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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '45864.a', 'ambient_counter': 1, 'ambient_order': 45864, 'ambient_tex': 'C_{21}\\times \\SL(2,13)', 'central': True, 'central_factor': False, 'centralizer_order': 45864, 'characteristic': True, 'core_order': 42, 'counter': 62, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '45864.a.1092.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1092.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1092.25', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1092, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,13)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '45864.a', 'aut_centralizer_order': None, 'aut_label': '1092.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['84.a1.a1', '156.a1.a1', '364.a1.a1', '546.a1.a1'], 'contains': ['2184.a1.a1', '3276.a1.a1', '7644.a1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5722, 6180, 5054, 6199, 5728, 9403, 4800, 9403], 'generators': [801250460, 772289600, 299262220], 'label': '45864.a.1092.a1.a1', 'mobius_quo': -1, 'mobius_sub': -1092, 'normal_closure': '1092.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['2184.a1.a1', '3276.a1.a1', '7644.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1092.a1.a1', 'projective_image': '1092.25', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1092.25', 'quotient_action_kernel_order': 1092, 'quotient_fusion': None, 'short_label': '1092.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '42.6', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 6, 'aut_gen_orders': [2, 6], 'aut_gens': [[1], [13], [11]], 'aut_group': '12.5', 'aut_hash': 5, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 12, 'aut_permdeg': 7, 'aut_perms': [24, 723], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1], [7, 1, 6, 1], [14, 1, 6, 1], [21, 1, 12, 1], [42, 1, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_6', '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], [3, 1, 2], [6, 1, 2], [7, 1, 6], [14, 1, 6], [21, 1, 12], [42, 1, 12]], 'center_label': '42.6', 'center_order': 42, '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', '3.1', '7.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1], [7, 1, 6, 1], [14, 1, 6, 1], [21, 1, 12, 1], [42, 1, 12, 1]], 'element_repr_type': 'PC', 'elementary': 42, 'eulerian_function': 1, 'exponent': 42, 'exponents_of_order': [1, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[1, 0, 12]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '42.6', 'hash': 6, 'hyperelementary': 42, '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': 12, 'irrQ_dim': 12, 'irrR_degree': 2, 'irrep_stats': [[1, 42]], 'label': '42.6', 'linC_count': 12, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 3, 'linQ_dim': 8, 'linQ_dim_count': 3, 'linR_count': 6, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C42', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, '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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 42, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 42, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2], [7, 6], [14, 6], [21, 12], [42, 12]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[13], [11]], 'outer_group': '12.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [24, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 7], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [6, 2], [12, 2]], 'representations': {'PC': {'code': 339347, 'gens': [1], 'pres': [3, -2, -3, -7, 6, 22]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [351, 2064, 1032]}, 'Perm': {'d': 12, 'gens': [39916800, 725760, 4320]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [42], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{42}', 'transitive_degree': 42, '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': '21.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1092, 'aut_gen_orders': [4, 2, 6, 6], 'aut_gens': [[191923980, 801250460, 366214657, 101363010, 772289600], [694913337, 801250460, 783613474, 241340500, 772289600], [696611110, 801250460, 173564837, 101363010, 772289600], [283951358, 279954980, 151834314, 743328740, 265474550], [424607007, 106189820, 175709615, 796423650, 77228960]], 'aut_group': None, 'aut_hash': 3088507494921977175, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 26208, 'aut_permdeg': 164, 'aut_perms': [176323844990587965822251066573793183871511140652867019999558170097287580717755736867362413983522733430079021532992991035892047479956774845885306990354988784245952494103520912816022233738031720692137814427387861267960354468891750923057762794285770346158370580400805766283706864293314994944998613, 6601560643528971822514793851568614737582078887332875910612866480394682092064568478039116456476989675683008165371456284616981607304016300034899592768189615406574691869723322901739516562288362772105134557041369749232146951228289514406113421853812521484588081586380580478383622352951809782933711, 122382963041592063547223747652352069362681408966718097194387055617509828380777672777489484039296853885611605440835957045261926719430139617288865953367084078866604061469289489901199271205047651142977360800835002670701522343677406589563437913081031151414909390930009236108006949433729423923528334, 225773694673787103557451871628532116737493258469245943343908519707296203828134907968710847513989967967332166241968117722049840430529754208240803683166838711579802232934294308314844067816819427181632385346683499960532633994787395808496850614564849009481687649637786363214791613529198013183260431], 'aut_phi_ratio': 2.1666666666666665, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 182, 1, 1], [3, 182, 2, 1], [4, 182, 1, 1], [6, 1, 2, 1], [6, 182, 1, 1], [6, 182, 2, 1], [7, 1, 6, 1], [7, 156, 1, 3], [7, 156, 6, 3], [12, 182, 1, 2], [12, 182, 2, 3], [13, 84, 2, 1], [14, 1, 6, 1], [14, 156, 1, 3], [14, 156, 6, 3], [21, 1, 12, 1], [21, 156, 2, 3], [21, 156, 12, 3], [21, 182, 6, 1], [21, 182, 12, 1], [26, 84, 2, 1], [28, 182, 6, 1], [39, 84, 4, 1], [42, 1, 12, 1], [42, 156, 2, 3], [42, 156, 12, 3], [42, 182, 6, 1], [42, 182, 12, 1], [78, 84, 4, 1], [84, 182, 6, 2], [84, 182, 12, 3], [91, 84, 12, 1], [182, 84, 12, 1], [273, 84, 24, 1], [546, 84, 24, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_6\\times \\PSL(2,13).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1092, 'autcentquo_group': '2184.b', 'autcentquo_hash': 7763277135502868404, 'autcentquo_nilpotent': False, 'autcentquo_order': 2184, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,13)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 182, 3], [4, 182, 1], [6, 1, 2], [6, 182, 3], [7, 1, 6], [7, 156, 21], [12, 182, 8], [13, 84, 2], [14, 1, 6], [14, 156, 21], [21, 1, 12], [21, 156, 42], [21, 182, 18], [26, 84, 2], [28, 182, 6], [39, 84, 4], [42, 1, 12], [42, 156, 42], [42, 182, 18], [78, 84, 4], [84, 182, 48], [91, 84, 12], [182, 84, 12], [273, 84, 24], [546, 84, 24]], 'center_label': '42.6', 'center_order': 42, 'central_product': True, 'central_quotient': '1092.25', 'commutator_count': 1, 'commutator_label': '2184.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '7.1', '1092.25'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2184.a', 1], ['3.1', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 182, 1, 1], [3, 182, 2, 1], [4, 182, 1, 1], [6, 1, 2, 1], [6, 182, 1, 1], [6, 182, 2, 1], [7, 1, 6, 1], [7, 156, 3, 1], [7, 156, 6, 3], [12, 182, 2, 2], [12, 182, 4, 1], [13, 84, 2, 1], [14, 1, 6, 1], [14, 156, 3, 1], [14, 156, 6, 3], [21, 1, 12, 1], [21, 156, 6, 1], [21, 156, 12, 3], [21, 182, 6, 1], [21, 182, 12, 1], [26, 84, 2, 1], [28, 182, 6, 1], [39, 84, 4, 1], [42, 1, 12, 1], [42, 156, 6, 1], [42, 156, 12, 3], [42, 182, 6, 1], [42, 182, 12, 1], [78, 84, 4, 1], [84, 182, 12, 2], [84, 182, 24, 1], [91, 84, 12, 1], [182, 84, 12, 1], [273, 84, 24, 1], [546, 84, 24, 1]], 'element_repr_type': 'GLFq', 'elementary': 1, 'eulerian_function': 63360, 'exponent': 1092, 'exponents_of_order': [3, 2, 2, 1], 'factors_of_aut_order': [2, 3, 7, 13], 'factors_of_order': [2, 3, 7, 13], 'faithful_reps': [[6, 0, 24], [12, 0, 36], [14, 0, 36]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 3852770923026822097, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 546, 'inner_gen_orders': [13, 1, 2, 1, 1], 'inner_gens': [[191923980, 801250460, 350065189, 101363010, 772289600], [191923980, 801250460, 366214657, 101363010, 772289600], [257520640, 801250460, 366214657, 101363010, 772289600], [191923980, 801250460, 366214657, 101363010, 772289600], [191923980, 801250460, 366214657, 101363010, 772289600]], 'inner_hash': 25, 'inner_nilpotent': False, 'inner_order': 1092, 'inner_split': True, 'inner_tex': '\\PSL(2,13)', 'inner_used': [1, 3], 'irrC_degree': 6, 'irrQ_degree': 144, 'irrQ_dim': 144, 'irrR_degree': 12, 'irrep_stats': [[1, 21], [6, 42], [7, 42], [12, 126], [13, 21], [14, 105]], 'label': '45864.a', 'linC_count': 24, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 1, 'linQ_dim': 30, 'linQ_dim_count': 1, 'linR_count': 12, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C21*SL(2,13)', '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, 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, 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': 60, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 357, 'number_divisions': 48, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 98, 'number_subgroup_classes': 118, 'number_subgroups': 8056, 'old_label': None, 'order': 45864, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1], [3, 548], [4, 182], [6, 548], [7, 3282], [12, 1456], [13, 168], [14, 3282], [21, 9840], [26, 168], [28, 1092], [39, 336], [42, 9840], [78, 336], [84, 8736], [91, 1008], [182, 1008], [273, 2016], [546, 2016]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [4826810, 4826810, 41219443], 'outer_gens': [[621357273, 106189820, 366214657, 796423650, 77228960], [191923980, 801250460, 147760232, 241340500, 772289600], [35298132, 405452040, 782163623, 685407020, 381317990]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [24, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 66, 'pgroup': 0, 'primary_abelian_invariants': [3, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [6, 1], [12, 2], [13, 1], [14, 4], [24, 1], [26, 1], [28, 5], [36, 2], [56, 1], [72, 9], [78, 1], [84, 4], [144, 7], [156, 1], [168, 5], [336, 1]], 'representations': {'GLFq': {'d': 2, 'q': 169, 'gens': [191923980, 801250460, 366214657, 101363010, 772289600]}, 'Perm': {'d': 66, 'gens': [8634324217977017890345388586798532954096929802700343467800341869486730667271742081348152544, 17002977331396247758184444848744511563022488077603235248457399820250011368545574683401344104, 25387365514523919795867393201337887212385781164015544726236273454978516553157934564890681603, 1312683, 1532400]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [21], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{21}\\times \\SL(2,13)', 'transitive_degree': 1176, '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': '1.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1092, 'aut_gen_orders': [12, 3], 'aut_gens': [[15381, 2053], [5753, 3703], [15753, 14334]], 'aut_group': '2184.b', 'aut_hash': 7763277135502868404, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2184, 'aut_permdeg': 91, 'aut_perms': [15685624209542281043180093832356955359558084980787576118939763356894651589906212972242836233730372715269387981677749662727246705895496015546, 88904264646742496335384702563170983777880925500795965825705028509132871588844625292831170146632406414409051897144147289726343368975320434687], 'aut_phi_ratio': 7.583333333333333, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 91, 1, 1], [3, 182, 1, 1], [6, 182, 1, 1], [7, 156, 1, 3], [13, 84, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PGL(2,13)', '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': 1092, 'autcentquo_group': '2184.b', 'autcentquo_hash': 7763277135502868404, 'autcentquo_nilpotent': False, 'autcentquo_order': 2184, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,13)', 'cc_stats': [[1, 1, 1], [2, 91, 1], [3, 182, 1], [6, 182, 1], [7, 156, 3], [13, 84, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1092.25', 'commutator_count': 1, 'commutator_label': '1092.25', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['1092.25'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 25, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 91, 1, 1], [3, 182, 1, 1], [6, 182, 1, 1], [7, 156, 3, 1], [13, 84, 2, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 495, 'exponent': 546, 'exponents_of_order': [2, 1, 1, 1], 'factors_of_aut_order': [2, 3, 7, 13], 'factors_of_order': [2, 3, 7, 13], 'faithful_reps': [[7, 1, 2], [12, 1, 3], [13, 1, 1], [14, 1, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1092.25', 'hash': 25, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 546, 'inner_gen_orders': [6, 3], 'inner_gens': [[15381, 1663], [5246, 2053]], 'inner_hash': 25, 'inner_nilpotent': False, 'inner_order': 1092, 'inner_split': True, 'inner_tex': '\\PSL(2,13)', 'inner_used': [1, 2], 'irrC_degree': 7, 'irrQ_degree': 13, 'irrQ_dim': 13, 'irrR_degree': 7, 'irrep_stats': [[1, 1], [7, 2], [12, 3], [13, 1], [14, 2]], 'label': '1092.25', 'linC_count': 2, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 13, 'linQ_degree_count': 1, 'linQ_dim': 13, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'PSL(2,13)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 9, 'number_divisions': 6, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 15, 'number_subgroup_classes': 16, 'number_subgroups': 942, 'old_label': None, 'order': 1092, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 91], [3, 182], [6, 182], [7, 468], [13, 168]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [1807], 'outer_gens': [[4604, 6652]], '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': None, 'perfect': True, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [13, 1], [14, 3], [36, 1]], 'representations': {'Lie': [{'d': 2, 'q': 13, 'gens': [2053, 15381], 'family': 'PSL'}, {'d': 2, 'q': 13, 'gens': [33787665, 1272582], 'family': 'PSU'}, {'d': 3, 'q': 13, 'gens': [58292859, 3262951455], 'family': 'Omega'}, {'d': 3, 'q': 13, 'gens': [58292859, 3262951455], 'family': 'POmega'}, {'d': 2, 'q': 13, 'gens': [2053, 15381], 'family': 'PSigmaL'}], 'GLFp': {'d': 3, 'p': 13, 'gens': [8354693709, 7376835470]}, 'Perm': {'d': 14, 'gens': [560517275, 132642186, 6268172431]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PSL(2,13)', 'transitive_degree': 14, 'wreath_data': None, 'wreath_product': False}
