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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '53240.bd', 'ambient_counter': 30, 'ambient_order': 53240, 'ambient_tex': 'D_{11}\\times C_{22}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 22, 'characteristic': False, 'core_order': 2662, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '53240.bd.20.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2662.11', 'subgroup_hash': 11, 'subgroup_order': 2662, 'subgroup_tex': 'C_{11}^2:C_{22}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '53240.bd', 'aut_centralizer_order': None, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2420.a1', 'complements': ['2662.a1', '2662.c1', '2662.d1'], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '10.b1', '10.d1'], 'contains': ['40.a1', '220.d1', '220.j1', '220.k1'], 'core': '20.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6141, 6690, 3461, 3607], 'generators': [2530, 29260, 4840, 20], 'label': '53240.bd.20.c1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.c1', 'normal_contained_in': ['4.c1', '10.b1', '10.d1'], 'normal_contains': ['40.a1', '220.d1'], 'normalizer': '1.a1', 'old_label': '20.c1', 'projective_image': '53240.bd', 'quotient_action_image': '10.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '20.c1', 'subgroup_fusion': None, 'weyl_group': '2420.r'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '22.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1320, 'aut_gen_orders': [120, 10, 40], 'aut_gens': [[1, 22, 242], [1321, 1804, 1782], [1949, 2024, 418], [459, 2398, 1848]], 'aut_group': None, 'aut_hash': 6456319880611744141, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 15972000, 'aut_permdeg': 131, 'aut_perms': [559707722508526613137358424789441003650977469003560512662183910696311567524454671644046737915238212524377335561946950475069298049618720403963982516919008472124198366412480941218665615476053707728279213192496666244263671438, 299482244759318200241095261244056313128174730178810014988398452858905800980757640910075837237318407702333276635561994342347792356194145509679115536236149178948140944952763130452836228474756433423459522620856866169492673730, 286041564568653707999317125414445551491459037457073553581120508464652649733048449871692622070100647048472013299259715195361338466862042360407400559551218217587927686526260298893651501592702130495464857852005794302520779389], 'aut_phi_ratio': 13200.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [11, 1, 10, 1], [11, 2, 60, 1], [11, 2, 600, 1], [22, 121, 10, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{10}\\times C_{11}^2.C_{10}.\\PSL(2,11).C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 10, 'autcent_group': '10.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 10, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': '1597200.a', 'autcentquo_hash': 6850908737282390520, 'autcentquo_nilpotent': False, 'autcentquo_order': 1597200, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{11}^2.\\GL(2,11)', 'cc_stats': [[1, 1, 1], [2, 121, 1], [11, 1, 10], [11, 2, 660], [22, 121, 10]], 'center_label': '11.1', 'center_order': 11, 'central_product': True, 'central_quotient': '242.4', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '11.1', '11.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 11, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['242.4', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [11, 1, 10, 1], [11, 2, 5, 12], [11, 2, 10, 60], [22, 121, 10, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 931, 'exponent': 22, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2662.11', 'hash': 11, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [2, 11, 11], 'inner_gens': [[1, 220, 2420], [45, 22, 242], [485, 22, 242]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 242, 'inner_split': False, 'inner_tex': 'C_{11}:D_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 22], [2, 660]], 'label': '2662.11', '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': 'C11^2:C22', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 682, 'number_divisions': 76, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 14, 'number_subgroup_classes': 176, 'number_subgroups': 776, 'old_label': None, 'order': 2662, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 121], [11, 1330], [22, 1210]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 660, 'outer_gen_orders': [30, 10, 20], 'outer_gen_pows': [1, 0, 1], 'outer_gens': [[21, 1166, 1320], [19, 2002, 660], [3, 1342, 1144]], 'outer_group': None, 'outer_hash': 2802544133637498110, 'outer_nilpotent': False, 'outer_order': 66000, 'outer_permdeg': 24, 'outer_perms': [134185021879546332617040, 234006645145397604480090, 239838297808345799996970], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_{10}\\times C_5.\\PSL(2,11).C_2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 33, 'pgroup': 0, 'primary_abelian_invariants': [2, 11], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [10, 14], [20, 60]], 'representations': {'PC': {'code': '327884058090999', 'gens': [1, 3, 4], 'pres': [4, -2, -11, -11, -11, 8, 2642, 38723]}, 'GLZq': {'d': 2, 'q': 121, 'gens': [1771617, 120309146, 159900563, 21592858]}, 'Perm': {'d': 33, 'gens': [17507657858252451032703720433996800, 288596374585786927779407037988761600, 559446352896534159156229830564864000, 4037913]}}, 'schur_multiplier': [11], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [22], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^2:C_{22}', 'transitive_degree': 242, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [110, 20, 10, 110, 55, 10], 'aut_gens': [[1, 10, 220, 2420], [5081, 27870, 11880, 2420], [22309, 44350, 5940, 42900], [47821, 50030, 45320, 41140], [3021, 41110, 24420, 41140], [14701, 9770, 34980, 2420], [32589, 32170, 40920, 3520]], 'aut_group': None, 'aut_hash': 906806283152441688, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10648000, 'aut_permdeg': 506, 'aut_perms': 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'aut_phi_ratio': 550.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 2, 1], [2, 121, 2, 1], [2, 1331, 2, 1], [5, 121, 2, 2], [10, 121, 2, 2], [10, 121, 4, 2], [10, 1331, 4, 4], [11, 2, 5, 1], [11, 10, 2, 1], [11, 10, 10, 1], [11, 20, 10, 1], [11, 20, 50, 1], [22, 2, 5, 1], [22, 10, 2, 1], [22, 10, 10, 1], [22, 20, 10, 1], [22, 20, 50, 1], [22, 110, 4, 1], [22, 110, 20, 1], [22, 242, 10, 1], [55, 242, 10, 2], [110, 242, 10, 2], [110, 242, 20, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^3.C_5.C_{10}^2.C_2^4', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': None, 'autcentquo_hash': 3149364867277236831, 'autcentquo_nilpotent': False, 'autcentquo_order': 2662000, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{11}^3.C_{10}.C_{10}^2.C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 11, 2], [2, 121, 2], [2, 1331, 2], [5, 121, 4], [10, 121, 12], [10, 1331, 16], [11, 2, 5], [11, 10, 12], [11, 20, 60], [22, 2, 5], [22, 10, 12], [22, 20, 60], [22, 110, 24], [22, 242, 10], [55, 242, 20], [110, 242, 60]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '26620.bb', 'commutator_count': 1, 'commutator_label': '1331.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '11.1', '11.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 30, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['1210.10', 1], ['2.1', 1], ['22.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 1, 2], [2, 121, 1, 2], [2, 1331, 1, 2], [5, 121, 4, 1], [10, 121, 4, 3], [10, 1331, 4, 4], [11, 2, 5, 1], [11, 10, 1, 2], [11, 10, 5, 2], [11, 20, 5, 12], [22, 2, 5, 1], [22, 10, 1, 2], [22, 10, 5, 2], [22, 20, 5, 12], [22, 110, 1, 4], [22, 110, 5, 4], [22, 242, 5, 2], [55, 242, 20, 1], [110, 242, 20, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4499712, 'exponent': 110, 'exponents_of_order': [3, 3, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[20, 1, 50]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '53240.bd', 'hash': 3100417070322456923, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 22, 11, 11], 'inner_gens': [[1, 48610, 20460, 21780], [4861, 10, 2200, 50820], [35421, 450, 220, 2420], [33881, 4850, 220, 2420]], 'inner_hash': 738845080847280697, 'inner_nilpotent': False, 'inner_order': 26620, 'inner_split': False, 'inner_tex': 'D_{11}\\times C_{11}:F_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 20, 'irrQ_degree': 100, 'irrQ_dim': 100, 'irrR_degree': 20, 'irrep_stats': [[1, 40], [2, 100], [10, 48], [20, 120]], 'label': '53240.bd', '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': 'D11*C22:F11', '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, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 34, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 308, 'number_divisions': 64, 'number_normal_subgroups': 63, 'number_subgroup_autclasses': 156, 'number_subgroup_classes': 440, 'number_subgroups': 94916, 'old_label': None, 'order': 53240, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 2927], [5, 484], [10, 22748], [11, 1330], [22, 6390], [55, 4840], [110, 14520]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 10, 10], 'outer_gen_pows': [0, 8, 0, 0], 'outer_gens': [[9, 45750, 20460, 42900], [1, 50830, 35860, 12100], [26621, 31530, 26400, 36300], [1, 19370, 5060, 31460]], 'outer_group': '400.221', 'outer_hash': 221, 'outer_nilpotent': True, 'outer_order': 400, 'outer_permdeg': 18, 'outer_perms': [355687428096000, 1307714284800, 6227475162, 39916842], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{10}^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [4, 8], [10, 12], [40, 4], [50, 8], [100, 24]], 'representations': {'PC': {'code': '17758002571555044466105400900421978247758065417477149017511461742040987647090309909', 'gens': [1, 3, 5, 6], 'pres': [7, -2, -5, -2, -11, -11, -2, -11, 14, 1020812, 50934, 58, 5603, 716104, 96261, 7718, 914765, 762312, 213463, 124, 2134446, 474333, 237180]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [32906036359581576, 18721992341619836, 11300846666707172, 1754382938723032, 36037487804644665, 32182222080390795, 41772741070013040]}, 'Perm': {'d': 35, 'gens': [340007756491608160105911900865578977880, 608909717286147822420363932861514282487, 938901755970236865128710790579787429294, 1242035941944727800399071423394049536000, 62659640997738622771558431091307779806, 1547473788333472666977512918876160000000, 1]}}, 'schur_multiplier': [2, 2, 22], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{11}\\times C_{22}:F_{11}', 'transitive_degree': 220, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 12], 'aut_gens': [[1, 2], [10, 13], [10, 15]], 'aut_group': '24.5', 'aut_hash': 5, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24, 'aut_permdeg': 7, 'aut_perms': [127, 857], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [5, 1, 4, 1], [10, 1, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4\\times S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '24.5', 'autcent_hash': 5, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4\\times S_3', '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, 3], [5, 1, 4], [10, 1, 12]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, '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', '5.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [5, 1, 4, 1], [10, 1, 4, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 6, 'exponent': 10, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '20.5', 'hash': 5, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 20]], 'label': '20.5', 'linC_count': 72, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 6, 'linQ_dim': 5, 'linQ_dim_count': 6, 'linR_count': 12, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C10', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 20, 'number_divisions': 8, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 10, 'number_subgroups': 10, 'old_label': None, 'order': 20, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 3], [5, 4], [10, 12]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 12], 'outer_gen_pows': [0, 0], 'outer_gens': [[10, 13], [10, 15]], 'outer_group': '24.5', 'outer_hash': 5, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [127, 857], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4\\times S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 4]], 'representations': {'PC': {'code': 2179, 'gens': [1, 2], 'pres': [3, -2, -2, -5, 16]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [141602720900, 706303489327]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [13320, 4001]}, 'Perm': {'d': 9, 'gens': [40320, 720, 96]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{10}', 'transitive_degree': 20, 'wreath_data': None, 'wreath_product': False}
