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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '819200000000.bk', 'ambient_counter': 37, 'ambient_order': 819200000000, 'ambient_tex': 'C_5^8.C_2^4.C_2^6.C_2^6.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': None, 'core_order': 100000000, 'counter': 3137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '819200000000.bk.8192._.BP', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8192.BP', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8192.wy', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': False, 'quotient_nilpotent': True, 'quotient_order': 8192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^{10}.D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': None, 'subgroup_order': 100000000, 'subgroup_tex': 'C_5^7.D_{10}.C_2^6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '819200000000.bk', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [408960, 256806603302699520, 17988815703407386989700099324103, 280217387520, 79855162553981242270800, 187770078784, 1046418123176218227238740762341024877382314733, 18315080354504923750785025451616, 304187470334006380589728680671521670496, 17988815623552244375224321174320, 1596967351909063915405745183405624423003490480, 599157138536674425969099896423791998743, 550550123649080654207995376539964704061884103, 180623520023, 1938901255416561016627296, 62762714095992151726279282496061391778121131520], 'label': '819200000000.bk.8192._.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '8192.BP', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8192._.BP', 'subgroup_fusion': None, 'weyl_group': None}
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label None does not appear in gps_groups
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': None, 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': None, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': None, 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 40, 1], [2, 80, 1], [2, 100, 1], [2, 200, 1], [2, 400, 3], [2, 800, 3], [2, 1000, 1], [2, 1250, 1], [2, 1600, 2], [2, 2000, 2], [2, 2500, 1], [2, 4000, 2], [2, 8000, 3], [2, 10000, 2], [2, 16000, 5], [2, 20000, 3], [2, 25000, 1], [2, 32000, 3], [2, 40000, 9], [2, 50000, 2], [2, 62500, 1], [2, 80000, 5], [2, 100000, 2], [2, 125000, 1], [2, 160000, 9], [2, 200000, 3], [2, 250000, 3], [2, 320000, 3], [2, 390625, 1], [2, 400000, 5], [2, 500000, 3], [2, 625000, 1], [2, 640000, 1], [2, 800000, 3], [2, 1000000, 2], [2, 1250000, 1], [4, 100, 2], [4, 200, 3], [4, 400, 2], [4, 1000, 2], [4, 1250, 2], [4, 2000, 9], [4, 2500, 5], [4, 4000, 9], [4, 5000, 9], [4, 8000, 7], [4, 10000, 20], [4, 16000, 4], [4, 20000, 21], [4, 25000, 2], [4, 40000, 31], [4, 50000, 13], [4, 62500, 8], [4, 80000, 25], [4, 100000, 43], [4, 125000, 20], [4, 160000, 12], [4, 200000, 65], [4, 250000, 42], [4, 320000, 4], [4, 390625, 2], [4, 400000, 67], [4, 500000, 63], [4, 625000, 8], [4, 640000, 2], [4, 781250, 3], [4, 800000, 54], [4, 1000000, 96], [4, 1250000, 32], [4, 1562500, 12], [4, 1600000, 28], [4, 2000000, 94], [4, 2500000, 54], [4, 3125000, 21], [4, 3200000, 14], [4, 4000000, 72], [4, 5000000, 84], [4, 6250000, 42], [4, 6400000, 6], [4, 8000000, 37], [4, 10000000, 93], [4, 12500000, 42], [4, 12800000, 1], [4, 16000000, 26], [4, 20000000, 66], [4, 25000000, 51], [4, 25600000, 1], [4, 32000000, 10], [4, 40000000, 36], [4, 50000000, 33], [4, 64000000, 7], [4, 80000000, 18], [4, 100000000, 21], [4, 128000000, 3], [4, 160000000, 6], [4, 200000000, 3], [4, 256000000, 3], [4, 320000000, 1], [4, 400000000, 1], [4, 640000000, 1], [5, 32, 1], [5, 64, 1], [5, 128, 1], [5, 256, 3], [5, 512, 1], [5, 1024, 2], [5, 2048, 1], [5, 4096, 4], [5, 8192, 3], [5, 16384, 5], [5, 32768, 2], [5, 65536, 3], [8, 4000, 4], [8, 20000, 10], [8, 40000, 3], [8, 80000, 6], [8, 160000, 4], [8, 200000, 12], [8, 400000, 26], [8, 800000, 29], [8, 1000000, 30], [8, 1600000, 17], [8, 2000000, 61], [8, 2500000, 12], [8, 3200000, 2], [8, 4000000, 94], [8, 5000000, 12], [8, 8000000, 72], [8, 10000000, 54], [8, 12500000, 30], [8, 16000000, 25], [8, 20000000, 113], [8, 25000000, 39], [8, 32000000, 16], [8, 40000000, 122], [8, 50000000, 75], [8, 64000000, 3], [8, 80000000, 60], [8, 100000000, 94], [8, 128000000, 2], [8, 160000000, 42], [8, 200000000, 105], [8, 320000000, 12], [8, 400000000, 56], [8, 640000000, 11], [8, 800000000, 32], [8, 1280000000, 4], [8, 1600000000, 14], [8, 2560000000, 2], [8, 3200000000, 7], [8, 5120000000, 2], [8, 6400000000, 3], [10, 160, 1], [10, 320, 2], [10, 640, 5], [10, 800, 1], [10, 1280, 3], [10, 1600, 3], [10, 2560, 7], [10, 3200, 8], [10, 4000, 1], [10, 5120, 6], [10, 6400, 12], [10, 8000, 2], [10, 10240, 10], [10, 12800, 18], [10, 16000, 5], [10, 20000, 1], [10, 20480, 10], [10, 25600, 20], [10, 32000, 13], [10, 40000, 2], [10, 40960, 14], [10, 51200, 26], [10, 64000, 23], [10, 80000, 6], [10, 81920, 15], [10, 100000, 1], [10, 102400, 38], [10, 128000, 37], [10, 160000, 17], [10, 163840, 10], [10, 200000, 3], [10, 204800, 32], [10, 256000, 43], [10, 320000, 25], [10, 327680, 9], [10, 400000, 7], [10, 409600, 32], [10, 500000, 1], [10, 512000, 41], [10, 640000, 35], [10, 655360, 4], [10, 800000, 7], [10, 819200, 32], [10, 1000000, 2], [10, 1024000, 52], [10, 1280000, 43], [10, 1600000, 17], [10, 1638400, 18], [10, 2000000, 6], [10, 2048000, 36], [10, 2500000, 1], [10, 2560000, 46], [10, 3200000, 15], [10, 3276800, 9], [10, 4000000, 7], [10, 4096000, 36], [10, 5000000, 1], [10, 5120000, 35], [10, 6400000, 14], [10, 8000000, 4], [10, 8192000, 19], [10, 10240000, 35], [10, 12800000, 12], [10, 16000000, 2], [10, 16384000, 12], [10, 20480000, 22], [10, 25600000, 7], [10, 40960000, 16], [10, 51200000, 3], [10, 81920000, 5], [10, 163840000, 1], [16, 1280000000, 4], [16, 6400000000, 10], [16, 12800000000, 3], [16, 25600000000, 2], [20, 800, 2], [20, 1600, 9], [20, 3200, 11], [20, 4000, 2], [20, 6400, 8], [20, 8000, 9], [20, 12800, 11], [20, 16000, 15], [20, 20000, 2], [20, 25600, 19], [20, 32000, 36], [20, 40000, 13], [20, 51200, 22], [20, 64000, 50], [20, 80000, 51], [20, 100000, 2], [20, 102400, 20], [20, 128000, 63], [20, 160000, 113], [20, 200000, 15], [20, 204800, 23], [20, 256000, 80], [20, 320000, 153], [20, 400000, 62], [20, 409600, 20], [20, 500000, 8], [20, 512000, 87], [20, 640000, 190], [20, 800000, 133], [20, 819200, 8], [20, 1000000, 34], [20, 1024000, 75], [20, 1280000, 190], [20, 1600000, 226], [20, 1638400, 1], [20, 2000000, 81], [20, 2048000, 63], [20, 2500000, 8], [20, 2560000, 213], [20, 3200000, 283], [20, 4000000, 164], [20, 4096000, 37], [20, 5000000, 32], [20, 5120000, 154], [20, 6400000, 290], [20, 8000000, 240], [20, 8192000, 10], [20, 10000000, 54], [20, 10240000, 111], [20, 12800000, 258], [20, 16000000, 238], [20, 16384000, 2], [20, 20000000, 84], [20, 20480000, 56], [20, 25600000, 172], [20, 32000000, 181], [20, 40000000, 93], [20, 40960000, 13], [20, 51200000, 98], [20, 64000000, 123], [20, 80000000, 66], [20, 81920000, 8], [20, 102400000, 52], [20, 128000000, 57], [20, 160000000, 36], [20, 204800000, 20], [20, 256000000, 35], [20, 320000000, 18], [20, 409600000, 7], [20, 512000000, 15], [20, 640000000, 6], [20, 819200000, 4], [20, 1024000000, 11], [20, 1280000000, 1], [20, 2048000000, 5], [20, 2560000000, 1], [20, 4096000000, 3], [40, 16000, 4], [40, 64000, 4], [40, 128000, 4], [40, 256000, 8], [40, 320000, 18], [40, 512000, 12], [40, 640000, 25], [40, 800000, 12], [40, 1024000, 8], [40, 1280000, 35], [40, 1600000, 38], [40, 2048000, 8], [40, 2560000, 37], [40, 3200000, 75], [40, 4096000, 4], [40, 5120000, 50], [40, 6400000, 116], [40, 8000000, 54], [40, 10000000, 12], [40, 10240000, 11], [40, 12800000, 82], [40, 16000000, 163], [40, 20000000, 12], [40, 20480000, 18], [40, 25600000, 107], [40, 32000000, 203], [40, 40000000, 54], [40, 51200000, 34], [40, 64000000, 153], [40, 80000000, 113], [40, 102400000, 20], [40, 128000000, 105], [40, 160000000, 122], [40, 256000000, 29], [40, 320000000, 60], [40, 512000000, 21], [40, 640000000, 42], [40, 1024000000, 6], [40, 1280000000, 12], [40, 2048000000, 1], [40, 2560000000, 11], [40, 5120000000, 4], [40, 10240000000, 2], [40, 20480000000, 2], [80, 5120000000, 4]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '819200000000.bk', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': None, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1'], 'composition_length': 29, 'conjugacy_classes_known': False, 'counter': 37, 'cyclic': False, 'derived_length': 5, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': [[1, 1, 1, 1], [2, 40, 1, 1], [2, 80, 1, 1], [2, 100, 1, 1], [2, 200, 1, 1], [2, 400, 1, 3], [2, 800, 1, 3], [2, 1000, 1, 1], [2, 1250, 1, 1], [2, 1600, 1, 2], [2, 2000, 1, 2], [2, 2500, 1, 1], [2, 4000, 1, 2], [2, 8000, 1, 3], [2, 10000, 1, 2], [2, 16000, 1, 5], [2, 20000, 1, 3], [2, 25000, 1, 1], [2, 32000, 1, 3], [2, 40000, 1, 9], [2, 50000, 1, 2], [2, 62500, 1, 1], [2, 80000, 1, 5], [2, 100000, 1, 2], [2, 125000, 1, 1], [2, 160000, 1, 9], [2, 200000, 1, 3], [2, 250000, 1, 3], [2, 320000, 1, 3], [2, 390625, 1, 1], [2, 400000, 1, 5], [2, 500000, 1, 3], [2, 625000, 1, 1], [2, 640000, 1, 1], [2, 800000, 1, 3], [2, 1000000, 1, 2], [2, 1250000, 1, 1], [4, 100, 2, 1], [4, 200, 1, 1], [4, 200, 2, 1], [4, 400, 1, 2], [4, 1000, 2, 1], [4, 1250, 2, 1], [4, 2000, 1, 1], [4, 2000, 2, 4], [4, 2500, 1, 1], [4, 2500, 2, 2], [4, 4000, 1, 5], [4, 4000, 2, 2], [4, 5000, 1, 3], [4, 5000, 2, 3], [4, 8000, 1, 5], [4, 8000, 2, 1], [4, 10000, 1, 6], [4, 10000, 2, 7], [4, 16000, 1, 4], [4, 20000, 1, 7], 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640000000, 2, 3], [8, 800000000, 1, 10], [8, 800000000, 2, 11], [8, 1280000000, 1, 4], [8, 1600000000, 1, 10], [8, 1600000000, 2, 2], [8, 2560000000, 1, 2], [8, 3200000000, 1, 5], [8, 3200000000, 2, 1], [8, 5120000000, 1, 2], [8, 6400000000, 1, 3], [10, 160, 1, 1], [10, 320, 1, 2], [10, 640, 1, 5], [10, 800, 1, 1], [10, 1280, 1, 3], [10, 1600, 1, 3], [10, 2560, 1, 7], [10, 3200, 1, 8], [10, 4000, 1, 1], [10, 5120, 1, 6], [10, 6400, 1, 12], [10, 8000, 1, 2], [10, 10240, 1, 10], [10, 12800, 1, 18], [10, 16000, 1, 5], [10, 20000, 1, 1], [10, 20480, 1, 10], [10, 25600, 1, 20], [10, 32000, 1, 13], [10, 40000, 1, 2], [10, 40960, 1, 14], [10, 51200, 1, 26], [10, 64000, 1, 23], [10, 80000, 1, 6], [10, 81920, 1, 15], [10, 100000, 1, 1], [10, 102400, 1, 38], [10, 128000, 1, 37], [10, 160000, 1, 17], [10, 163840, 1, 10], [10, 200000, 1, 3], [10, 204800, 1, 32], [10, 256000, 1, 43], [10, 320000, 1, 25], [10, 327680, 1, 9], [10, 400000, 1, 7], [10, 409600, 1, 32], [10, 500000, 1, 1], [10, 512000, 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'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': False, 'metacyclic': False, 'monomial': None, 'name': 'C5^8.C2^4.C2^6.C2^6.C2^5', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 51, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 69, 0, 0, 0, 0, 139, 0, 0, 0, 151, 0, 0, 0, 247, 0, 0, 0, 447, 0, 0, 771, 0, 0, 451, 0, 275, 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'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': 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36494234484792, 20487864320085, 43636490240114, 14966784000143, 1529937920172, 2893578240201, 3101450240230, 723394560259, 118487040288, 113290240317, 314406400346, 45212160375, 32350080404, 11303040433, 1455104491, 1968288520, 189034149, 56515778, 36118367, 19683516, 1381094, 163123, 61906039603228, 178589306552377, 75784192000086, 5235998720115, 13778944000144, 2445762560173, 3272499200202, 1085091840231, 551157760260, 1085091840289, 137789440318, 314870400347, 34447360376, 62570400405, 8611840434, 3633120492, 1688728521, 85446150, 43059779, 15811408, 16887917, 1262195, 841724]}, 'Perm': {'d': 40, 'gens': [251219854706359226335953759091591359774169909744, 106272226996016255620868091293328189157458882516, 815364730064996402493973806809289354392570097446, 376788476681190917074547721924439277486713702933, 584584059649611808195578668707113962168265091724]}}, 'schur_multiplier': None, 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 5, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5^8.C_2^4.C_2^6.C_2^6.C_2^5', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': None}
-
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[3415701612, 1372384777867763196, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 1099504540658219364, 13160704529065404, 2227251], [776196452329421113, 2091831012752434770, 4836323119, 269008239319142400, 494447461210502713, 45237780972039621, 776196453778350109, 776196452359635934, 750167282679811650, 1827603218452219963, 737383278877670451, 13160703092503774], [288173604925795057, 558932552770641272, 513717263489289690, 1978453934, 26072418278542582, 507231458718732579, 249695277050419200, 26072418255206400, 1959915270, 1076860262189383486, 507231460166529618, 249695279012158395], [45237782413726395, 70932026830578274, 288173603484914979, 507231458728194734, 256097827041804579, 513717264937529562, 533259328411020184, 750167282672559043, 288173604945133534, 691924263117993248, 256097827063965538, 513717263496936018], [494447459789961134, 1759698473423541210, 494447462648555365, 776196449449344000, 776196453796197564, 45237780985141787, 507231460168029381, 507231458719819785, 513717263491147311, 1827603218931989101, 737383282275566967, 776196453795060546], [737383280855351644, 2104760860979487282, 763412540547355218, 494447457822796880, 269008240779402980, 288173603484914979, 494447461219924644, 507231457279948880, 507231460146913950, 1038550199122895648, 513717264937529562, 269008240780132444], [750167279803007078, 294703613783433976, 45237780994241782, 776196452341425711, 45237781006215658, 249695281886742319, 494447462646697603, 13160703115758058, 737383282273709323, 1038550197645772088, 26072418289418926, 737383283710633603]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 6442450944, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 1572864.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 1, 4, 1], [2, 2, 3, 2], [2, 2, 6, 1], [2, 2, 16, 1], [2, 4, 12, 1], [2, 4, 96, 1], [2, 8, 6, 1], [2, 8, 12, 1], [2, 8, 16, 1], [2, 8, 48, 1], [2, 16, 2, 1], [2, 16, 24, 1], [2, 32, 1, 1], [2, 64, 1, 1], [4, 8, 48, 1], [4, 16, 6, 1], [4, 16, 24, 1], [4, 16, 48, 1], [4, 32, 3, 1], [4, 32, 12, 2], [4, 64, 3, 1], [4, 64, 4, 1], [4, 128, 12, 1], [4, 256, 2, 1], [8, 256, 6, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 28], [2, 4, 108], [2, 8, 82], [2, 16, 26], [2, 32, 1], [2, 64, 1], [4, 8, 48], [4, 16, 78], [4, 32, 27], [4, 64, 7], [4, 128, 12], [4, 256, 2], [8, 256, 6]], 'center_label': '8.5', 'center_order': 8, 'central_product': None, 'central_quotient': '1024.dia', 'commutator_count': 1, 'commutator_label': '256.55643', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 597, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 28], [2, 4, 1, 108], [2, 8, 1, 82], [2, 16, 1, 26], [2, 32, 1, 1], [2, 64, 1, 1], [4, 8, 1, 48], [4, 16, 1, 78], [4, 32, 1, 27], [4, 64, 1, 7], [4, 128, 1, 12], [4, 256, 1, 2], [8, 256, 1, 6]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': None, 'exponent': 8, 'exponents_of_order': [13], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '256.55643', 'frattini_quotient': '32.51', 'hash': 583603832557243529, 'hyperelementary': 2, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2], 'inner_gens': [[3415701612, 2104760860978762236, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 1827603220889318550, 13160704529065404, 2227251], [494447457833715128, 1372384777867763196, 13160704529065404, 763412539119896678, 1134021, 494447461227208812, 256097827032728070, 26072421151989612, 249695279017955004, 647232745756754432, 256097825603020880, 2227251], [3415701612, 886867527468659076, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 2231996450286268230, 13160704529065404, 2227251], [3415701612, 2104760860978762236, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 1465504277843187564, 13160704529065404, 2227251], [3415701612, 1372384777867763196, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 1099504540660038090, 13160704529065404, 2227251], [3415701612, 1372384777867763196, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 2219149944505612950, 13160704529065404, 2227251], [3415701612, 1372384777867763196, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 1865996713148574324, 13160704529065404, 2227251], [3415701612, 2104760860978762236, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 2231996448377493444, 13160704529065404, 2227251], [3415701612, 1372384777867763196, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 2206449459931795230, 13160704529065404, 2227251], [13160704521444870, 294703613781617294, 494447461227208812, 288173606372218356, 2227251, 13160704529065404, 513717260621273528, 249695279017955004, 26072421151989612, 1099504540658219364, 513717263477320350, 1134021], [3415701612, 886867527468659076, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 1491051264288750750, 13160704529065404, 2227251], [3415701612, 1372384777867763196, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 1099504540660038090, 13160704529065404, 2227251]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 1024, 'inner_split': None, 'inner_tex': 'C_2^7:D_4', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 32], [2, 120], [4, 216], [8, 66]], 'label': '8192.wy', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^10.D4', 'ngens': 12, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [1, 7, 35, 55, 119, 135, 239, 447, 771, 451, 275, 155, 31, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 29, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 434, 'number_divisions': 434, 'number_normal_subgroups': 2722, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 8192, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 1663], [4, 4992], [8, 1536]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 6291456, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': False, 'ratrep_stats': [[1, 32], [2, 120], [4, 216], [8, 66]], 'representations': {'PC': {'code': '29727309218498437082027581886779596488827248641415259081989795200570909623097363789108595848626321662267209454257825968463238486223287752683534', 'gens': [1, 2, 4, 6, 7, 8, 9, 10, 11, 12, 13], 'pres': [13, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 66301, 66, 84398, 10012, 1251, 62624, 13653, 146, 51497, 165989, 127938, 71791, 35924, 189299, 236295, 143124, 17505, 8782, 31832, 107661, 53386, 26723, 347369, 248582, 101955, 51008, 17483, 455544, 62437, 31250]}, 'Perm': {'d': 20, 'gens': [3415701612, 1372384777867763196, 256097825603020880, 269008243663771740, 1134021, 494447461227208812, 256097827032728070, 513717260621273528, 249695279017955004, 1099504540658219364, 13160704529065404, 2227251]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 5, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 4, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^{10}.D_4', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': None}
