-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1568.459', 'ambient_counter': 459, 'ambient_order': 1568, 'ambient_tex': 'D_{28}.D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 784, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1568.459.2.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': '784.136', 'subgroup_hash': 136, 'subgroup_order': 784, 'subgroup_tex': 'C_{28}.D_{14}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '1568.459', 'aut_centralizer_order': 14, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 14, 'centralizer': '56.a1.a1', 'complements': ['784.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.c1.b1', '4.g1.a1', '4.i1.a1', '14.b1.a1', '14.d1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5722, 787, 4556, 701, 7627, 1900, 5135, 1239], 'generators': [1, 16, 28, 224, 784, 56], 'label': '1568.459.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.b1', '4.c1.a1', '14.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '784.131', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '56.7'}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '56.13', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [12, 3, 2, 84, 12, 12], 'aut_gens': [[1, 14, 28], [403, 182, 763], [11, 126, 252], [13, 161, 756], [401, 154, 427], [397, 70, 259], [13, 273, 147]], 'aut_group': None, 'aut_hash': 6223294693065232497, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 16128, 'aut_permdeg': 62, 'aut_perms': [11204156475005236874714036183339668107813058968918466625610615015774072550227388409502, 6136707513670685354054050478783636502512631097349476948452033237801959329897169926711, 17043806162174525034949936347436566232552971819204807760035368602201248140861875321943, 24353486348287043239099199407895425655098980113591244978565328680777665466356102025700, 27680327416060526362853259274909130207867087707895347533451142182840619278558436120901, 17576343474083293833697080688692139336298919065795629602677882897593108497269739434802], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [4, 2, 2, 1], [4, 14, 4, 1], [7, 1, 6, 1], [7, 2, 3, 1], [7, 2, 18, 1], [14, 1, 6, 1], [14, 1, 12, 1], [14, 2, 3, 1], [14, 2, 6, 1], [14, 2, 18, 1], [14, 2, 36, 1], [28, 2, 12, 2], [28, 2, 72, 1], [28, 14, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{14}.(C_6^2\\times D_4).C_2^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '192.1410', 'autcent_hash': 1410, 'autcent_nilpotent': True, 'autcent_order': 192, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5:C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '84.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 84, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [4, 2, 2], [4, 14, 4], [7, 1, 6], [7, 2, 21], [14, 1, 18], [14, 2, 63], [28, 2, 96], [28, 14, 24]], 'center_label': '28.4', 'center_order': 28, 'central_product': True, 'central_quotient': '28.3', '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', '7.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 136, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['56.3', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 2, 1, 2], [4, 14, 1, 4], [7, 1, 6, 1], [7, 2, 3, 1], [7, 2, 6, 3], [14, 1, 6, 3], [14, 2, 3, 3], [14, 2, 6, 9], [28, 2, 6, 4], [28, 2, 12, 6], [28, 14, 6, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 9576, 'exponent': 28, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '392.42', 'hash': 136, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [1, 2, 14], 'inner_gens': [[1, 14, 28], [1, 14, 756], [1, 70, 28]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 28, 'inner_split': False, 'inner_tex': 'D_{14}', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 56], [2, 182]], 'label': '784.136', 'linC_count': 2304, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 60, 'linQ_dim': 16, 'linQ_dim_count': 60, 'linR_count': 144, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C28.D14', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 18, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 238, 'number_divisions': 44, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 46, 'number_subgroup_classes': 100, 'number_subgroups': 256, 'old_label': None, 'order': 784, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 3], [4, 60], [7, 48], [14, 144], [28, 528]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 6, 12], 'outer_gen_pows': [0, 0, 196, 0, 0], 'outer_gens': [[13, 14, 28], [393, 14, 28], [1, 210, 28], [11, 14, 420], [9, 210, 91]], 'outer_group': '576.8204', 'outer_hash': 8204, 'outer_nilpotent': True, 'outer_order': 576, 'outer_permdeg': 16, 'outer_perms': [4103646624000, 2789745235200, 4103606747520, 4103606707344, 4016429146803], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4:C_6^2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 7], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [6, 12], [12, 16], [24, 6]], 'representations': {'PC': {'code': 56890514146085047905978465941, 'gens': [1, 3, 4], 'pres': [6, -2, -7, -2, -2, -2, -7, 12, 518, 1311, 69, 1576, 88, 1745]}, 'GLZN': {'d': 2, 'p': 58, 'gens': [5841209, 4487599, 195135, 5795737, 196795, 11121441]}, 'Perm': {'d': 24, 'gens': [1126440054589218969600, 45787363776001, 68361751180800, 46230, 45787363776000, 28104890400830251008000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 14], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{28}.D_{14}', 'transitive_degree': 112, 'wreath_data': None, 'wreath_product': False}
-
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': 84, 'aut_gen_orders': [6, 42, 28, 6, 6, 12, 6], 'aut_gens': [[1, 2, 4, 112], [41, 2, 36, 616], [25, 254, 44, 168], [841, 1150, 4, 112], [789, 954, 52, 1288], [73, 254, 12, 1512], [85, 478, 68, 336], [5, 1122, 92, 616]], 'aut_group': None, 'aut_hash': 5396240729116554762, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 112896, 'aut_permdeg': 84, 'aut_perms': [1391885834060170478139511707931760289889661691725542566613764507711995822243602641458815499759753161168852253210627042814303360, 1934091641320306198514777633755279605526625298285130088060427213745898625530373824160995611708315191310533091458811014390021340, 247019331894784301554366469752196232192374587444208801580676309093282223535815832465087655938661411516714372376857709030943110, 2763828141181224689659558104531244966788997622727760784622175374065736331341467242619043160027716823029032609696780856599168448, 947471486092297008984124215075912181479077126770172500570202022704268249956605664667110497248516105859200404211366094493262899, 1739902459521220292016952736275514103686501344550913382513432625220194502666189769036637351537649444434150794419939367274053471, 744210791874159161242590801534402285032265468780207517661896964873266740483578064622617199627154236133014018794051666865710457], 'aut_phi_ratio': 168.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 28, 1, 1], [4, 2, 1, 2], [4, 28, 1, 1], [4, 28, 2, 1], [7, 2, 3, 2], [7, 4, 9, 1], [8, 196, 2, 1], [14, 2, 3, 2], [14, 2, 6, 1], [14, 4, 3, 1], [14, 4, 9, 1], [14, 4, 18, 1], [14, 28, 6, 1], [28, 2, 6, 1], [28, 4, 3, 3], [28, 4, 18, 2], [28, 28, 6, 1], [28, 28, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_7^2.C_6^2.C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': None, 'autcentquo_hash': 2402488623396407456, 'autcentquo_nilpotent': False, 'autcentquo_order': 14112, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_7^2.C_6^2.C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 28, 1], [4, 2, 2], [4, 28, 3], [7, 2, 6], [7, 4, 9], [8, 196, 2], [14, 2, 12], [14, 4, 30], [14, 28, 6], [28, 2, 6], [28, 4, 45], [28, 28, 18]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '784.131', 'commutator_count': 1, 'commutator_label': '196.7', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '7.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 459, '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, 28, 1, 1], [4, 2, 1, 2], [4, 28, 1, 3], [7, 2, 3, 2], [7, 4, 3, 3], [8, 196, 1, 2], [14, 2, 3, 2], [14, 2, 6, 1], [14, 4, 3, 4], [14, 4, 6, 3], [14, 28, 6, 1], [28, 2, 6, 1], [28, 4, 3, 3], [28, 4, 6, 6], [28, 28, 6, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 10752, 'exponent': 56, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [[4, 0, 36]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '392.41', 'hash': 459, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 28, 'inner_gen_orders': [2, 2, 14, 14], 'inner_gens': [[1, 30, 108, 112], [85, 2, 60, 1512], [9, 58, 4, 112], [1, 282, 4, 112]], 'inner_hash': 131, 'inner_nilpotent': False, 'inner_order': 784, 'inner_split': True, 'inner_tex': 'D_{14}:D_{14}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 50], [4, 85]], 'label': '1568.459', 'linC_count': 36, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 28, 'linQ_dim': 20, 'linQ_dim_count': 22, 'linR_count': 18, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D28.D14', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 143, 'number_divisions': 40, 'number_normal_subgroups': 44, 'number_subgroup_autclasses': 109, 'number_subgroup_classes': 150, 'number_subgroups': 1134, 'old_label': None, 'order': 1568, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 31], [4, 88], [7, 48], [8, 392], [14, 312], [28, 696]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6, 6], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[57, 58, 52, 1456], [29, 2, 108, 1456], [1, 2, 4, 1064], [785, 2, 44, 1232]], 'outer_group': '144.197', 'outer_hash': 197, 'outer_nilpotent': True, 'outer_order': 144, 'outer_permdeg': 14, 'outer_perms': [362880, 5040, 6227388864, 39916803], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6^2', '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, 2], [4, 1], [6, 8], [12, 16], [24, 2], [48, 3]], 'representations': {'PC': {'code': 17191640609193022219189311068770927761797470265, 'gens': [1, 2, 3, 6], 'pres': [7, 2, 2, 2, 2, 7, 2, 7, 392, 421, 2270, 639, 58, 2915, 80, 3364, 31764, 124, 32941]}, 'Perm': {'d': 30, 'gens': [8875250776078774264755030913002, 8864346369515082901490005042610, 4497833883397, 5809939015885, 7212929033498, 18641806647569066593293742080000, 27441626230439300629480034304000]}}, 'schur_multiplier': [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_{28}.D_{14}', 'transitive_degree': 112, '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}
