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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1584.67', 'ambient_counter': 67, 'ambient_order': 1584, 'ambient_tex': 'D_{792}', 'central': False, 'central_factor': False, 'centralizer_order': 792, 'characteristic': True, 'core_order': 4, 'counter': 59, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1584.67.396.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '396.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '396.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 396, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{198}', 'simple': False, 'solvable': True, 'special_labels': ['U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1584.67', 'aut_centralizer_order': 95040, 'aut_label': '396.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 95040, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '132.a1.a1', '198.a1.a1', '198.b1.a1', '198.b1.b1'], 'contains': ['792.a1.a1'], 'core': '396.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7369, 6993, 2399, 6585, 7054, 7539, 7658, 7539], 'generators': [1188], 'label': '1584.67.396.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '396.a1.a1', 'normal_contained_in': ['36.a1.a1', '132.a1.a1', '198.a1.a1'], 'normal_contains': ['792.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '396.a1.a1', 'projective_image': '792.25', 'quotient_action_image': '2.1', 'quotient_action_kernel': '198.4', 'quotient_action_kernel_order': 198, 'quotient_fusion': None, 'short_label': '396.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [3]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', '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], [4, 1, 2]], 'center_label': '4.1', 'center_order': 4, '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', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 4, 'exponents_of_order': [2], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '2.1', '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 4]], 'label': '4.1', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C4', 'ngens': 1, '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': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 4, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 3, 'number_subgroups': 3, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 1], [4, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[3]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1]], 'representations': {'PC': {'code': 5, 'gens': [1], 'pres': [2, -2, -2, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [46]}, 'Lie': [{'d': 2, 'q': 3, 'gens': [56, 15], 'family': 'CSOPlus'}], 'GLFp': {'d': 2, 'p': 3, 'gens': [21]}, 'Perm': {'d': 4, 'gens': [22, 7]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4', 'transitive_degree': 4, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 3960, 'aut_gen_orders': [18, 120, 180, 30, 30, 18], 'aut_gens': [[1, 2], [1257, 746], [679, 1570], [53, 314], [793, 562], [325, 1270], [731, 878]], 'aut_group': None, 'aut_hash': 2750653646408301733, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 190080, 'aut_permdeg': 792, 'aut_perms': 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'aut_phi_ratio': 396.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 396, 2, 1], [3, 2, 1, 1], [4, 2, 1, 1], [6, 2, 1, 1], [8, 2, 2, 1], [9, 2, 3, 1], [11, 2, 5, 1], [12, 2, 2, 1], [18, 2, 3, 1], [22, 2, 5, 1], [24, 2, 4, 1], [33, 2, 10, 1], [36, 2, 6, 1], [44, 2, 10, 1], [66, 2, 10, 1], [72, 2, 12, 1], [88, 2, 20, 1], [99, 2, 30, 1], [132, 2, 20, 1], [198, 2, 30, 1], [264, 2, 40, 1], [396, 2, 60, 1], [792, 2, 120, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{99}.C_{60}.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1980, 'autcentquo_group': None, 'autcentquo_hash': 7697546556299087385, 'autcentquo_nilpotent': False, 'autcentquo_order': 47520, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{99}.C_{30}.C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 396, 2], [3, 2, 1], [4, 2, 1], [6, 2, 1], [8, 2, 2], [9, 2, 3], [11, 2, 5], [12, 2, 2], [18, 2, 3], [22, 2, 5], [24, 2, 4], [33, 2, 10], [36, 2, 6], [44, 2, 10], [66, 2, 10], [72, 2, 12], [88, 2, 20], [99, 2, 30], [132, 2, 20], [198, 2, 30], [264, 2, 40], [396, 2, 60], [792, 2, 120]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '792.25', 'commutator_count': 1, 'commutator_label': '396.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 67, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 396, 1, 2], [3, 2, 1, 1], [4, 2, 1, 1], [6, 2, 1, 1], [8, 2, 2, 1], [9, 2, 3, 1], [11, 2, 5, 1], [12, 2, 2, 1], [18, 2, 3, 1], [22, 2, 5, 1], [24, 2, 4, 1], [33, 2, 10, 1], [36, 2, 6, 1], [44, 2, 10, 1], [66, 2, 10, 1], [72, 2, 12, 1], [88, 2, 20, 1], [99, 2, 30, 1], [132, 2, 20, 1], [198, 2, 30, 1], [264, 2, 40, 1], [396, 2, 60, 1], [792, 2, 120, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 792, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 1, 120]], 'familial': True, 'frattini_label': '12.2', 'frattini_quotient': '132.9', 'hash': 67, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 396, 'inner_gen_orders': [2, 396], 'inner_gens': [[1, 1582], [5, 2]], 'inner_hash': 25, 'inner_nilpotent': False, 'inner_order': 792, 'inner_split': False, 'inner_tex': 'D_{396}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 240, 'irrQ_dim': 240, 'irrR_degree': 2, 'irrep_stats': [[1, 4], [2, 395]], 'label': '1584.67', 'linC_count': 120, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 4, 'linQ_dim': 20, 'linQ_dim_count': 4, 'linR_count': 120, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D792', '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, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 399, 'number_divisions': 26, 'number_normal_subgroups': 27, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 66, 'number_subgroups': 2364, 'old_label': None, 'order': 1584, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 793], [3, 2], [4, 2], [6, 2], [8, 4], [9, 6], [11, 10], [12, 4], [18, 6], [22, 10], [24, 8], [33, 20], [36, 12], [44, 20], [66, 20], [72, 24], [88, 40], [99, 60], [132, 40], [198, 60], [264, 80], [396, 120], [792, 240]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 2, 2, 30], 'outer_gen_pows': [1408, 1408, 0, 330], 'outer_gens': [[1409, 1010], [1409, 398], [1, 218], [551, 1202]], 'outer_group': '240.208', 'outer_hash': 208, 'outer_nilpotent': True, 'outer_order': 240, 'outer_permdeg': 16, 'outer_perms': [40279680, 362880, 1307674368000, 6227026593], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{30}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 28, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 2], [6, 2], [8, 1], [10, 2], [12, 1], [20, 3], [24, 1], [40, 2], [60, 2], [80, 1], [120, 1], [240, 1]], 'representations': {'PC': {'code': 1202941996938997147046784599807845591982060000119, 'gens': [1, 2], 'pres': [7, -2, -2, -2, -2, -3, -3, -11, 22149, 36, 33182, 58, 44131, 80, 54884, 137, 64517, 166, 70566]}, 'Perm': {'d': 28, 'gens': [868708690480067649339017647, 7891827264921600, 13916445459840000, 21069517179110400, 12145280938112229701713920000, 4364893, 23454917710790789398855680000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{792}', 'transitive_degree': 792, 'wreath_data': None, 'wreath_product': False}
-
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 990, 'aut_gen_orders': [30, 30, 30, 6], 'aut_gens': [[1, 2], [49, 94], [95, 238], [101, 382], [109, 262]], 'aut_group': None, 'aut_hash': 4676639020669913352, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 11880, 'aut_permdeg': 198, 'aut_perms': [5472016787768452843848087026436369699809196834011976419326714317015425008377424481334962170464217514508561968842044448941854282395247242361231244589749803147691392297100597192403784343277723733748839389775944116750389967941902047578616727762939071634116760692447647639222291435060375744034530604019172297850149496204636373623882633571860184739776524022957278230759078193, 3983713445047449321170146108588407152529085132713279173321954786780828100858511937283653796579462113122193005787185511170689900924843812803512759849500743614810196370348916312123491309676449269483706509973217522293063824822306467245426110708181075676079541371123599407047225935727653588767676666200024041239645648593203581579263704285688163013128547410947751117933132751, 18621095868459628348654863474698836961523279219559163372431563970903258291122088581979142784794290030067362792264572542129919349270250257256951759166306987168264308046656152357443752372224598911778819697576730923128881948462189683468412377881707654585450657088817916369927035137376031599249920511536743767631046085426349025050868008065379294798124834696889991630262172215, 16023925158070106671457671140016145742431213762158477269431055484045528872707778707997076139340811125490379780340280887639457901998516396625555479985781131946536120501947123764171633627965120261576346410041050058113677796489443914685618583713863520275067480472912609445917337573630256308248131130243966398984862810629989232751007480480387385135924145143801598829893315851], 'aut_phi_ratio': 99.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 99, 2, 1], [3, 2, 1, 1], [6, 2, 1, 1], [9, 2, 3, 1], [11, 2, 5, 1], [18, 2, 3, 1], [22, 2, 5, 1], [33, 2, 10, 1], [66, 2, 10, 1], [99, 2, 30, 1], [198, 2, 30, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{99}.C_{30}.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 990, 'autcentquo_group': '5940.d', 'autcentquo_hash': 4717361004838527357, 'autcentquo_nilpotent': False, 'autcentquo_order': 5940, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_{99}:C_{30}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 99, 2], [3, 2, 1], [6, 2, 1], [9, 2, 3], [11, 2, 5], [18, 2, 3], [22, 2, 5], [33, 2, 10], [66, 2, 10], [99, 2, 30], [198, 2, 30]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '198.3', 'commutator_count': 1, 'commutator_label': '99.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 9, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [['198.3', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 99, 1, 2], [3, 2, 1, 1], [6, 2, 1, 1], [9, 2, 3, 1], [11, 2, 5, 1], [18, 2, 3, 1], [22, 2, 5, 1], [33, 2, 10, 1], [66, 2, 10, 1], [99, 2, 30, 1], [198, 2, 30, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 198, 'exponents_of_order': [2, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 1, 30]], 'familial': True, 'frattini_label': '3.1', 'frattini_quotient': '132.9', 'hash': 9, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 198, 'inner_gen_orders': [2, 99], 'inner_gens': [[1, 394], [5, 2]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 198, 'inner_split': True, 'inner_tex': 'D_{99}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 60, 'irrQ_dim': 60, 'irrR_degree': 2, 'irrep_stats': [[1, 4], [2, 98]], 'label': '396.9', 'linC_count': 30, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 3, 'linQ_dim': 16, 'linQ_dim_count': 3, 'linR_count': 30, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D198', 'ngens': 5, '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': 13, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 102, 'number_divisions': 14, 'number_normal_subgroups': 15, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 30, 'number_subgroups': 480, 'old_label': None, 'order': 396, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 199], [3, 2], [6, 2], [9, 6], [11, 10], [18, 6], [22, 10], [33, 20], [66, 20], [99, 60], [198, 60]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 30], 'outer_gen_pows': [352, 0], 'outer_gens': [[353, 218], [111, 238]], 'outer_group': '60.13', 'outer_hash': 13, 'outer_nilpotent': True, 'outer_order': 60, 'outer_permdeg': 12, 'outer_perms': [40279680, 368673], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{30}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [6, 2], [10, 2], [20, 2], [60, 2]], 'representations': {'PC': {'code': 57201180091164480332600119, 'gens': [1, 2], 'pres': [5, -2, -2, -3, -3, -11, 3941, 26, 5882, 57, 7683, 78, 9004]}, 'GLFp': {'d': 2, 'p': 197, 'gens': [1498493109, 1358484794]}, 'Perm': {'d': 22, 'gens': [5353116803292348847, 479001600, 58755318410460672000, 4364893, 112426456502987827200]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{198}', 'transitive_degree': 198, 'wreath_data': None, 'wreath_product': False}
