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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1584.309', 'ambient_counter': 309, 'ambient_order': 1584, 'ambient_tex': 'C_{264}:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 792, 'characteristic': True, 'core_order': 3, 'counter': 84, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1584.309.528.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '528.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '528.32', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 32, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 528, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{264}:C_2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1584.309', 'aut_centralizer_order': 5280, 'aut_label': '528.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5280, 'centralizer': '2.b1.a1', 'complements': ['3.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '176.a1.a1', '264.b1.a1', '264.e1.a1'], 'contains': ['1584.a1.a1'], 'core': '528.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1602, 8576, 8983, 1632, 8150, 3710, 2136, 3710], 'generators': [1056], 'label': '1584.309.528.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '528.b1.a1', 'normal_contained_in': ['48.b1.a1', '176.a1.a1', '264.b1.a1'], 'normal_contains': ['1584.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '528.b1.a1', 'projective_image': '1584.309', 'quotient_action_image': '2.1', 'quotient_action_kernel': '264.4', 'quotient_action_kernel_order': 264, 'quotient_fusion': None, 'short_label': '528.b1.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': '3.1', '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], [2]], '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], [3, 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], [3, 1, 2]], 'center_label': '3.1', 'center_order': 3, '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': ['3.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '3.1', 'hash': 1, 'hyperelementary': 3, '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, 3]], 'label': '3.1', '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': 'C3', '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': 3, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 3, 'order_factorization_type': 1, 'order_stats': [[1, 1], [3, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[2]], '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': 3, 'pgroup': 3, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -3]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [7]}, 'Lie': [{'d': 1, 'q': 3, 'gens': [3], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [7]}, 'Perm': {'d': 3, 'gens': [4]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [3], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3', 'transitive_degree': 3, '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': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 330, 'aut_gen_orders': [22, 30, 22, 30, 10, 10, 30], 'aut_gens': [[1, 6], [1009, 402], [457, 294], [437, 1326], [1465, 42], [437, 1218], [769, 246], [97, 1338]], 'aut_group': None, 'aut_hash': 6678131497129254218, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10560, 'aut_permdeg': 72, 'aut_perms': [871702835118514239857861591608488009385269921179919581635806035995636964160925030287469325416546466231, 59976450335874111530438033902614769930494491445007330348871151298047716809551281468595591225900396451030, 11247108754226778563817210644516462368160724538752546674835339036823020248114251154321792571388996432053, 14885761557689573570843682349865390973231738785938839741328702188930172484332985396837945758295464985618, 41829083600798090909177885139352270265912388400843072513590516196699794751754062618328269911135903262276, 1108285287670553983067322440678980491302336413862866277704508238345017371352505672969722458212577780893, 60769434961182221975291730833491059490642129357763221188761357930303963890319755443174871052141474343257], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 66, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 66, 1, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 66, 2, 1], [8, 2, 2, 1], [8, 66, 2, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 2, 4, 1], [12, 66, 2, 1], [22, 2, 5, 1], [24, 2, 4, 2], [24, 2, 8, 1], [24, 66, 4, 1], [33, 2, 10, 2], [33, 2, 20, 1], [44, 2, 10, 1], [66, 2, 10, 2], [66, 2, 20, 1], [88, 2, 20, 1], [132, 2, 20, 2], [132, 2, 40, 1], [264, 2, 40, 2], [264, 2, 80, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{33}.(C_2^5\\times C_{10})', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 66, 1], [3, 1, 2], [3, 2, 3], [4, 1, 2], [4, 66, 1], [6, 1, 2], [6, 2, 3], [6, 66, 2], [8, 2, 2], [8, 66, 2], [11, 2, 5], [12, 1, 4], [12, 2, 6], [12, 66, 2], [22, 2, 5], [24, 2, 16], [24, 66, 4], [33, 2, 40], [44, 2, 10], [66, 2, 40], [88, 2, 20], [132, 2, 80], [264, 2, 160]], 'center_label': '12.2', 'center_order': 12, 'central_product': True, 'central_quotient': '132.9', 'commutator_count': 1, 'commutator_label': '66.4', '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': 309, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['528.64', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 66, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 66, 1, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 66, 2, 1], [8, 2, 2, 1], [8, 66, 2, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 2, 4, 1], [12, 66, 2, 1], [22, 2, 5, 1], [24, 2, 4, 2], [24, 2, 8, 1], [24, 66, 4, 1], [33, 2, 10, 2], [33, 2, 20, 1], [44, 2, 10, 1], [66, 2, 10, 2], [66, 2, 20, 1], [88, 2, 20, 1], [132, 2, 20, 2], [132, 2, 40, 1], [264, 2, 40, 2], [264, 2, 80, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 264, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 0, 80]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '396.27', 'hash': 309, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [2, 66], 'inner_gens': [[1, 1182], [409, 6]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 132, 'inner_split': True, 'inner_tex': 'D_{66}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 160, 'irrQ_dim': 160, 'irrR_degree': 4, 'irrep_stats': [[1, 24], [2, 390]], 'label': '1584.309', 'linC_count': 80, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 20, 'linQ_dim': 18, 'linQ_dim_count': 20, 'linR_count': 40, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C264:C6', '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': 38, 'number_characteristic_subgroups': 42, 'number_conjugacy_classes': 414, 'number_divisions': 38, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 88, 'number_subgroup_classes': 88, 'number_subgroups': 720, 'old_label': None, 'order': 1584, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 67], [3, 8], [4, 68], [6, 140], [8, 136], [11, 10], [12, 148], [22, 10], [24, 296], [33, 80], [44, 20], [66, 80], [88, 40], [132, 160], [264, 320]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 2, 10], 'outer_gen_pows': [1452, 0, 0, 132], 'outer_gens': [[1057, 1446], [1, 390], [1, 258], [1061, 1158]], 'outer_group': '80.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 80, 'outer_permdeg': 13, 'outer_perms': [720, 479001600, 3628800, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{10}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 6], [8, 3], [10, 2], [16, 1], [20, 5], [40, 5], [80, 3], [160, 1]], 'representations': {'PC': {'code': 759431968955741394251365827319462665570100019, 'gens': [1, 3], 'pres': [7, -2, -3, -2, -2, -2, -3, -11, 14, 24824, 58, 21843, 80, 54604, 102, 64517, 166, 70566]}, 'GLFq': {'d': 2, 'q': 529, 'gens': [60990786680, 25011069600, 59184244894, 14655553110, 42017735864, 14803589000, 47817360872]}, 'Perm': {'d': 25, 'gens': [25903229683152198510265, 4124304, 6706022400, 8807280, 12136560, 3, 672254861098236159744000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{264}:C_6', 'transitive_degree': 528, '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': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 110, 'aut_gen_orders': [2, 2, 2, 10, 22], 'aut_gens': [[1, 2], [265, 134], [1, 398], [1, 134], [1, 290], [481, 178]], 'aut_group': '1760.1272', 'aut_hash': 1272, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1760, 'aut_permdeg': 28, 'aut_perms': [22988254553903335866756358583, 29325761720439972480, 24460313391511159680, 294559195653662324094847520753, 97727683545779933631202549080], 'aut_phi_ratio': 11.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 22, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 22, 1, 1], [6, 1, 2, 1], [6, 22, 2, 1], [8, 2, 2, 1], [8, 22, 2, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 22, 2, 1], [22, 2, 5, 1], [24, 2, 4, 1], [24, 22, 4, 1], [33, 2, 10, 1], [44, 2, 10, 1], [66, 2, 10, 1], [88, 2, 20, 1], [132, 2, 20, 1], [264, 2, 40, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4\\times F_{11}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 22, 1], [3, 1, 2], [4, 1, 2], [4, 22, 1], [6, 1, 2], [6, 22, 2], [8, 2, 2], [8, 22, 2], [11, 2, 5], [12, 1, 4], [12, 22, 2], [22, 2, 5], [24, 2, 4], [24, 22, 4], [33, 2, 10], [44, 2, 10], [66, 2, 10], [88, 2, 20], [132, 2, 20], [264, 2, 40]], 'center_label': '12.2', 'center_order': 12, 'central_product': True, 'central_quotient': '44.3', 'commutator_count': 1, 'commutator_label': '22.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 32, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['176.4', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 22, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 22, 1, 1], [6, 1, 2, 1], [6, 22, 2, 1], [8, 2, 2, 1], [8, 22, 2, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 22, 2, 1], [22, 2, 5, 1], [24, 2, 4, 1], [24, 22, 4, 1], [33, 2, 10, 1], [44, 2, 10, 1], [66, 2, 10, 1], [88, 2, 20, 1], [132, 2, 20, 1], [264, 2, 40, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 264, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 0, 40]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '132.7', 'hash': 32, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [2, 22], 'inner_gens': [[1, 218], [313, 2]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 44, 'inner_split': True, 'inner_tex': 'D_{22}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 4, 'irrep_stats': [[1, 24], [2, 126]], 'label': '528.32', 'linC_count': 40, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 8, 'linQ_dim': 16, 'linQ_dim_count': 8, 'linR_count': 20, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C264:C2', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 22, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 150, 'number_divisions': 22, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 40, 'number_subgroups': 184, 'old_label': None, 'order': 528, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 23], [3, 2], [4, 24], [6, 46], [8, 48], [11, 10], [12, 48], [22, 10], [24, 96], [33, 20], [44, 20], [66, 20], [88, 40], [132, 40], [264, 80]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 10], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[265, 482], [1, 86], [265, 82]], 'outer_group': '40.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 40, 'outer_permdeg': 11, 'outer_perms': [720, 3628800, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{10}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 3], [8, 1], [10, 2], [20, 3], [40, 2], [80, 1]], 'representations': {'PC': {'code': 57041259466494386042887472126000019, 'gens': [1, 2], 'pres': [6, -2, -2, -2, -2, -3, -11, 2617, 31, 7850, 50, 8259, 69, 4804, 118, 17285]}, 'GLFp': {'d': 2, 'p': 109, 'gens': [90651445, 139863133]}, 'Perm': {'d': 22, 'gens': [7426796651898992047, 53902317833844480000, 6706022400, 112177098605924352000, 161058154786873344000, 4364893]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{264}:C_2', 'transitive_degree': 264, 'wreath_data': None, 'wreath_product': False}
