720000]}}, 'schur_multiplier': [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_4\\times C_{12}):D_{14}', 'transitive_degree': 336, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'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}
