Formats: - HTML - YAML - JSON - 2026-07-22T01:14:58.021371
  • gps_subgroup_search • Show schema
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.dk', 'ambient_counter': 89, 'ambient_order': 3888, 'ambient_tex': 'C_3^3:S_3^2:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1944, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.dk.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, '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': '1944.3900', 'subgroup_hash': 3900, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • gps_subgroup_data • Show schema
    {'ambient': '3888.dk', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '31104.mn', 'aut_weyl_index': 2, 'centralizer': '3888.a1', 'complements': ['1944.b1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '6.c1', '6.d1', '18.c1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9454, 5855, 1360, 5020], 'generators': [627, 23, 100111334478, 12936672635, 101069337600, 373661250631, 80640, 56], 'label': '3888.dk.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '3888.dk', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '3888.dk'}
  • gps_groups • Show schema
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [24, 24, 6, 6, 12, 12], 'aut_gens': [[482630400, 88698763573, 23, 311, 78, 45360, 193999276800, 280259481600], [25909632000, 361726047135, 713, 627, 697, 80640, 193999276800, 200222668800], [287404588800, 456053109582, 94, 285, 311, 45360, 193999276800, 280259481600], [287404588800, 88216168804, 314, 311, 627, 45360, 200222668800, 286482873600], [180587232000, 456053154841, 288, 697, 56, 45360, 193999276800, 280259481600], [268244524800, 448908047431, 288, 78, 697, 45360, 200222668800, 193999276800], [281173939200, 368871189664, 67, 697, 56, 45360, 280259481600, 286482873600]], 'aut_group': None, 'aut_hash': 4525354900239470050, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 62208, 'aut_permdeg': 324, 'aut_perms': 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219185478706271715143973518606331731557115041285667405145683475152306239017864763991254499043545017607029384335893909222789801331162449565987380081280289848119049267926698760307355777561371869245457160587135805475561521364224097720739858078507080798043699678941596153063434631244434313358054182223622625393605891765067812281466767431990134027623277691607687652017434178878066245650333623036495747712574267884607619656896256400302582074145625919733624621391038977125075194025187463769578915458404060246194259933185380084430193066501501814591009219589773951678263320589154292103049192616834709928010706974432606827374945567241289439605105613756449321670804288825030613295818575], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 4, 2, 3], [3, 4, 4, 1], [3, 8, 4, 2], [3, 8, 8, 2], [4, 81, 4, 1], [6, 18, 1, 2], [6, 18, 2, 1], [6, 36, 1, 1], [6, 36, 2, 3], [6, 36, 4, 1], [6, 162, 1, 1], [12, 162, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^5.C_2^2.C_2.C_2^5', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 4525354900239470050, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^5.C_4.C_2^5.C_2', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 81, 1], [3, 2, 3], [3, 4, 11], [3, 8, 24], [4, 81, 4], [6, 18, 4], [6, 36, 11], [6, 162, 1], [12, 162, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1944.3900', 'commutator_count': 1, 'commutator_label': '243.67', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3900, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 1], [3, 2, 1, 3], [3, 4, 1, 5], [3, 4, 2, 3], [3, 8, 1, 8], [3, 8, 2, 8], [4, 81, 2, 2], [6, 18, 1, 4], [6, 36, 1, 5], [6, 36, 2, 3], [6, 162, 1, 1], [12, 162, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 6, 'exponent': 12, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 0, 8]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1944.3900', 'hash': 3900, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 2, 3, 3, 3, 3, 3], 'inner_gens': [[482630400, 88698763573, 23, 311, 78, 45360, 286482873600, 200222668800], [482630400, 88698763573, 23, 333, 627, 80640, 286482873600, 280259481600], [482630400, 88698763573, 23, 697, 56, 45360, 193999276800, 280259481600], [482630400, 88698763935, 713, 311, 78, 45360, 193999276800, 280259481600], [482630400, 88698763984, 67, 311, 78, 45360, 193999276800, 280259481600], [482630400, 88698844213, 23, 311, 78, 45360, 193999276800, 280259481600], [287404588800, 456053073973, 23, 311, 78, 45360, 193999276800, 280259481600], [199308211200, 88698763573, 23, 311, 78, 45360, 193999276800, 280259481600]], 'inner_hash': 3900, 'inner_nilpotent': False, 'inner_order': 1944, 'inner_split': False, 'inner_tex': 'C_3^4:(C_4\\times S_3)', 'inner_used': [1, 2, 4, 6, 7, 8], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 12], [4, 22], [8, 24]], 'label': '1944.3900', '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': 'C3^4:(C4*S3)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 66, 'number_divisions': 48, 'number_normal_subgroups': 37, 'number_subgroup_autclasses': 272, 'number_subgroup_classes': 812, 'number_subgroups': 11288, 'old_label': None, 'order': 1944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 99], [3, 242], [4, 324], [6, 630], [12, 648]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [482630423, 0, 23, 23], 'outer_gens': [[482630400, 88216133173, 23, 333, 627, 80640, 200222668800, 193999276800], [482630400, 88698763573, 23, 311, 78, 45360, 193999276800, 200222668800], [482630400, 88698763570, 23, 627, 676, 80640, 193999276800, 200222668800], [482630400, 88698763573, 23, 78, 333, 45360, 193999276800, 280259481600]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [16, 7, 143, 11656], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 12], [8, 14], [16, 8]], 'representations': {'PC': {'code': 13201382199767612046543952598601895083243415212343, 'gens': [1, 3, 4, 5, 7, 8], 'pres': [8, 2, 2, 3, 3, 2, 3, 3, 3, 16, 194, 5379, 395, 1924, 3612, 116, 4613, 3469, 710, 110599, 2343]}, 'Perm': {'d': 15, 'gens': [482630400, 88698763573, 23, 311, 78, 45360, 193999276800, 280259481600]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:(C_4\\times S_3)', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [6, 3, 2, 2, 12], 'aut_gens': [[100115008562, 193121112394], [262492957494, 461322126948], [100115008614, 193121112822], [262975587842, 448428965521], [269198979894, 460839496548], [268240977313, 460843125354]], 'aut_group': '62208.l', 'aut_hash': 1820680360968750972, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 62208, 'aut_permdeg': 648, 'aut_perms': 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'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 2, 1], [2, 18, 2, 1], [2, 81, 1, 1], [3, 2, 1, 1], [3, 4, 2, 2], [3, 4, 4, 1], [3, 8, 2, 2], [3, 8, 4, 1], [3, 16, 1, 1], [3, 16, 2, 2], [3, 16, 4, 1], [4, 162, 4, 1], [6, 18, 2, 1], [6, 18, 4, 1], [6, 36, 2, 2], [6, 36, 4, 2], [6, 36, 8, 1], [6, 72, 2, 2], [6, 72, 4, 1], [6, 162, 1, 1], [12, 324, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3^5.D_4', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '62208.l', 'autcentquo_hash': 1820680360968750972, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3^5.D_4', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 18, 2], [2, 81, 1], [3, 2, 1], [3, 4, 8], [3, 8, 8], [3, 16, 9], [4, 162, 4], [6, 18, 6], [6, 36, 20], [6, 72, 8], [6, 162, 1], [12, 324, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '3888.dk', 'commutator_count': 1, 'commutator_label': '486.259', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 89, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 18, 1, 2], [2, 81, 1, 1], [3, 2, 1, 1], [3, 4, 1, 4], [3, 4, 2, 2], [3, 8, 1, 4], [3, 8, 2, 2], [3, 16, 1, 3], [3, 16, 2, 3], [4, 162, 2, 2], [6, 18, 1, 2], [6, 18, 2, 2], [6, 36, 1, 8], [6, 36, 2, 6], [6, 72, 1, 4], [6, 72, 2, 2], [6, 162, 1, 1], [12, 324, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 48, 'exponent': 12, 'exponents_of_order': [5, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 0, 8], [16, 0, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '3888.dk', 'hash': 5387043051655160496, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 12], 'inner_gens': [[100115008562, 361729756237], [13415754873, 193121112394]], 'inner_hash': 5387043051655160496, 'inner_nilpotent': False, 'inner_order': 3888, 'inner_split': True, 'inner_tex': 'C_3^3:S_3^2:C_4', 'inner_used': [1, 2], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 10], [4, 32], [8, 16], [16, 9]], 'label': '3888.dk', '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': None, 'name': 'C3^3:S3^2:C4', 'ngens': 2, '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, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 28, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 75, 'number_divisions': 54, 'number_normal_subgroups': 29, 'number_subgroup_autclasses': 378, 'number_subgroup_classes': 894, 'number_subgroups': 19656, 'old_label': None, 'order': 3888, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 135], [3, 242], [4, 648], [6, 1566], [12, 1296]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 12936672713, 0, 0], 'outer_gens': [[100115043861, 193121112615], [268240977329, 361250674070], [262017549414, 193121112737], [100115043842, 193121112781]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [126, 55, 289, 288], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 14], [8, 18], [16, 7], [32, 3]], 'representations': {'PC': {'code': '21836155762007731365262521521083754232986598708595860964407876720108632757517292242214866487', 'gens': [1, 3, 5, 6, 8, 9], 'pres': [9, 2, 2, 2, 3, 3, 2, 3, 3, 3, 18, 4330, 44930, 35705, 74, 57603, 23484, 38884, 562, 143213, 21398, 22379, 18014, 158, 81654, 9087, 4560, 3463, 916, 23336, 104993, 2969]}, 'Perm': {'d': 15, 'gens': [100115008562, 193121112394]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3:S_3^2:C_4', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
  • gps_groups • Show 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}