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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4, 8, 16, 64], [1, 138, 4, 8, 16, 64], [1, 2, 4, 8, 16, 192], [1, 2, 4, 8, 144, 64], [1, 2, 132, 8, 16, 64], [1, 130, 4, 8, 16, 64], [129, 2, 4, 8, 16, 64], [1, 2, 4, 8, 56, 64], [1, 2, 44, 8, 16, 64], [1, 42, 4, 8, 16, 64], [41, 2, 4, 8, 16, 64], [1, 2, 4, 8, 152, 64], [1, 2, 4, 8, 16, 104], [1, 2, 4, 8, 144, 224], [1, 42, 164, 8, 16, 64], [137, 2, 132, 8, 16, 64]], 'aut_group': None, 'aut_hash': 3946057693156513511, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 32768, 'aut_permdeg': 40, 'aut_perms': [62253486830217823812214039883424196728041477490, 34528300961214088970440281419211347, 34528300961026115284486793616843347, 34528300961214088970430571450406867, 83740161780362771167617505861101244113850406867, 187973685953487802406867, 17507940983102618023828712311885015, 17507940983128577088608766160909015, 20411656176137461649626542458742618949840909015, 25959064782932176909015, 8250311271801328320228501630781170, 17507940983128577088611644488781015, 26039022544809779111574874073817490, 20411656176128204019915320926878359098601477490, 34528300961108372066308837072920893], 'aut_phi_ratio': 256.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 4, 2], [2, 4, 2, 5], [2, 8, 1, 1], [4, 4, 2, 8], [4, 8, 1, 15]], 'aut_supersolvable': True, 'aut_tex': 'C_2^{15}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': None, 'autcent_hash': 3946057693156513511, 'autcent_nilpotent': True, 'autcent_order': 32768, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{15}', '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, 7], [2, 2, 8], [2, 4, 10], [2, 8, 1], [4, 4, 16], [4, 8, 15]], 'center_label': '8.5', 'center_order': 8, 'central_product': False, 'central_quotient': '32.51', 'commutator_count': 1, 'commutator_label': '8.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 30836, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 8], [2, 4, 1, 10], [2, 8, 1, 1], [4, 4, 2, 8], [4, 8, 1, 15]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 9999360, 'exponent': 4, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '32.51', 'hash': 30836, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2, 1, 2, 2], 'inner_gens': [[1, 2, 4, 8, 152, 64], [1, 2, 4, 8, 16, 104], [1, 2, 4, 8, 144, 224], [1, 2, 4, 8, 16, 64], [137, 2, 132, 8, 16, 64], [1, 42, 164, 8, 16, 64]], 'inner_hash': 51, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': None, 'inner_tex': 'C_2^5', 'inner_used': [1, 2, 3, 5, 6], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 16], [4, 10]], 'label': '256.30836', 'linC_count': 512, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 448, 'linQ_dim': 12, 'linQ_dim_count': 448, 'linR_count': 448, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^3.C2^5', 'ngens': 5, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 39, 'number_characteristic_subgroups': 389, 'number_conjugacy_classes': 58, 'number_divisions': 50, 'number_normal_subgroups': 427, 'number_subgroup_autclasses': 921, 'number_subgroup_classes': 1642, 'number_subgroups': 4583, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 71], [4, 184]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 138, 4, 8, 16, 64], [1, 2, 4, 8, 16, 192], [1, 2, 4, 8, 144, 64], [1, 2, 132, 8, 16, 64], [1, 130, 4, 8, 16, 64], [129, 2, 4, 8, 16, 64], [1, 2, 4, 8, 56, 64], [1, 2, 44, 8, 16, 64], [1, 42, 4, 8, 16, 64], [41, 2, 4, 8, 16, 64], [1, 2, 4, 8, 16, 64], [1, 2, 4, 8, 16, 64], [1, 2, 4, 8, 16, 64], [1, 2, 4, 8, 16, 64], [1, 2, 4, 8, 16, 64]], 'outer_group': '1024.djt', 'outer_hash': 1957374279625110839, 'outer_nilpotent': True, 'outer_order': 1024, 'outer_permdeg': 1024, 'outer_perms': 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0, 0, 0, 0, 0], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^{10}', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 24, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [4, 18]], 'representations': {'PC': {'code': 189053800771951928804432, 'gens': [1, 2, 3, 4, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 6084, 1460, 116, 2926, 3158, 166]}, 'Perm': {'d': 24, 'gens': [30565061585856699558891, 57497792735172310983170, 7157856296914278654330, 85884254104388440742789, 411291376991681760000, 17764, 110672728362006644292480, 138670916530467965835364]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3.C_2^5', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
Hide schema
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id: 102078722
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 30836, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
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id: 102078733
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 30836, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
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id: 102078744
{'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 30836, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
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id: 102078755
{'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 30836, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 168, 'size': 1}
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id: 102078766
{'aut_label': '2D', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 30836, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 160, 'size': 1}
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id: 102078776
{'aut_label': '2E', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 30836, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 40, 'size': 1}
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id: 102078777
{'aut_label': '2F', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 30836, 'group_order': 256, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 136, 'size': 1}
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id: 102078778
{'aut_label': '2G', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 30836, 'group_order': 256, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 8, 'size': 1}
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id: 102078779
{'aut_label': '2H', 'centralizer': '2.c1.a1', 'counter': 9, 'group_counter': 30836, 'group_order': 256, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 2, 'size': 2}
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id: 102078723
{'aut_label': '2I', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 30836, 'group_order': 256, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 1, 'size': 2}
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id: 102078724
{'aut_label': '2H', 'centralizer': '2.c1.a1', 'counter': 11, 'group_counter': 30836, 'group_order': 256, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 130, 'size': 2}
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id: 102078725
{'aut_label': '2H', 'centralizer': '2.c1.a1', 'counter': 12, 'group_counter': 30836, 'group_order': 256, 'label': '2K', 'order': 2, 'powers': [1], 'representative': 34, 'size': 2}
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id: 102078726
{'aut_label': '2I', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 30836, 'group_order': 256, 'label': '2L', 'order': 2, 'powers': [1], 'representative': 129, 'size': 2}
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id: 102078727
{'aut_label': '2I', 'centralizer': '2.b1.a1', 'counter': 14, 'group_counter': 30836, 'group_order': 256, 'label': '2M', 'order': 2, 'powers': [1], 'representative': 33, 'size': 2}
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id: 102078728
{'aut_label': '2H', 'centralizer': '2.c1.a1', 'counter': 15, 'group_counter': 30836, 'group_order': 256, 'label': '2N', 'order': 2, 'powers': [1], 'representative': 162, 'size': 2}
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id: 102078729
{'aut_label': '2I', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 30836, 'group_order': 256, 'label': '2O', 'order': 2, 'powers': [1], 'representative': 161, 'size': 2}
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id: 102078730
{'aut_label': '2P', 'centralizer': '4.a1.a1', 'counter': 17, 'group_counter': 30836, 'group_order': 256, 'label': '2P', 'order': 2, 'powers': [1], 'representative': 4, 'size': 4}
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id: 102078731
{'aut_label': '2P', 'centralizer': '4.a1.a1', 'counter': 18, 'group_counter': 30836, 'group_order': 256, 'label': '2Q', 'order': 2, 'powers': [1], 'representative': 12, 'size': 4}
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id: 102078732
{'aut_label': '2R', 'centralizer': '4.a1.a1', 'counter': 19, 'group_counter': 30836, 'group_order': 256, 'label': '2R', 'order': 2, 'powers': [1], 'representative': 6, 'size': 4}
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id: 102078734
{'aut_label': '2S', 'centralizer': '4.a1.a1', 'counter': 20, 'group_counter': 30836, 'group_order': 256, 'label': '2S', 'order': 2, 'powers': [1], 'representative': 5, 'size': 4}
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id: 102078735
{'aut_label': '2T', 'centralizer': '4.a1.a1', 'counter': 21, 'group_counter': 30836, 'group_order': 256, 'label': '2T', 'order': 2, 'powers': [1], 'representative': 3, 'size': 4}
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id: 102078736
{'aut_label': '2R', 'centralizer': '4.a1.a1', 'counter': 22, 'group_counter': 30836, 'group_order': 256, 'label': '2U', 'order': 2, 'powers': [1], 'representative': 38, 'size': 4}
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id: 102078737
{'aut_label': '2S', 'centralizer': '4.a1.a1', 'counter': 23, 'group_counter': 30836, 'group_order': 256, 'label': '2V', 'order': 2, 'powers': [1], 'representative': 133, 'size': 4}
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id: 102078738
{'aut_label': '2T', 'centralizer': '4.a1.a1', 'counter': 24, 'group_counter': 30836, 'group_order': 256, 'label': '2W', 'order': 2, 'powers': [1], 'representative': 131, 'size': 4}
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id: 102078739
{'aut_label': '2X', 'centralizer': '4.a1.a1', 'counter': 25, 'group_counter': 30836, 'group_order': 256, 'label': '2X', 'order': 2, 'powers': [1], 'representative': 7, 'size': 4}
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id: 102078740
{'aut_label': '2X', 'centralizer': '4.a1.a1', 'counter': 26, 'group_counter': 30836, 'group_order': 256, 'label': '2Y', 'order': 2, 'powers': [1], 'representative': 39, 'size': 4}
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id: 102078741
{'aut_label': '2Z', 'centralizer': '8.dp1.a1', 'counter': 27, 'group_counter': 30836, 'group_order': 256, 'label': '2Z', 'order': 2, 'powers': [1], 'representative': 83, 'size': 8}
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id: 102078742
{'aut_label': '4A1', 'centralizer': '4.bz1.a1', 'counter': 28, 'group_counter': 30836, 'group_order': 256, 'label': '4A1', 'order': 4, 'powers': [2], 'representative': 64, 'size': 4}
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id: 102078743
{'aut_label': '4A1', 'centralizer': '4.bz1.a1', 'counter': 29, 'group_counter': 30836, 'group_order': 256, 'label': '4A-1', 'order': 4, 'powers': [2], 'representative': 192, 'size': 4}
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id: 102078745
{'aut_label': '4B1', 'centralizer': '4.x1.a1', 'counter': 30, 'group_counter': 30836, 'group_order': 256, 'label': '4B1', 'order': 4, 'powers': [3], 'representative': 16, 'size': 4}
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id: 102078746
{'aut_label': '4B1', 'centralizer': '4.x1.a1', 'counter': 31, 'group_counter': 30836, 'group_order': 256, 'label': '4B-1', 'order': 4, 'powers': [3], 'representative': 48, 'size': 4}
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id: 102078747
{'aut_label': '4C1', 'centralizer': '4.bw1.a1', 'counter': 32, 'group_counter': 30836, 'group_order': 256, 'label': '4C1', 'order': 4, 'powers': [4], 'representative': 66, 'size': 4}
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id: 102078748
{'aut_label': '4C1', 'centralizer': '4.bw1.a1', 'counter': 33, 'group_counter': 30836, 'group_order': 256, 'label': '4C-1', 'order': 4, 'powers': [4], 'representative': 194, 'size': 4}
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id: 102078749
{'aut_label': '4D1', 'centralizer': '4.ca1.a1', 'counter': 34, 'group_counter': 30836, 'group_order': 256, 'label': '4D1', 'order': 4, 'powers': [2], 'representative': 65, 'size': 4}
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id: 102078750
{'aut_label': '4D1', 'centralizer': '4.ca1.a1', 'counter': 35, 'group_counter': 30836, 'group_order': 256, 'label': '4D-1', 'order': 4, 'powers': [2], 'representative': 193, 'size': 4}
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id: 102078751
{'aut_label': '4E1', 'centralizer': '4.t1.a1', 'counter': 36, 'group_counter': 30836, 'group_order': 256, 'label': '4E1', 'order': 4, 'powers': [4], 'representative': 17, 'size': 4}
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id: 102078752
{'aut_label': '4E1', 'centralizer': '4.t1.a1', 'counter': 37, 'group_counter': 30836, 'group_order': 256, 'label': '4E-1', 'order': 4, 'powers': [4], 'representative': 49, 'size': 4}
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id: 102078753
{'aut_label': '4F1', 'centralizer': '4.bd1.a1', 'counter': 38, 'group_counter': 30836, 'group_order': 256, 'label': '4F1', 'order': 4, 'powers': [5], 'representative': 22, 'size': 4}
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id: 102078754
{'aut_label': '4F1', 'centralizer': '4.bd1.a1', 'counter': 39, 'group_counter': 30836, 'group_order': 256, 'label': '4F-1', 'order': 4, 'powers': [5], 'representative': 54, 'size': 4}
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id: 102078756
{'aut_label': '4G1', 'centralizer': '4.ce1.a1', 'counter': 40, 'group_counter': 30836, 'group_order': 256, 'label': '4G1', 'order': 4, 'powers': [4], 'representative': 67, 'size': 4}
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id: 102078757
{'aut_label': '4G1', 'centralizer': '4.ce1.a1', 'counter': 41, 'group_counter': 30836, 'group_order': 256, 'label': '4G-1', 'order': 4, 'powers': [4], 'representative': 195, 'size': 4}
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id: 102078758
{'aut_label': '4H1', 'centralizer': '4.be1.a1', 'counter': 42, 'group_counter': 30836, 'group_order': 256, 'label': '4H1', 'order': 4, 'powers': [6], 'representative': 23, 'size': 4}
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id: 102078759
{'aut_label': '4H1', 'centralizer': '4.be1.a1', 'counter': 43, 'group_counter': 30836, 'group_order': 256, 'label': '4H-1', 'order': 4, 'powers': [6], 'representative': 55, 'size': 4}
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id: 102078760
{'aut_label': '4I', 'centralizer': '8.dv1.a1', 'counter': 44, 'group_counter': 30836, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [5], 'representative': 80, 'size': 8}
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id: 102078761
{'aut_label': '4J', 'centralizer': '8.x1.a1', 'counter': 45, 'group_counter': 30836, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [3], 'representative': 68, 'size': 8}
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id: 102078762
{'aut_label': '4K', 'centralizer': '8.i1.a1', 'counter': 46, 'group_counter': 30836, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [5], 'representative': 20, 'size': 8}
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id: 102078763
{'aut_label': '4L', 'centralizer': '8.f1.a1', 'counter': 47, 'group_counter': 30836, 'group_order': 256, 'label': '4L', 'order': 4, 'powers': [3], 'representative': 18, 'size': 8}
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id: 102078764
{'aut_label': '4M', 'centralizer': '8.fd1.a1', 'counter': 48, 'group_counter': 30836, 'group_order': 256, 'label': '4M', 'order': 4, 'powers': [2], 'representative': 84, 'size': 8}
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id: 102078765
{'aut_label': '4N', 'centralizer': '8.ec1.a1', 'counter': 49, 'group_counter': 30836, 'group_order': 256, 'label': '4N', 'order': 4, 'powers': [7], 'representative': 82, 'size': 8}
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id: 102078767
{'aut_label': '4O', 'centralizer': '8.bb1.a1', 'counter': 50, 'group_counter': 30836, 'group_order': 256, 'label': '4O', 'order': 4, 'powers': [8], 'representative': 70, 'size': 8}
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id: 102078768
{'aut_label': '4P', 'centralizer': '8.dw1.a1', 'counter': 51, 'group_counter': 30836, 'group_order': 256, 'label': '4P', 'order': 4, 'powers': [6], 'representative': 81, 'size': 8}
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id: 102078769
{'aut_label': '4Q', 'centralizer': '8.x1.a1', 'counter': 52, 'group_counter': 30836, 'group_order': 256, 'label': '4Q', 'order': 4, 'powers': [3], 'representative': 69, 'size': 8}
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id: 102078770
{'aut_label': '4R', 'centralizer': '8.j1.a1', 'counter': 53, 'group_counter': 30836, 'group_order': 256, 'label': '4R', 'order': 4, 'powers': [6], 'representative': 21, 'size': 8}
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id: 102078771
{'aut_label': '4S', 'centralizer': '8.h1.a1', 'counter': 54, 'group_counter': 30836, 'group_order': 256, 'label': '4S', 'order': 4, 'powers': [4], 'representative': 19, 'size': 8}
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id: 102078772
{'aut_label': '4T', 'centralizer': '8.eq1.a1', 'counter': 55, 'group_counter': 30836, 'group_order': 256, 'label': '4T', 'order': 4, 'powers': [4], 'representative': 86, 'size': 8}
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id: 102078773
{'aut_label': '4U', 'centralizer': '8.ez1.a1', 'counter': 56, 'group_counter': 30836, 'group_order': 256, 'label': '4U', 'order': 4, 'powers': [8], 'representative': 85, 'size': 8}
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id: 102078774
{'aut_label': '4V', 'centralizer': '8.bb1.a1', 'counter': 57, 'group_counter': 30836, 'group_order': 256, 'label': '4V', 'order': 4, 'powers': [8], 'representative': 71, 'size': 8}
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id: 102078775
{'aut_label': '4W', 'centralizer': '8.ep1.a1', 'counter': 58, 'group_counter': 30836, 'group_order': 256, 'label': '4W', 'order': 4, 'powers': [3], 'representative': 87, 'size': 8}
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gps_qchar • Show schema
Hide schema
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id: 1085740
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 1085751
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
-
id: 1085762
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1], 'schur_index': 1}
-
id: 1085773
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1], 'schur_index': 1}
-
id: 1085784
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1], 'schur_index': 1}
-
id: 1085786
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1], 'schur_index': 1}
-
id: 1085787
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
-
id: 1085788
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1], 'schur_index': 1}
-
id: 1085789
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
-
id: 1085741
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
-
id: 1085742
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1], 'schur_index': 1}
-
id: 1085743
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1], 'schur_index': 1}
-
id: 1085744
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1], 'schur_index': 1}
-
id: 1085745
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
-
id: 1085746
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1], 'schur_index': 1}
-
id: 1085747
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1], 'schur_index': 1}
-
id: 1085748
{'cdim': 1, 'counter': 17, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1q', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
-
id: 1085749
{'cdim': 1, 'counter': 18, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1r', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1], 'schur_index': 1}
-
id: 1085750
{'cdim': 1, 'counter': 19, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1s', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1], 'schur_index': 1}
-
id: 1085752
{'cdim': 1, 'counter': 20, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1t', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
-
id: 1085753
{'cdim': 1, 'counter': 21, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1u', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1], 'schur_index': 1}
-
id: 1085754
{'cdim': 1, 'counter': 22, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1v', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1], 'schur_index': 1}
-
id: 1085755
{'cdim': 1, 'counter': 23, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1w', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1], 'schur_index': 1}
-
id: 1085756
{'cdim': 1, 'counter': 24, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1x', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
-
id: 1085757
{'cdim': 1, 'counter': 25, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1y', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1], 'schur_index': 1}
-
id: 1085758
{'cdim': 1, 'counter': 26, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1z', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
-
id: 1085759
{'cdim': 1, 'counter': 27, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1aa', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1], 'schur_index': 1}
-
id: 1085760
{'cdim': 1, 'counter': 28, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1ab', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1], 'schur_index': 1}
-
id: 1085761
{'cdim': 1, 'counter': 29, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1ac', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
-
id: 1085763
{'cdim': 1, 'counter': 30, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1ad', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
-
id: 1085764
{'cdim': 1, 'counter': 31, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1ae', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1], 'schur_index': 1}
-
id: 1085765
{'cdim': 1, 'counter': 32, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.1af', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1], 'schur_index': 1}
-
id: 1085766
{'cdim': 2, 'counter': 33, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.2a', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 0, 4, 0, 4, 0, 0, 0, -4, 4, 0, 0, 0, 0, -4, 0, 4, 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], 'schur_index': 1}
-
id: 1085767
{'cdim': 2, 'counter': 34, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.2b', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 0, 4, 0, 4, 0, 0, 0, 4, -4, 0, 0, 0, 0, 4, 0, -4, 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], 'schur_index': 1}
-
id: 1085768
{'cdim': 2, 'counter': 35, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.2c', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, -4, 4, 4, 4, 0, -4, 0, -4, 0, 0, 0, -4, -4, 0, 0, 0, 0, 4, 0, 4, 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], 'schur_index': 1}
-
id: 1085769
{'cdim': 2, 'counter': 36, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.2d', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, -4, 4, 4, 4, 0, -4, 0, -4, 0, 0, 0, 4, 4, 0, 0, 0, 0, -4, 0, -4, 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], 'schur_index': 1}
-
id: 1085770
{'cdim': 2, 'counter': 37, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.2e', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, 4, -4, -4, 4, -4, -4, 4, -4, 4, 4, -4, 4, -4, 4, 0, 0, 0, -4, 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], 'schur_index': 1}
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id: 1085771
{'cdim': 2, 'counter': 38, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.2f', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, 4, -4, -4, 4, -4, -4, 4, 4, 4, -4, -4, -4, 4, -4, 0, 0, 0, 4, 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], 'schur_index': 1}
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id: 1085772
{'cdim': 2, 'counter': 39, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.2g', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, 4, -4, -4, 4, -4, 4, -4, -4, -4, 4, 4, 4, -4, -4, 0, 0, 0, 4, 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], 'schur_index': 1}
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id: 1085774
{'cdim': 2, 'counter': 40, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.2h', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, -4, 4, -4, -4, 4, -4, 4, -4, 4, -4, -4, 4, -4, 4, 4, 0, 0, 0, -4, 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], 'schur_index': 1}
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id: 1085775
{'cdim': 4, 'counter': 41, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.4a', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, -4, -4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 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], 'schur_index': 1}
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id: 1085776
{'cdim': 4, 'counter': 42, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.4b', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, -4, -4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 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], 'schur_index': 1}
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id: 1085777
{'cdim': 4, 'counter': 43, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.4c', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 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], 'schur_index': 1}
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id: 1085778
{'cdim': 4, 'counter': 44, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.4d', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 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], 'schur_index': 1}
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id: 1085779
{'cdim': 4, 'counter': 45, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.4e', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, -4, -4, -4, -4, 4, 0, -4, 0, 4, 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], 'schur_index': 1}
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id: 1085780
{'cdim': 4, 'counter': 46, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.4f', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, -4, -4, -4, 4, -4, 0, 4, 0, -4, 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], 'schur_index': 1}
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id: 1085781
{'cdim': 4, 'counter': 47, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.4g', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, 0, 0, -4, 0, -4, 0, 4, 4, 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], 'schur_index': 1}
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id: 1085782
{'cdim': 4, 'counter': 48, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.4h', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, 0, 0, 4, 0, 4, 0, -4, -4, 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], 'schur_index': 1}
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id: 1085783
{'cdim': 4, 'counter': 49, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.4i', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, 4, -4, -4, 4, -4, -4, 0, 0, -4, 0, 4, 0, -4, 4, 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], 'schur_index': 1}
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id: 1085785
{'cdim': 4, 'counter': 50, 'faithful': False, 'group': '256.30836', 'group_order': 256, 'image': None, 'label': '256.30836.4j', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, 4, -4, -4, 4, -4, -4, 0, 0, 4, 0, -4, 0, 4, -4, 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], 'schur_index': 1}
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gps_char • Show schema
Hide schema
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id: 1484820
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 256, 'label': '256.30836.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 1484839
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 27, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 128, 'label': '256.30836.1aa', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 1484840
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 28, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 128, 'label': '256.30836.1ab', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 1484841
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 29, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 128, 'label': '256.30836.1ac', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 1484843
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 30, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 128, 'label': '256.30836.1ad', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 1484844
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 31, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 128, 'label': '256.30836.1ae', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 1484845
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 32, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 128, 'label': '256.30836.1af', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 1484831
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.bd1.a1', 'kernel_order': 128, 'label': '256.30836.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 1484842
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.be1.a1', 'kernel_order': 128, 'label': '256.30836.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 1484853
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.bb1.a1', 'kernel_order': 128, 'label': '256.30836.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 1484864
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.bc1.a1', 'kernel_order': 128, 'label': '256.30836.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 1484874
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.z1.a1', 'kernel_order': 128, 'label': '256.30836.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 1484875
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.ba1.a1', 'kernel_order': 128, 'label': '256.30836.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 1484876
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.x1.a1', 'kernel_order': 128, 'label': '256.30836.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 1484877
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.y1.a1', 'kernel_order': 128, 'label': '256.30836.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 1484821
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1.a1', 'kernel_order': 128, 'label': '256.30836.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 1484822
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.a1', 'kernel_order': 128, 'label': '256.30836.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 1484823
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.a1', 'kernel_order': 128, 'label': '256.30836.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 1484824
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1.a1', 'kernel_order': 128, 'label': '256.30836.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 1484825
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.n1.a1', 'kernel_order': 128, 'label': '256.30836.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 1484826
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.o1.a1', 'kernel_order': 128, 'label': '256.30836.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 1484827
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.l1.a1', 'kernel_order': 128, 'label': '256.30836.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 1484828
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 17, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.m1.a1', 'kernel_order': 128, 'label': '256.30836.1q', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 1484829
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 18, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.s1.a1', 'kernel_order': 128, 'label': '256.30836.1r', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
-
id: 1484830
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 19, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.r1.a1', 'kernel_order': 128, 'label': '256.30836.1s', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 1484832
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 20, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.q1.a1', 'kernel_order': 128, 'label': '256.30836.1t', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 1484833
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 21, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.p1.a1', 'kernel_order': 128, 'label': '256.30836.1u', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 1484834
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 22, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.w1.a1', 'kernel_order': 128, 'label': '256.30836.1v', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 1484835
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 23, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.v1.a1', 'kernel_order': 128, 'label': '256.30836.1w', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 1484836
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 24, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.u1.a1', 'kernel_order': 128, 'label': '256.30836.1x', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 1484837
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 25, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.t1.a1', 'kernel_order': 128, 'label': '256.30836.1y', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 1484838
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 26, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 128, 'label': '256.30836.1z', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 1484846
{'center': '4.br1.a1', 'center_index': 4, 'center_order': 64, 'counter': 33, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bf1.b1', 'kernel_order': 16, 'label': '256.30836.2a1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 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]]]}
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id: 1484847
{'center': '4.br1.a1', 'center_index': 4, 'center_order': 64, 'counter': 34, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bf1.b1', 'kernel_order': 16, 'label': '256.30836.2a2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 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]]]}
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id: 1484848
{'center': '4.br1.a1', 'center_index': 4, 'center_order': 64, 'counter': 35, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bf1.a1', 'kernel_order': 16, 'label': '256.30836.2b1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 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]]]}
-
id: 1484849
{'center': '4.br1.a1', 'center_index': 4, 'center_order': 64, 'counter': 36, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bf1.a1', 'kernel_order': 16, 'label': '256.30836.2b2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 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]]]}
-
id: 1484850
{'center': '4.br1.a1', 'center_index': 4, 'center_order': 64, 'counter': 37, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bf1.c1', 'kernel_order': 16, 'label': '256.30836.2c1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 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]]]}
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id: 1484851
{'center': '4.br1.a1', 'center_index': 4, 'center_order': 64, 'counter': 38, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bf1.c1', 'kernel_order': 16, 'label': '256.30836.2c2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 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]]]}
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id: 1484852
{'center': '4.br1.a1', 'center_index': 4, 'center_order': 64, 'counter': 39, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bf1.d1', 'kernel_order': 16, 'label': '256.30836.2d1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 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]]]}
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id: 1484854
{'center': '4.br1.a1', 'center_index': 4, 'center_order': 64, 'counter': 40, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bf1.d1', 'kernel_order': 16, 'label': '256.30836.2d2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 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]]]}
-
id: 1484855
{'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 41, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bg1.c1', 'kernel_order': 16, 'label': '256.30836.2e1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 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]]]}
-
id: 1484856
{'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 42, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bg1.c1', 'kernel_order': 16, 'label': '256.30836.2e2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 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]]]}
-
id: 1484857
{'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 43, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bg1.a1', 'kernel_order': 16, 'label': '256.30836.2f1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 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]]]}
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id: 1484858
{'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 44, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bg1.a1', 'kernel_order': 16, 'label': '256.30836.2f2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 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]]]}
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id: 1484859
{'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 45, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bg1.d1', 'kernel_order': 16, 'label': '256.30836.2g1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 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]]]}
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id: 1484860
{'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 46, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bg1.d1', 'kernel_order': 16, 'label': '256.30836.2g2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 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]]]}
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id: 1484861
{'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 47, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bg1.b1', 'kernel_order': 16, 'label': '256.30836.2h1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 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]]]}
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id: 1484862
{'center': '4.c1.a1', 'center_index': 4, 'center_order': 64, 'counter': 48, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.bg1.b1', 'kernel_order': 16, 'label': '256.30836.2h2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 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]]]}
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id: 1484863
{'center': '16.e1.a1', 'center_index': 16, 'center_order': 16, 'counter': 49, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.i1.b1', 'kernel_order': 8, 'label': '256.30836.4a', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 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]], [[-4, 0]], [[0, 0]], [[4, 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]]]}
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id: 1484865
{'center': '16.e1.a1', 'center_index': 16, 'center_order': 16, 'counter': 50, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.i1.a1', 'kernel_order': 8, 'label': '256.30836.4b', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 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]], [[4, 0]], [[0, 0]], [[-4, 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]]]}
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id: 1484866
{'center': '16.c1.a1', 'center_index': 16, 'center_order': 16, 'counter': 51, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.b1.a1', 'kernel_order': 8, 'label': '256.30836.4c', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 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]]]}
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id: 1484867
{'center': '16.c1.a1', 'center_index': 16, 'center_order': 16, 'counter': 52, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.b1.b1', 'kernel_order': 8, 'label': '256.30836.4d', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 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]]]}
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id: 1484868
{'center': '16.b1.a1', 'center_index': 16, 'center_order': 16, 'counter': 53, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.g1.b1', 'kernel_order': 8, 'label': '256.30836.4e', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 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, 0]], [[0, 0]]]}
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id: 1484869
{'center': '16.b1.a1', 'center_index': 16, 'center_order': 16, 'counter': 54, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.g1.a1', 'kernel_order': 8, 'label': '256.30836.4f', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 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, 0]], [[0, 0]]]}
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id: 1484870
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 55, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.c1.b1', 'kernel_order': 8, 'label': '256.30836.4g', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 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]]]}
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id: 1484871
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 56, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.c1.a1', 'kernel_order': 8, 'label': '256.30836.4h', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[-4, 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]]]}
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id: 1484872
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 57, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.h1.b1', 'kernel_order': 8, 'label': '256.30836.4i', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[4, 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]]]}
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id: 1484873
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 58, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.30836', 'group_counter': 30836, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.h1.a1', 'kernel_order': 8, 'label': '256.30836.4j', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 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]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 30878216
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.30836.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.30836', 'subgroup_hash': 30836, 'subgroup_order': 256, 'subgroup_tex': 'C_2^3.C_2^5', 'supersolvable': True, 'sylow': 2}
-
id: 30878970
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879081
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879192
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1009', 'subgroup_hash': 1009, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879303
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1090', 'subgroup_hash': 1090, 'subgroup_order': 128, 'subgroup_tex': 'C_2.D_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879414
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1144', 'subgroup_hash': 1144, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879525
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1074', 'subgroup_hash': 1074, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879636
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1169', 'subgroup_hash': 1169, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879747
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.h1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1266', 'subgroup_hash': 1266, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30878217
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.i1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1204', 'subgroup_hash': 1204, 'subgroup_order': 128, 'subgroup_tex': 'C_2.D_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878328
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.j1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1212', 'subgroup_hash': 1212, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30878439
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.k1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1214', 'subgroup_hash': 1214, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30878550
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.l1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1150', 'subgroup_hash': 1150, 'subgroup_order': 128, 'subgroup_tex': 'C_2.D_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878661
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.m1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1143', 'subgroup_hash': 1143, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30878772
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.n1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1293', 'subgroup_hash': 1293, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30878883
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.o1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1212', 'subgroup_hash': 1212, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30878937
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.p1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1204', 'subgroup_hash': 1204, 'subgroup_order': 128, 'subgroup_tex': 'C_2.D_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878948
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.q1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1150', 'subgroup_hash': 1150, 'subgroup_order': 128, 'subgroup_tex': 'C_2.D_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878959
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.r1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1212', 'subgroup_hash': 1212, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30878971
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.s1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1212', 'subgroup_hash': 1212, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30878982
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.t1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1354', 'subgroup_hash': 1354, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878993
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.u1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1053', 'subgroup_hash': 1053, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879004
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.v1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1044', 'subgroup_hash': 1044, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879015
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.w1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1358', 'subgroup_hash': 1358, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879026
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.x1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1417', 'subgroup_hash': 1417, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879037
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.y1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1416', 'subgroup_hash': 1416, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879048
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.z1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1467', 'subgroup_hash': 1467, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879059
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.ba1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1467', 'subgroup_hash': 1467, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879070
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.bb1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1417', 'subgroup_hash': 1417, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879082
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.bc1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1429', 'subgroup_hash': 1429, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879093
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.bd1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1468', 'subgroup_hash': 1468, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879104
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.2.be1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1467', 'subgroup_hash': 1467, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879115
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
-
id: 30879126
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879137
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879148
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879159
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879170
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879181
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879193
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879204
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879215
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879226
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879237
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879248
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879259
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879270
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879281
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879292
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879304
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879315
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879326
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.196', 'subgroup_hash': 196, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879337
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879348
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879359
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.205', 'subgroup_hash': 205, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879370
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.58', 'subgroup_hash': 58, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879381
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.61', 'subgroup_hash': 61, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879392
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.62', 'subgroup_hash': 62, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879403
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.66', 'subgroup_hash': 66, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879415
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.204', 'subgroup_hash': 204, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879426
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.66', 'subgroup_hash': 66, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879437
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.58', 'subgroup_hash': 58, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879448
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.195', 'subgroup_hash': 195, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879459
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.61', 'subgroup_hash': 61, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879470
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.66', 'subgroup_hash': 66, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879481
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.66', 'subgroup_hash': 66, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879492
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.62', 'subgroup_hash': 62, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879503
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879514
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879526
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879537
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879548
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879559
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879570
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879581
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879592
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879603
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879614
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879625
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879637
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879648
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.196', 'subgroup_hash': 196, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879659
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879670
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879681
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.58', 'subgroup_hash': 58, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879692
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.58', 'subgroup_hash': 58, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879703
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.66', 'subgroup_hash': 66, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879714
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.66', 'subgroup_hash': 66, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879725
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.61', 'subgroup_hash': 61, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879736
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.58', 'subgroup_hash': 58, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879748
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.66', 'subgroup_hash': 66, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879759
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.66', 'subgroup_hash': 66, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879770
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.61', 'subgroup_hash': 61, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879781
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.61', 'subgroup_hash': 61, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879792
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.204', 'subgroup_hash': 204, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879803
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.66', 'subgroup_hash': 66, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879814
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879825
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 97, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879836
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 98, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879847
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 99, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878218
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 100, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878229
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 101, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878240
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878251
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878262
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878273
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.207', 'subgroup_hash': 207, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878284
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 106, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.209', 'subgroup_hash': 209, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878295
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 107, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878306
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 108, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878317
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 109, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878329
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 110, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.cz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878340
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.da1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878351
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 112, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.db1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.77', 'subgroup_hash': 77, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878362
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878373
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878384
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 115, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.de1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.80', 'subgroup_hash': 80, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878395
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.df1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878406
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878417
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878428
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.di1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878440
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878451
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 121, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878462
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 64, 'counter': 122, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878473
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 123, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878484
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 124, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878495
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 125, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.do1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.71', 'subgroup_hash': 71, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878506
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 126, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878517
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 127, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878528
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 128, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878539
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 129, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ds1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878551
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 130, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878562
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 131, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.du1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878573
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 132, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 133, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.77', 'subgroup_hash': 77, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878595
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 134, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.77', 'subgroup_hash': 77, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878606
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 135, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878617
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 136, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.dz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878628
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 137, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ea1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878639
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 138, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.eb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.eb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.80', 'subgroup_hash': 80, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878650
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 139, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ec1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ec1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.74', 'subgroup_hash': 74, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878662
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 140, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ed1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ed1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878673
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 141, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ee1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ee1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878684
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 142, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ef1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ef1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.205', 'subgroup_hash': 205, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878695
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 143, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.eg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.eg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.71', 'subgroup_hash': 71, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878706
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 144, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.eh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.eh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878717
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 145, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ei1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ei1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878728
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 146, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ej1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ej1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.74', 'subgroup_hash': 74, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878739
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 147, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ek1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ek1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878750
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 148, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.el1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.el1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.77', 'subgroup_hash': 77, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878761
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 149, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.em1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.em1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878773
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 150, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.en1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.en1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878784
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 151, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.eo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.eo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878795
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 152, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ep1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ep1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878806
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 153, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.eq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.eq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878817
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 154, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.er1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.er1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.209', 'subgroup_hash': 209, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878828
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 155, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.es1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.es1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878839
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 156, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.et1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.et1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.71', 'subgroup_hash': 71, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878850
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 157, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.eu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.eu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878861
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 158, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ev1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ev1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878872
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 159, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ew1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ew1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878884
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 160, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ex1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ex1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878895
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 161, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ey1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ey1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878906
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 162, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ez1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ez1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878917
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 163, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fa1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fa1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878928
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 164, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.80', 'subgroup_hash': 80, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878932
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 165, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.77', 'subgroup_hash': 77, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878933
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 166, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878934
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 167, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fe1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fe1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878935
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 168, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ff1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ff1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.77', 'subgroup_hash': 77, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878936
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 169, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.74', 'subgroup_hash': 74, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878938
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 170, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878939
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 171, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878940
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 172, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878941
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 173, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.71', 'subgroup_hash': 71, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878942
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 174, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.67', 'subgroup_hash': 67, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878943
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 175, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878944
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 176, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878945
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 177, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878946
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 178, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878947
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 179, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878949
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 180, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878950
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 181, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.74', 'subgroup_hash': 74, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878951
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 182, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.ft1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ft1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.80', 'subgroup_hash': 80, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878952
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 183, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878953
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 184, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.78', 'subgroup_hash': 78, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878954
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 185, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878955
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 186, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.77', 'subgroup_hash': 77, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878956
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 187, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.4.fy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.fy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.77', 'subgroup_hash': 77, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878957
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 188, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30878958
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 189, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30878960
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 190, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30878961
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 191, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878962
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 192, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878963
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 193, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878964
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 194, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878965
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 195, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878966
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 196, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878967
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 197, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878968
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 198, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878969
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 199, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878972
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 200, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878973
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 201, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878974
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 202, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878975
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 203, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30878976
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 204, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30878977
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 205, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878978
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 206, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878979
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 207, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878980
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 208, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878981
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 209, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878983
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 210, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878984
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 211, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878985
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 212, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878986
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 213, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878987
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 214, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878988
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 215, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878989
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 216, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878990
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 217, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30878991
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 218, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878992
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 219, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878994
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 220, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878995
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 221, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878996
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 222, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878997
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 223, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878998
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 224, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878999
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 225, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879000
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 226, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879001
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 227, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879002
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 228, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879003
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 229, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879005
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 32, 'counter': 230, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879006
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 231, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879007
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 232, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879008
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 233, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879009
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 234, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879010
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 235, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879011
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 236, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879012
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 237, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879013
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 238, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879014
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 239, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879016
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 240, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879017
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 241, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879018
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 242, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879019
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 243, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 30879020
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 244, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879021
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 245, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879022
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 246, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879023
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 247, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879024
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 248, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879025
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 249, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879027
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 250, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879028
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 251, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879029
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 252, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879030
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 253, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879031
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 254, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879032
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 255, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879033
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 256, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879034
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 257, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879035
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 258, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879036
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 259, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879038
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 260, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879039
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 261, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879040
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 262, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879041
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 263, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879042
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 264, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879043
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 265, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.cz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879044
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 266, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.da1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879045
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 267, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.db1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879046
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 268, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879047
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 269, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879049
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 270, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.de1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879050
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 271, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.df1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879051
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 272, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879052
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 273, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879053
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 274, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.di1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879054
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 275, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879055
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 276, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879056
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 277, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879057
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 278, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879058
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 279, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879060
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 280, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.do1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879061
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 281, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879062
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 282, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879063
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 283, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879064
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 284, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ds1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879065
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 285, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879066
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 286, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.du1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879067
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 287, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879068
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 288, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879069
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 289, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879071
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 290, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879072
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 291, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.dz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879073
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 292, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ea1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879074
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 293, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.eb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.eb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879075
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 294, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ec1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ec1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879076
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 295, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ed1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ed1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879077
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 296, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ee1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ee1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879078
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 297, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ef1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ef1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879079
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 298, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.eg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.eg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879080
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 299, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.eh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.eh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879083
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 300, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ei1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ei1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879084
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 301, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ej1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ej1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879085
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 302, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ek1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ek1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879086
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 303, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.el1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.el1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879087
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 304, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.em1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.em1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879088
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 305, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.en1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.en1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879089
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 306, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.eo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.eo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879090
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 307, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ep1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ep1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879091
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 308, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.eq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.eq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879092
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 309, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.er1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.er1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879094
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 310, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.es1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.es1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879095
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 311, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.et1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.et1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879096
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 312, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.eu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.eu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879097
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 313, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ev1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ev1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879098
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 314, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ew1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ew1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879099
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 315, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ex1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ex1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879100
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 316, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ey1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ey1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879101
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 317, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ez1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ez1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879102
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 318, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fa1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fa1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879103
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 319, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879105
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 320, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879106
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 321, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879107
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 322, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fe1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fe1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879108
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 323, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ff1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ff1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879109
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 324, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879110
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 32, 'counter': 325, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879111
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 326, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879112
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 327, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879113
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 328, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879114
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 329, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879116
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 330, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879117
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 331, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879118
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 332, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879119
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 333, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879120
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 334, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879121
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 335, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879122
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 336, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879123
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 337, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.ft1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.ft1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879124
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 338, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879125
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 339, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879127
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 340, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879128
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 341, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879129
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 32, 'counter': 342, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.8.fy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.fy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879130
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.fz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.fz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879131
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.fz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.fz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879132
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.ga1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ga1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879133
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.ga1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ga1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879134
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879135
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879136
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879138
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879139
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879140
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879141
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.ge1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ge1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879142
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.ge1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ge1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879143
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879144
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879145
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879146
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879147
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879149
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879150
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879151
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879152
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879153
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879154
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879155
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879156
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879157
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879158
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gl1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gl1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879160
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gl1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gl1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879161
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879162
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879163
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gm1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gm1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879164
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gm1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gm1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879165
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879166
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879167
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gn1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gn1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879168
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gn1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gn1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879169
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.go1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.go1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879171
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.go1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.go1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879172
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879173
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879174
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879175
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879176
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879177
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gr1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879178
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879179
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879180
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879182
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879183
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879184
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879185
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879186
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879187
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879188
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879189
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879190
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879191
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879194
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gy1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879195
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879196
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.gz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.gz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879197
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.ha1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ha1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879198
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.ha1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.ha1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879199
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879200
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879201
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879202
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879203
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879205
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879206
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.he1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.he1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879207
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.he1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.he1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879208
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879209
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879210
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879211
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879212
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hg1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hg1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879213
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hg1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hg1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 30879214
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879216
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879217
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hh1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hh1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879218
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hh1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hh1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30879219
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879220
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879221
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hi1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hi1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879222
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.8.hi1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.hi1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879223
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 427, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879224
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 428, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879225
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 429, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879227
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 430, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879228
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 431, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879229
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 432, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879230
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 433, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879231
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 434, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879232
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 435, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879233
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 436, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879234
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 437, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879235
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 438, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879236
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 439, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879238
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 440, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879239
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 441, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879240
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 16, 'counter': 442, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879241
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 443, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879242
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 444, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879243
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 445, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879244
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 446, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879245
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 447, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879246
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 448, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879247
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 449, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879249
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 450, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879250
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 451, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879251
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 452, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879252
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 453, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879253
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 454, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879254
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 455, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879255
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 456, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879256
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 457, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879257
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 458, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879258
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 459, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879260
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 460, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bf1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bf1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879261
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 461, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bf1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bf1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879262
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 462, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879263
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 463, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879264
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 464, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bg1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bg1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879265
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 465, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.16.bg1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.bg1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879266
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879267
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879268
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879269
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879271
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879272
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879273
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879274
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879275
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879276
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879277
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879278
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879279
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879280
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879282
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879283
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879284
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879285
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879286
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879287
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879288
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879289
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879290
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879291
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879293
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879294
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879295
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879296
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879297
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879298
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879299
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879300
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879301
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879302
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879305
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879306
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879307
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879308
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879309
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879310
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879311
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879312
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879313
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879314
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.co1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.co1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879316
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879317
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879318
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879319
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879320
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879321
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cr1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879322
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879323
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879324
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879325
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ct1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ct1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879327
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879328
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879329
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879330
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879331
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879332
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879333
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879334
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879335
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.cz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879336
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.da1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879338
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.db1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879339
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879340
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879341
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.de1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879342
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.df1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879343
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879344
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879345
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.di1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879346
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879347
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879349
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879350
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879351
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879352
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.do1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879353
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879354
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879355
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879356
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ds1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879357
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879358
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.du1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879360
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879361
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879362
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879363
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879364
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879365
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879366
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879367
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dy1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879368
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879369
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.dz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.dz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879371
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ea1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879372
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ea1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ea1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879373
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879374
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879375
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ec1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ec1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879376
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ec1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ec1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879377
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ed1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ed1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879378
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ed1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ed1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879379
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ee1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ee1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879380
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ee1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ee1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879382
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ef1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ef1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879383
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ef1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ef1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879384
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879385
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879386
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879387
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879388
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ei1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ei1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879389
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ei1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ei1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879390
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ej1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ej1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879391
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ej1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ej1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879393
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ek1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ek1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879394
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ek1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ek1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879395
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.el1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.el1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879396
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.el1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.el1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879397
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.em1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.em1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879398
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.em1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.em1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879399
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879400
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879401
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879402
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879404
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879405
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879406
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879407
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879408
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879409
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879410
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879411
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879412
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.m1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879413
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.n1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879416
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.o1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879417
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.en1.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.en1.p1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879418
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879419
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879420
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ep1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ep1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879421
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879422
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.er1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.er1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879423
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.es1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.es1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879424
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.et1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.et1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879425
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.et1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.et1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879427
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879428
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.eu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.eu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879429
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ev1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ev1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879430
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ev1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ev1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879431
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ew1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ew1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879432
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ew1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ew1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879433
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ex1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ex1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879434
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ex1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ex1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879435
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ey1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ey1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879436
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ey1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ey1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879438
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ez1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ez1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879439
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ez1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ez1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879440
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fa1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fa1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879441
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fa1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fa1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879442
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879443
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879444
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879445
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fe1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fe1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879446
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ff1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ff1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879447
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879449
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879450
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879451
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879452
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879453
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879454
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879455
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879456
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879457
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879458
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879460
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879461
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879462
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ft1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ft1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879463
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879464
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879465
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879466
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879467
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879468
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879469
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879471
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879472
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fy1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879473
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879474
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.fz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.fz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879475
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ga1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ga1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879476
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ga1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ga1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879477
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879478
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879479
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879480
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879482
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879483
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879484
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ge1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ge1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879485
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879486
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879487
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879488
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879489
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879490
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879491
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879493
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879494
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879495
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.go1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.go1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879496
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879497
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879498
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879499
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879500
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879501
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879502
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879504
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879505
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879506
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879507
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.gz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.gz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879508
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ha1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ha1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30879509
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879510
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879511
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879512
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879513
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879515
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879516
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 30879517
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879518
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879519
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879520
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.e2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879521
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879522
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.f2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879523
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879524
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.g2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879527
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879528
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hc1.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hc1.h2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879529
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879530
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.he1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.he1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879531
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879532
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879533
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879534
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879535
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879536
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879538
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879539
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879540
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879541
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879542
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879543
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ho1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ho1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879544
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879545
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879546
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879547
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879549
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879550
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879551
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ht1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ht1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879552
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ht1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ht1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879553
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879554
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879555
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879556
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879557
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879558
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879560
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879561
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879562
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879563
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.hz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.hz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879564
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ia1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ia1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879565
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ib1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ib1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879566
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ic1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ic1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879567
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.id1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.id1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879568
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ie1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ie1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879569
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.if1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.if1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879571
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ig1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ig1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 30879572
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ih1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ih1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879573
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ii1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ii1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879574
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ij1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ij1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879575
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879576
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879577
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879578
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879579
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879580
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879582
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879583
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879584
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879585
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.e2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879586
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879587
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.f2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879588
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879589
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.g2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879590
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879591
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ik1.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ik1.h2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879593
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.il1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.il1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879594
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.il1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.il1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879595
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.im1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.im1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879596
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.im1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.im1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879597
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.in1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.in1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879598
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.in1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.in1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879599
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.io1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.io1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879600
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.io1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.io1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879601
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ip1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ip1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879602
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ip1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ip1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879604
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879605
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879606
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ir1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ir1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879607
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ir1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ir1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879608
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.is1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.is1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879609
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.is1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.is1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879610
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.it1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.it1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879611
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.it1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.it1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879612
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879613
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879615
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879616
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879617
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879618
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879619
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ix1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ix1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879620
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ix1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ix1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879621
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879622
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iy1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879623
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879624
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.iz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.iz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879626
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ja1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ja1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879627
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.ja1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.ja1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879628
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879629
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879630
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879631
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879632
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879633
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879634
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879635
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879638
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879639
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879640
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879641
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879642
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879643
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879644
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879645
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879646
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.m1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879647
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.n1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879649
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.o1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879650
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jd1.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jd1.p1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879651
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879652
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879653
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879654
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879655
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879656
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879657
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879658
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879660
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879661
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.e2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879662
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879663
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.f2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879664
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879665
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.g2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879666
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879667
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.je1.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.je1.h2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879668
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879669
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879671
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879672
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879673
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879674
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879675
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879676
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879677
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879678
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879679
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879680
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879682
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.m1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879683
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.n1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879684
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.o1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879685
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jf1.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jf1.p1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879686
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879687
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879688
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879689
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879690
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879691
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879693
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879694
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879695
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879696
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879697
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879698
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879699
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.m1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879700
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.n1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879701
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.o1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879702
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.16.jg1.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.jg1.p1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 30879704
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 860, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.51', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^5', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'D', 'Phi', 'S', 'U1', 'L1', 'D1', 'C5'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879705
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 861, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879706
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 862, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879707
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 863, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879708
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 864, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879709
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 865, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879710
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 866, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879711
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 867, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879712
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 868, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879713
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 869, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879715
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 870, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879716
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 871, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879717
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 872, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879718
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 873, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879719
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 874, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879720
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 875, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879721
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 876, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879722
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 877, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879723
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 878, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879724
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 879, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879726
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 880, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879727
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 881, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879728
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 882, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.32.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879729
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879730
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879731
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879732
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879733
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879734
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879735
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879737
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879738
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879739
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879740
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879741
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879742
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879743
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879744
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879745
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879746
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879749
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879750
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879751
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879752
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879753
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879754
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879755
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879756
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879757
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879758
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879760
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879761
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879762
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879763
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879764
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879765
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879766
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879767
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879768
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879769
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879771
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879772
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879773
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879774
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879775
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879776
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879777
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879778
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879779
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879780
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879782
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879783
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879784
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ci1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ci1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879785
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ci1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ci1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879786
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ci1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ci1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879787
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879788
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879789
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cj1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879790
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cj1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879791
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cj1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879793
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cj1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879794
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cj1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879795
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cj1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cj1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879796
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879797
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ck1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ck1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879798
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ck1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ck1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879799
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 946, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ck1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ck1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879800
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879801
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879802
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cl1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cl1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879804
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cl1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cl1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879805
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879806
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879807
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cm1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cm1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879808
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cm1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cm1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879809
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879810
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879811
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879812
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.co1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.co1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879813
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.co1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.co1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879815
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.co1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.co1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879816
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879817
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cp1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cp1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879818
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879819
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cp1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cp1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879820
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879821
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879822
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879823
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879824
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879826
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879827
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879828
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879829
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879830
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879831
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.cz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879832
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.da1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879833
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.db1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879834
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879835
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879837
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.de1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879838
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.df1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879839
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879840
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879841
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.di1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879842
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879843
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879844
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879845
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879846
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879848
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.do1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879849
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30879850
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879851
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879852
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ds1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879853
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879854
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.du1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879855
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879856
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30879857
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878219
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878220
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.dz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878221
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ea1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878222
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878223
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878224
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eb1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eb1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878225
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eb1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eb1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878226
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ec1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ec1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878227
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ec1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ec1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878228
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ec1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ec1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878230
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ec1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ec1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878231
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ed1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ed1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878232
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ed1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ed1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878233
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ed1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ed1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878234
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ed1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ed1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878235
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ee1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ee1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878236
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ee1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ee1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878237
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ef1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ef1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878238
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ef1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ef1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878239
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ef1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ef1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878241
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ef1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ef1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878242
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878243
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eg1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878244
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878245
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eg1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eg1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878246
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878247
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878248
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ei1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ei1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878249
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ei1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ei1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878250
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ei1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ei1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878252
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ei1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ei1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878253
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ej1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ej1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878254
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ej1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ej1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878255
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ek1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ek1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878256
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ek1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ek1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878257
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ek1.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ek1.a3', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878258
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ek1.a4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ek1.a4', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878259
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.el1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.el1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878260
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.el1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.el1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 30878261
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.em1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.em1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878263
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.en1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.en1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878264
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878265
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ep1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ep1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878266
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878267
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.er1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.er1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878268
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.es1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.es1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878269
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.et1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.et1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878270
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.eu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.eu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878271
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ev1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ev1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878272
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ew1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ew1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878274
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ex1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ex1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878275
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ey1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ey1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878276
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ez1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ez1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878277
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fa1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fa1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878278
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878279
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878280
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878281
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fe1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fe1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878282
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fe1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fe1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878283
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fe1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fe1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878285
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fe1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fe1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878286
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ff1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ff1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878287
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ff1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ff1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878288
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ff1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ff1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878289
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ff1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ff1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878290
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878291
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878292
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fg1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fg1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878293
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fg1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fg1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878294
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878296
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878297
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878298
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878299
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fi1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fi1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878300
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fi1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fi1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878301
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878302
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fj1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fj1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878303
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878304
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fj1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fj1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878305
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878307
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878308
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878309
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fl1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fl1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878310
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fl1.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fl1.a3', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878311
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fl1.a4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fl1.a4', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878312
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878313
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fm1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fm1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878314
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878315
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fm1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fm1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878316
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 30878318
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878319
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878320
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fo1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fo1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878321
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878322
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878323
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878324
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878325
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ft1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ft1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878326
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878327
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878330
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878331
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878332
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878333
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.fz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.fz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878334
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ga1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ga1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878335
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878336
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878337
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gb1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gb1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878338
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gb1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gb1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878339
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878341
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878342
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gc1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gc1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878343
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gc1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gc1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878344
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878345
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878346
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878347
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878348
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ge1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ge1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878349
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ge1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ge1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878350
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878352
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878353
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gf1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gf1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878354
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gf1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gf1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878355
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gf1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gf1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878356
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gf1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gf1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878357
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gf1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gf1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878358
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gf1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gf1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878359
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878360
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gg1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878361
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878363
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gg1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gg1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878364
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878365
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878366
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gh1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gh1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878367
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gh1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gh1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878368
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878369
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878370
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gi1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gi1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878371
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gi1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gi1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878372
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878374
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878375
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878376
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878377
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gk1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gk1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878378
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gk1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gk1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878379
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gk1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gk1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878380
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gk1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gk1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878381
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gk1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gk1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878382
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gk1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gk1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878383
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878385
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878386
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gl1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gl1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878387
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gl1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gl1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878388
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878389
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878390
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gm1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gm1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878391
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gm1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gm1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878392
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878393
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878394
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gn1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gn1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878396
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gn1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gn1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878397
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.go1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.go1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878398
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.go1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.go1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878399
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.go1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.go1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878400
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.go1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.go1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878401
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878402
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gp1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gp1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878403
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878404
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gp1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gp1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878405
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878407
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gq1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gq1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878408
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878409
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gq1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gq1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878410
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878411
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gr1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gr1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878412
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gr1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878413
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gr1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gr1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878414
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878415
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gs1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gs1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878416
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878418
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gs1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gs1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878419
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878420
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878421
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gt1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gt1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878422
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gt1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gt1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878423
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gt1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gt1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878424
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gt1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gt1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878425
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gt1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gt1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878426
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gt1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gt1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878427
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878429
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878430
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gu1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gu1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878431
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gu1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gu1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878432
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878433
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878434
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gv1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gv1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878435
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gv1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gv1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878436
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878437
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878438
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gw1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gw1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878441
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gw1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gw1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878442
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878443
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878444
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gx1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gx1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878445
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gx1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gx1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878446
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gx1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gx1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878447
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gx1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gx1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878448
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gx1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gx1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878449
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gx1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gx1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878450
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878452
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gy1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878453
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gy1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gy1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878454
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gy1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gy1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878455
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878456
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878457
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gz1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gz1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878458
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.gz1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.gz1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878459
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ha1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ha1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878460
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ha1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ha1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878461
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ha1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ha1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878463
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.ha1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.ha1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878464
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878465
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878466
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hb1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hb1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878467
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hb1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hb1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878468
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878469
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878470
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hc1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hc1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878471
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hc1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hc1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878472
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878474
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878475
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878476
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878477
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hd1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hd1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878478
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hd1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hd1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878479
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hd1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hd1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878480
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hd1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hd1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878481
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.he1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.he1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878482
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.he1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.he1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878483
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.he1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.he1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878485
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.he1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.he1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878486
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878487
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878488
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hf1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hf1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878489
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hf1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hf1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878490
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878491
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878492
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878493
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hh1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hh1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878494
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878496
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hh1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hh1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878497
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878498
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878499
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hi1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hi1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878500
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hi1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hi1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878501
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878502
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878503
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878504
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878505
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878507
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878508
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878509
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878510
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878511
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878512
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878513
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878514
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878515
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878516
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.m1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878518
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.n1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878519
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.o1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878520
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.p1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878521
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.q1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878522
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.r1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878523
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.s1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878524
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.t1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878525
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.u1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878526
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.v1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878527
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.w1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878529
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.x1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878530
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.y1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878531
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.z1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878532
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ba1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878533
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bb1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878534
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bc1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878535
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bd1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878536
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.be1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878537
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bf1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878538
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bg1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878540
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bh1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878541
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bi1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878542
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bj1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878543
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bk1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878544
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bl1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878545
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bm1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878546
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bn1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878547
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bo1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878548
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bp1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878549
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bq1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878552
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.br1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878553
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bs1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878554
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bt1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878555
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bu1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878556
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bv1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878557
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bw1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878558
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bx1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878559
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.by1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878560
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.bz1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878561
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ca1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878563
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cb1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878564
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cc1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878565
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cd1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878566
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ce1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878567
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cf1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878568
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cg1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878569
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ch1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878570
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ci1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878571
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cj1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878572
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ck1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878574
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cl1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878575
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cm1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878576
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cn1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878577
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.co1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878578
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cp1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878579
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cq1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878580
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cr1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878581
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cs1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878582
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ct1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878583
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cu1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878585
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cv1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878586
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cw1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878587
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cx1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878588
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cy1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878589
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.cz1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878590
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.da1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878591
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.db1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878592
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dc1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878593
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dd1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878594
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.de1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878596
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.df1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878597
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dg1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878598
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dh1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878599
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.di1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878600
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dj1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878601
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dk1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878602
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dl1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878603
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dm1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878604
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dn1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878605
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.do1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878607
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dp1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878608
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dq1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878609
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dr1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878610
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ds1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878611
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dt1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878612
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.du1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878613
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dv1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878614
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dw1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878615
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dx1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878616
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dy1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878618
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.dz1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878619
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ea1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878620
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.eb1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878621
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ec1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878622
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ed1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878623
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ee1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878624
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ef1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878625
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.eg1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878626
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.eh1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878627
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ei1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878629
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ej1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878630
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ek1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878631
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.el1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878632
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.em1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878633
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.en1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 30878634
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.eo1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878635
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ep1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878636
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.eq1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878637
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.er1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878638
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.es1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878640
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.et1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878641
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.eu1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878642
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ev1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878643
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ew1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878644
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.32.hk1.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.hk1.ex1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 30878645
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 1385, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878646
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 1386, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878647
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 1387, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.263', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 263, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878648
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 1388, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878649
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 1389, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878651
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 1390, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878652
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 1391, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.263', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 263, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878653
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1392, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.219', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 219, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878654
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1393, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.219', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 219, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878655
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1394, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.219', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 219, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878656
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1395, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.h1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.219', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 219, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878657
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1396, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.232', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 232, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878658
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1397, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.232', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 232, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878659
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1398, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.232', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 232, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878660
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 1399, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.30836.64.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.232', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 232, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878663
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878664
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878665
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878666
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878667
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878668
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878669
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878670
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878671
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878672
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878674
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878675
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878676
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878677
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1413, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878678
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1414, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878679
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1415, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878680
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878681
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878682
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878683
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878685
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878686
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878687
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878688
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878689
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878690
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878691
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878692
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1427, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878693
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1428, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878694
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1429, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878696
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1430, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878697
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1431, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878698
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878699
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878700
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878701
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878702
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878703
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878704
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878705
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878707
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878708
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878709
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878710
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1443, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878711
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1444, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878712
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1445, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878713
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1446, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878714
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1447, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, '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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id: 30878715
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878716
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878718
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878719
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878720
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878721
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878722
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878723
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878724
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.by1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878725
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878726
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.bz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878727
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878729
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878730
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1461, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878731
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1462, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878732
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1463, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878733
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878734
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878735
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878736
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878737
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878738
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878740
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878741
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878742
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878743
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1473, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878744
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1474, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878745
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1475, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878746
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878747
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878748
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878749
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878751
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cr1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878752
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878753
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878754
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.ct1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.ct1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878755
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878756
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878757
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878758
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1487, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878759
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878760
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878762
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cy1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878763
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 1491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cy1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878764
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.cz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878765
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.da1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878766
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.da1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.da1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878767
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.db1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878768
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.db1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.db1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878769
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878770
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878771
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 1499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878774
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.de1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878775
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1501, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.df1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878776
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1502, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878777
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1503, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.64.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 30878778
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878779
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878780
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878781
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878782
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878783
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878785
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878786
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878787
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878788
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878789
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878790
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878791
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.m1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878792
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.n1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878793
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.o1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878794
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.di1.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.di1.p1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878796
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878797
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878798
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878799
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878800
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878801
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878802
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878803
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878804
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878805
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878807
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878808
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878809
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.m1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878810
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.n1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878811
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.o1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878812
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dj1.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dj1.p1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878813
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878814
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878815
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878816
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878818
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878819
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878820
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878821
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878822
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878823
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878824
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878825
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878826
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.m1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878827
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.n1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878829
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.o1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878830
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dk1.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dk1.p1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878831
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878832
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878833
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878834
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878835
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878836
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878837
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878838
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878840
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.i1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878841
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.j1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878842
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.k1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878843
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.l1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878844
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.m1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878845
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.n1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878846
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.o1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878847
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dl1.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dl1.p1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878848
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878849
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878851
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878852
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878853
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878854
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878855
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878856
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878857
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878858
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.e2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878859
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878860
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.f2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878862
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878863
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.g2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878864
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878865
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dm1.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dm1.h2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878866
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878867
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878868
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878869
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878870
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878871
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878873
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878874
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878875
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 30878876
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.e2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878877
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878878
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.f2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878879
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878880
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.g2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878881
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878882
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.dn1.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.dn1.h2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878885
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878886
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878887
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878888
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878889
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878890
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878891
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878892
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878893
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878894
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.e2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878896
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878897
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.f2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878898
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.g1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878899
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.g2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878900
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.h1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878901
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.30836.64.do1.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.do1.h2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 30878902
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 1616, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.30836.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.2222', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2222, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^3', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878903
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 1617, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.30836.128.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.2264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2:C_2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878904
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 1618, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.30836.128.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.2264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2:C_2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878905
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 1619, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.30836.128.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.2222', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2222, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878907
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 1620, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.30836.128.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.2182', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2182, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878908
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 1621, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.30836.128.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.2201', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2201, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878909
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 1622, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.30836.128.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.2222', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2222, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878910
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1623, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878911
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1624, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878912
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1625, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878913
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1626, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.h1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878914
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1627, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878915
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1628, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878916
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1629, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 30878918
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1630, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878919
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1631, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878920
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1632, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878921
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1633, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878922
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1634, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878923
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1635, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878924
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1636, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878925
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1637, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878926
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1638, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878927
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1639, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878929
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1640, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878930
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1641, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.30836.128.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 30878931
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.30836', 'ambient_counter': 30836, 'ambient_order': 256, 'ambient_tex': 'C_2^3.C_2^5', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 1642, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.30836.256.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '256.30836', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30836, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.C_2^5', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
Hide schema
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id: 30878216
{'ambient': '256.30836', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '32.a1.a1', 'complements': ['256.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.i1.a1', '2.j1.a1', '2.k1.a1', '2.l1.a1', '2.m1.a1', '2.n1.a1', '2.o1.a1', '2.p1.a1', '2.q1.a1', '2.r1.a1', '2.s1.a1', '2.t1.a1', '2.u1.a1', '2.v1.a1', '2.w1.a1', '2.x1.a1', '2.y1.a1', '2.z1.a1', '2.ba1.a1', '2.bb1.a1', '2.bc1.a1', '2.bd1.a1', '2.be1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4739, 3748, 7159, 4999, 4741, 3746, 7153, 5010], 'generators': [1, 2, 4, 64, 16], 'label': '256.30836.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.q1.a1', '2.p1.a1', '2.s1.a1', '2.r1.a1', '2.u1.a1', '2.t1.a1', '2.w1.a1', '2.v1.a1', '2.i1.a1', '2.h1.a1', '2.k1.a1', '2.j1.a1', '2.m1.a1', '2.l1.a1', '2.o1.a1', '2.n1.a1', '2.x1.a1', '2.y1.a1', '2.z1.a1', '2.ba1.a1', '2.bb1.a1', '2.bc1.a1', '2.bd1.a1', '2.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
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id: 30878217
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.i1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.d1', '128.i1.b1', '128.i1.c1', '128.m1.a1', '128.m1.b1', '128.l1.a1', '128.l1.b1', '128.n1.a1', '128.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.j1.a1', '4.k1.a1', '4.u1.a1', '4.v1.a1', '4.bb1.a1', '4.bd1.a1', '4.cs1.a1', '4.cu1.a1', '4.cz1.a1', '4.df1.a1', '4.do1.a1', '4.dq1.a1', '4.dv1.a1', '4.ec1.a1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3909, 8166, 6572, 2156, 3912, 8105, 6554, 2227], 'generators': [65, 2, 4, 16], 'label': '256.30836.2.i1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.i1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.k1.a1', '4.j1.a1', '4.u1.a1', '4.v1.a1', '4.bd1.a1', '4.bb1.a1', '4.cs1.a1', '4.cu1.a1', '4.df1.a1', '4.cz1.a1', '4.do1.a1', '4.dq1.a1', '4.ec1.a1', '4.dv1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
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id: 30878218
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cp1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.y1.a1', '2.z1.a1'], 'contains': ['8.bd1.a1', '8.bj1.a1', '8.bk1.a1', '8.ct1.a1', '8.cu1.a1', '8.dg1.a1', '8.dk1.a1'], 'core': '4.cp1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7474, 8964, 5539, 8796, 7479, 8960, 5534, 8815], 'generators': [17, 18, 4], 'label': '256.30836.4.cp1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cp1.a1', 'normal_contained_in': ['2.c1.a1', '2.y1.a1', '2.z1.a1'], 'normal_contains': ['8.bd1.a1', '8.bj1.a1', '8.bk1.a1', '8.ct1.a1', '8.cu1.a1', '8.dg1.a1', '8.dk1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cp1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 30878219
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dy1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.ez1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bc1.a1', '16.gd1.a1', '16.gd1.b1', '16.gk1.a1', '16.gm1.a1', '16.gw1.a1', '16.hb1.a1'], 'contains': ['64.e1.a1', '64.dg1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5017, -1, 6606, -1, 5015, -1, 6600, -1], 'generators': [85, 32], 'label': '256.30836.32.dy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '32.dy1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dy1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 30878220
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bd1.a1', '16.gc1.a1', '16.gc1.b1', '16.gh1.a1', '16.gq1.a1', '16.gx1.a1', '16.hb1.a1'], 'contains': ['64.e1.a1', '64.dh1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5523, -1, 7114, -1, 5516, -1, 7107, -1], 'generators': [71, 32], 'label': '256.30836.32.dz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '32.dz1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dz1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 30878221
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ea1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.ep1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.gd1.a1', '16.gd1.b1', '16.gj1.a1', '16.gn1.a1', '16.gx1.a1', '16.ha1.a1'], 'contains': ['64.e1.a1', '64.bg1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3325, -1, 6583, -1, 3327, -1, 6577, -1], 'generators': [87, 8], 'label': '256.30836.32.ea1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '32.ea1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ea1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 30878222
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.eb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.eo1.a1', '16.fv1.a1', '16.hc1.a1', '16.hc1.a2', '16.hc1.b1', '16.hc1.b2'], 'contains': ['64.u1.a1', '64.v1.a1', '64.z1.a1', '64.di1.a1', '64.di1.c1', '64.di1.f1', '64.di1.l1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8388, -1, 909, -1, 8392, -1, 908, -1], 'generators': [1, 2, 32], 'label': '256.30836.32.eb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.eb1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eb1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 30878223
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.eb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.eo1.b1', '16.fv1.a1', '16.hc1.c1', '16.hc1.c2', '16.hc1.d1', '16.hc1.d2'], 'contains': ['64.u1.a1', '64.v1.b1', '64.z1.a1', '64.di1.b1', '64.di1.d1', '64.di1.k1', '64.di1.m1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8388, -1, 3703, -1, 8392, -1, 3699, -1], 'generators': [129, 2, 32], 'label': '256.30836.32.eb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.eb1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eb1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 30878224
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.eb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.eo1.a1', '16.fv1.b1', '16.hc1.e1', '16.hc1.e2', '16.hc1.f1', '16.hc1.f2'], 'contains': ['64.u1.b1', '64.v1.a1', '64.z1.a1', '64.di1.e1', '64.di1.g1', '64.di1.i1', '64.di1.o1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8388, -1, 1006, -1, 8392, -1, 1005, -1], 'generators': [1, 138, 32], 'label': '256.30836.32.eb1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.eb1.c1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eb1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878225
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.eb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.eo1.b1', '16.fv1.b1', '16.hc1.g1', '16.hc1.g2', '16.hc1.h1', '16.hc1.h2'], 'contains': ['64.u1.b1', '64.v1.b1', '64.z1.a1', '64.di1.h1', '64.di1.j1', '64.di1.n1', '64.di1.p1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8388, -1, 3369, -1, 8392, -1, 3366, -1], 'generators': [129, 138, 32], 'label': '256.30836.32.eb1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.eb1.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eb1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878226
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ec1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.ep1.a1', '16.fw1.a1', '16.hc1.a1', '16.hc1.a2', '16.hc1.c1', '16.hc1.c2'], 'contains': ['64.u1.a1', '64.w1.a1', '64.x1.a1', '64.dj1.a1', '64.dj1.b1', '64.dj1.i1', '64.dj1.j1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8415, -1, 631, -1, 8419, -1, 630, -1], 'generators': [2, 4, 32], 'label': '256.30836.32.ec1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ec1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ec1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879302
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.di1.a1', '8.gc1.a1', '8.gc1.b1'], 'contains': ['32.r1.a1', '32.x1.a1', '32.bd1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5519, -1, 5533, -1, 5522, -1, 5529, -1], 'generators': [7, 80], 'label': '256.30836.16.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.di1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cl1.a1', 'old_label': '16.cf1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878227
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ec1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.b1', '16.ep1.a1', '16.fw1.a1', '16.hc1.b1', '16.hc1.b2', '16.hc1.d1', '16.hc1.d2'], 'contains': ['64.u1.a1', '64.w1.b1', '64.x1.a1', '64.dj1.c1', '64.dj1.d1', '64.dj1.k1', '64.dj1.l1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8415, -1, 3314, -1, 8419, -1, 3310, -1], 'generators': [2, 140, 32], 'label': '256.30836.32.ec1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ec1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ec1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878228
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ec1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.ep1.a1', '16.fw1.b1', '16.hc1.e1', '16.hc1.e2', '16.hc1.g1', '16.hc1.g2'], 'contains': ['64.u1.b1', '64.w1.a1', '64.x1.a1', '64.dj1.e1', '64.dj1.f1', '64.dj1.m1', '64.dj1.n1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8415, -1, 825, -1, 8419, -1, 825, -1], 'generators': [138, 4, 32], 'label': '256.30836.32.ec1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ec1.c1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ec1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878229
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cq1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.z1.a1', '2.ba1.a1'], 'contains': ['8.bd1.a1', '8.bo1.a1', '8.bp1.a1', '8.cy1.a1', '8.da1.a1', '8.dl1.a1', '8.dm1.a1'], 'core': '4.cq1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7981, 970, 5850, 8096, 7985, 969, 5845, 8114], 'generators': [81, 82, 4], 'label': '256.30836.4.cq1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cq1.a1', 'normal_contained_in': ['2.a1.a1', '2.z1.a1', '2.ba1.a1'], 'normal_contains': ['8.bd1.a1', '8.bp1.a1', '8.bo1.a1', '8.da1.a1', '8.cy1.a1', '8.dl1.a1', '8.dm1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cq1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878230
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ec1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.b1', '16.ep1.a1', '16.fw1.b1', '16.hc1.f1', '16.hc1.f2', '16.hc1.h1', '16.hc1.h2'], 'contains': ['64.u1.b1', '64.w1.b1', '64.x1.a1', '64.dj1.g1', '64.dj1.h1', '64.dj1.o1', '64.dj1.p1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8415, -1, 3328, -1, 8419, -1, 3324, -1], 'generators': [138, 140, 32], 'label': '256.30836.32.ec1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ec1.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ec1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878231
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ed1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.eq1.a1', '16.fx1.a1', '16.hc1.a1', '16.hc1.b1', '16.hc1.c2', '16.hc1.d2'], 'contains': ['64.u1.a1', '64.y1.a1', '64.ba1.a1', '64.dk1.a1', '64.dk1.d1', '64.dk1.j1', '64.dk1.k1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8521, -1, 2438, -1, 8525, -1, 2436, -1], 'generators': [5, 2, 32], 'label': '256.30836.32.ed1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ed1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ed1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878232
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ed1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.eq1.a1', '16.fx1.a1', '16.hc1.a2', '16.hc1.b2', '16.hc1.c1', '16.hc1.d1'], 'contains': ['64.u1.a1', '64.y1.a1', '64.ba1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.i1', '64.dk1.l1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8521, -1, 2424, -1, 8525, -1, 2422, -1], 'generators': [141, 2, 32], 'label': '256.30836.32.ed1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ed1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ed1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878233
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ed1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.eq1.a1', '16.fx1.b1', '16.hc1.e1', '16.hc1.f1', '16.hc1.g2', '16.hc1.h2'], 'contains': ['64.u1.b1', '64.y1.a1', '64.ba1.a1', '64.dk1.f1', '64.dk1.g1', '64.dk1.m1', '64.dk1.p1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8521, -1, 2521, -1, 8525, -1, 2519, -1], 'generators': [5, 138, 32], 'label': '256.30836.32.ed1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ed1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ed1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878234
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ed1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.eq1.a1', '16.fx1.b1', '16.hc1.e2', '16.hc1.f2', '16.hc1.g1', '16.hc1.h1'], 'contains': ['64.u1.b1', '64.y1.a1', '64.ba1.a1', '64.dk1.e1', '64.dk1.h1', '64.dk1.n1', '64.dk1.o1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8521, -1, 2535, -1, 8525, -1, 2533, -1], 'generators': [141, 138, 32], 'label': '256.30836.32.ed1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ed1.b2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ed1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878235
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ee1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bk1.a1', '16.er1.a1', '16.fz1.a1'], 'contains': ['64.u1.a1', '64.bc1.a1', '64.be1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3440, -1, 6491, -1, 3442, -1, 6485, -1], 'generators': [2, 16], 'label': '256.30836.32.ee1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '32.ee1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ee1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878236
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ee1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bk1.a1', '16.er1.a1', '16.fz1.b1'], 'contains': ['64.u1.b1', '64.bc1.a1', '64.be1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3440, -1, 6514, -1, 3442, -1, 6508, -1], 'generators': [138, 16], 'label': '256.30836.32.ee1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '32.ee1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ee1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878237
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ef1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1', '16.et1.a1', '16.ge1.a1', '16.hc1.a1', '16.hc1.a2', '16.hc1.e1', '16.hc1.e2'], 'contains': ['64.v1.a1', '64.w1.a1', '64.y1.a1', '64.dl1.a1', '64.dl1.b1', '64.dl1.i1', '64.dl1.j1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8468, -1, 47, -1, 8472, -1, 47, -1], 'generators': [1, 4, 32], 'label': '256.30836.32.ef1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ef1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ef1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878238
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ef1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.b1', '16.et1.a1', '16.ge1.a1', '16.hc1.b1', '16.hc1.b2', '16.hc1.f1', '16.hc1.f2'], 'contains': ['64.v1.a1', '64.w1.b1', '64.y1.a1', '64.dl1.c1', '64.dl1.d1', '64.dl1.k1', '64.dl1.l1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8468, -1, 1243, -1, 8472, -1, 1241, -1], 'generators': [1, 140, 32], 'label': '256.30836.32.ef1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ef1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ef1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878239
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ef1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1', '16.et1.b1', '16.ge1.a1', '16.hc1.c1', '16.hc1.c2', '16.hc1.g1', '16.hc1.g2'], 'contains': ['64.v1.b1', '64.w1.a1', '64.y1.a1', '64.dl1.e1', '64.dl1.f1', '64.dl1.m1', '64.dl1.n1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8468, -1, 923, -1, 8472, -1, 922, -1], 'generators': [129, 4, 32], 'label': '256.30836.32.ef1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ef1.c1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ef1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878263
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.en1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.hd1.a1', '16.hi1.a1', '16.hi1.b1', '16.hj1.a1', '16.hk1.a1', '16.hl1.a1'], 'contains': ['64.f1.a1', '64.bi1.a1', '64.bi1.b1', '64.bv1.a1', '64.bv1.b1', '64.cy1.a1', '64.cy1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8175, -1, 5148, -1, 8179, -1, 5143, -1], 'generators': [1, 8, 160], 'label': '256.30836.32.en1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.en1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.en1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878264
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.eo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.he1.a1', '16.hi1.a1', '16.hi1.b1', '16.hm1.a1', '16.hn1.a1', '16.ho1.a1'], 'contains': ['64.f1.a1', '64.bj1.a1', '64.bw1.a1', '64.bw1.b1', '64.cz1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8202, -1, 5134, -1, 8206, -1, 5130, -1], 'generators': [4, 8, 160], 'label': '256.30836.32.eo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.eo1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eo1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879499
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dd1.a1', '8.gx1.a1', '8.gx1.b1'], 'contains': ['32.do1.a1', '32.dq1.a1', '32.dr1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4359, -1, 6023, -1, 4361, -1, 6019, -1], 'generators': [7, 16], 'label': '256.30836.16.gs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '16.gs1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878240
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cr1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.i1', '64.di1.e1', '64.di1.h1', '64.di1.j1', '64.di1.p1', '64.di1.n1', '64.di1.g1', '64.di1.o1', '64.di1.k1', '64.di1.m1', '64.di1.l1', '64.di1.f1', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.e2', '64.do1.f1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.g1', '64.do1.h1', '64.do1.g2', '64.dk1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.d1', '64.dk1.e1', '64.dk1.f1', '64.dk1.g1', '64.dk1.h1', '64.dk1.m1', '64.dk1.n1', '64.dk1.o1', '64.dk1.p1', '64.dk1.i1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.f2', '64.dm1.b1', '64.dm1.d2', '64.dm1.h1', '64.dm1.h2', '64.dm1.d1', '64.dm1.b2', '64.dm1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '2.p1.a1', '2.x1.a1'], 'contains': ['8.be1.a1', '8.bf1.a1', '8.bm1.a1', '8.dn1.a1', '8.ds1.a1', '8.dy1.a1', '8.fp1.a1'], 'core': '4.cr1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1311, 6747, 7633, 2342, 1313, 6745, 7626, 2347], 'generators': [19, 4, 64], 'label': '256.30836.4.cr1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cr1.a1', 'normal_contained_in': ['2.p1.a1', '2.h1.a1', '2.x1.a1'], 'normal_contains': ['8.be1.a1', '8.bm1.a1', '8.bf1.a1', '8.ds1.a1', '8.dn1.a1', '8.dy1.a1', '8.fp1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cr1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878241
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ef1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.b1', '16.et1.b1', '16.ge1.a1', '16.hc1.d1', '16.hc1.d2', '16.hc1.h1', '16.hc1.h2'], 'contains': ['64.v1.b1', '64.w1.b1', '64.y1.a1', '64.dl1.g1', '64.dl1.h1', '64.dl1.o1', '64.dl1.p1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8468, -1, 3341, -1, 8472, -1, 3338, -1], 'generators': [129, 140, 32], 'label': '256.30836.32.ef1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ef1.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ef1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878242
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.eg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bn1.a1', '16.eu1.a1', '16.gf1.a1', '16.hc1.a1', '16.hc1.b2', '16.hc1.e1', '16.hc1.f2'], 'contains': ['64.v1.a1', '64.x1.a1', '64.ba1.a1', '64.dm1.a1', '64.dm1.b1', '64.dm1.e1', '64.dm1.f1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8495, -1, 645, -1, 8499, -1, 644, -1], 'generators': [1, 6, 32], 'label': '256.30836.32.eg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.eg1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878243
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.eg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bn1.a1', '16.eu1.a1', '16.gf1.a1', '16.hc1.a2', '16.hc1.b1', '16.hc1.e2', '16.hc1.f1'], 'contains': ['64.v1.a1', '64.x1.a1', '64.ba1.a1', '64.dm1.a2', '64.dm1.b2', '64.dm1.e2', '64.dm1.f2'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8495, -1, 659, -1, 8499, -1, 658, -1], 'generators': [137, 6, 32], 'label': '256.30836.32.eg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.eg1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eg1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878244
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.eg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bn1.a1', '16.eu1.b1', '16.gf1.a1', '16.hc1.c1', '16.hc1.d2', '16.hc1.g1', '16.hc1.h2'], 'contains': ['64.v1.b1', '64.x1.a1', '64.ba1.a1', '64.dm1.c1', '64.dm1.d1', '64.dm1.g1', '64.dm1.h1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8495, -1, 2591, -1, 8499, -1, 2588, -1], 'generators': [129, 6, 32], 'label': '256.30836.32.eg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.eg1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eg1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878245
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.eg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bn1.a1', '16.eu1.b1', '16.gf1.a1', '16.hc1.c2', '16.hc1.d1', '16.hc1.g2', '16.hc1.h1'], 'contains': ['64.v1.b1', '64.x1.a1', '64.ba1.a1', '64.dm1.c2', '64.dm1.d2', '64.dm1.g2', '64.dm1.h2'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8495, -1, 2548, -1, 8499, -1, 2547, -1], 'generators': [9, 6, 32], 'label': '256.30836.32.eg1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.eg1.b2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eg1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878246
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.eh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bp1.a1', '16.ey1.a1', '16.gg1.a1'], 'contains': ['64.v1.a1', '64.bd1.a1', '64.bf1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4747, -1, 6277, -1, 4744, -1, 6272, -1], 'generators': [1, 68], 'label': '256.30836.32.eh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.x1.a1', 'old_label': '32.eh1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878247
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.eh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bp1.a1', '16.ey1.b1', '16.gg1.a1'], 'contains': ['64.v1.b1', '64.bd1.a1', '64.bf1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4747, -1, 6314, -1, 4744, -1, 6309, -1], 'generators': [129, 68], 'label': '256.30836.32.eh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.x1.a1', 'old_label': '32.eh1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eh1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878248
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ei1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.a1', '16.fb1.a1', '16.gi1.a1', '16.hc1.a1', '16.hc1.c1', '16.hc1.e2', '16.hc1.g2'], 'contains': ['64.w1.a1', '64.z1.a1', '64.ba1.a1', '64.dn1.a1', '64.dn1.b1', '64.dn1.c1', '64.dn1.d1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8548, -1, 394, -1, 8552, -1, 394, -1], 'generators': [3, 4, 32], 'label': '256.30836.32.ei1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ei1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ei1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878249
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ei1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.a1', '16.fb1.a1', '16.gi1.a1', '16.hc1.a2', '16.hc1.c2', '16.hc1.e1', '16.hc1.g1'], 'contains': ['64.w1.a1', '64.z1.a1', '64.ba1.a1', '64.dn1.a2', '64.dn1.b2', '64.dn1.c2', '64.dn1.d2'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8548, -1, 422, -1, 8552, -1, 422, -1], 'generators': [139, 4, 32], 'label': '256.30836.32.ei1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ei1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ei1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878250
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ei1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.b1', '16.fb1.a1', '16.gi1.a1', '16.hc1.b1', '16.hc1.d1', '16.hc1.f2', '16.hc1.h2'], 'contains': ['64.w1.b1', '64.z1.a1', '64.ba1.a1', '64.dn1.e1', '64.dn1.f1', '64.dn1.g1', '64.dn1.h1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8548, -1, 2493, -1, 8552, -1, 2491, -1], 'generators': [139, 140, 32], 'label': '256.30836.32.ei1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ei1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ei1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878265
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ep1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.he1.a1', '16.hj1.a1', '16.hp1.a1', '16.hp1.b1', '16.hq1.a1', '16.hr1.a1'], 'contains': ['64.f1.a1', '64.bk1.a1', '64.bx1.a1', '64.da1.a1', '64.da1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8149, -1, 5532, -1, 8153, -1, 5527, -1], 'generators': [6, 8, 160], 'label': '256.30836.32.ep1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.ep1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ep1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878266
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.eq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.hd1.a1', '16.hm1.a1', '16.hp1.a1', '16.hp1.b1', '16.hy1.a1', '16.hz1.a1'], 'contains': ['64.f1.a1', '64.bm1.a1', '64.bz1.a1', '64.bz1.b1', '64.dc1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8096, -1, 5559, -1, 8099, -1, 5555, -1], 'generators': [3, 8, 160], 'label': '256.30836.32.eq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.eq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879500
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gt1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dk1.a1', '8.gx1.a1', '8.gx1.b1'], 'contains': ['32.do1.a1', '32.dt1.a1', '32.dx1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4322, -1, 5966, -1, 4324, -1, 5961, -1], 'generators': [21, 18], 'label': '256.30836.16.gt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dk1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '16.gt1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gt1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878251
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cs1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.i1', '64.di1.e1', '64.di1.h1', '64.di1.j1', '64.di1.p1', '64.di1.n1', '64.di1.g1', '64.di1.o1', '64.di1.k1', '64.di1.m1', '64.di1.l1', '64.di1.f1', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.e2', '64.do1.f1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.g1', '64.do1.h1', '64.do1.g2', '64.dk1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.d1', '64.dk1.e1', '64.dk1.f1', '64.dk1.g1', '64.dk1.h1', '64.dk1.m1', '64.dk1.n1', '64.dk1.o1', '64.dk1.p1', '64.dk1.i1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.f2', '64.dm1.b1', '64.dm1.d2', '64.dm1.h1', '64.dm1.h2', '64.dm1.d1', '64.dm1.b2', '64.dm1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '2.q1.a1', '2.x1.a1'], 'contains': ['8.be1.a1', '8.bg1.a1', '8.bl1.a1', '8.do1.a1', '8.dt1.a1', '8.eh1.a1', '8.ff1.a1'], 'core': '4.cs1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2995, 5621, 7666, 551, 2996, 5619, 7660, 553], 'generators': [67, 4, 16], 'label': '256.30836.4.cs1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cs1.a1', 'normal_contained_in': ['2.q1.a1', '2.i1.a1', '2.x1.a1'], 'normal_contains': ['8.be1.a1', '8.bl1.a1', '8.bg1.a1', '8.do1.a1', '8.dt1.a1', '8.ff1.a1', '8.eh1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cs1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878252
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ei1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.b1', '16.fb1.a1', '16.gi1.a1', '16.hc1.b2', '16.hc1.d2', '16.hc1.f1', '16.hc1.h1'], 'contains': ['64.w1.b1', '64.z1.a1', '64.ba1.a1', '64.dn1.e2', '64.dn1.f2', '64.dn1.g2', '64.dn1.h2'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8548, -1, 2507, -1, 8552, -1, 2505, -1], 'generators': [3, 140, 32], 'label': '256.30836.32.ei1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ei1.b2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ei1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878253
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ej1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.br1.a1', '16.fc1.a1', '16.gj1.a1'], 'contains': ['64.w1.a1', '64.bb1.a1', '64.bg1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2772, -1, 6174, -1, 2631, -1, 6168, -1], 'generators': [83, 4], 'label': '256.30836.32.ej1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.be1.a1', 'old_label': '32.ej1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ej1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878254
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ej1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.br1.b1', '16.fc1.a1', '16.gj1.a1'], 'contains': ['64.w1.b1', '64.bb1.a1', '64.bg1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2772, -1, 6223, -1, 2631, -1, 6217, -1], 'generators': [83, 140], 'label': '256.30836.32.ej1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.be1.a1', 'old_label': '32.ej1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ej1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878255
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ek1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.fe1.a1', '16.gl1.a1', '16.hc1.a1', '16.hc1.d1', '16.hc1.f1', '16.hc1.g1'], 'contains': ['64.x1.a1', '64.y1.a1', '64.z1.a1', '64.do1.a1', '64.do1.d2', '64.do1.f2', '64.do1.g1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8442, -1, 868, -1, 8445, -1, 866, -1], 'generators': [5, 6, 32], 'label': '256.30836.32.ek1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ek1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ek1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878256
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ek1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.fe1.a1', '16.gl1.a1', '16.hc1.a2', '16.hc1.d2', '16.hc1.f2', '16.hc1.g2'], 'contains': ['64.x1.a1', '64.y1.a1', '64.z1.a1', '64.do1.b2', '64.do1.c1', '64.do1.e1', '64.do1.h2'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8442, -1, 881, -1, 8445, -1, 880, -1], 'generators': [141, 6, 32], 'label': '256.30836.32.ek1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ek1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ek1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878257
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ek1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.fe1.a1', '16.gl1.a1', '16.hc1.b1', '16.hc1.c1', '16.hc1.e1', '16.hc1.h1'], 'contains': ['64.x1.a1', '64.y1.a1', '64.z1.a1', '64.do1.a2', '64.do1.d1', '64.do1.f1', '64.do1.g2'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8442, -1, 811, -1, 8445, -1, 811, -1], 'generators': [133, 6, 32], 'label': '256.30836.32.ek1.a3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ek1.a3', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ek1.a3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878258
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ek1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.fe1.a1', '16.gl1.a1', '16.hc1.b2', '16.hc1.c2', '16.hc1.e2', '16.hc1.h2'], 'contains': ['64.x1.a1', '64.y1.a1', '64.z1.a1', '64.do1.b1', '64.do1.c2', '64.do1.e2', '64.do1.h1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8442, -1, 895, -1, 8445, -1, 894, -1], 'generators': [13, 6, 32], 'label': '256.30836.32.ek1.a4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ek1.a4', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ek1.a4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878259
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.el1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cn1.a1', '16.ft1.a1', '16.ha1.a1'], 'contains': ['64.be1.a1', '64.bf1.a1', '64.bg1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1666, -1, 6404, -1, 1666, -1, 6398, -1], 'generators': [69, 18], 'label': '256.30836.32.el1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ft1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ft1.a1', 'old_label': '32.el1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.el1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878260
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.el1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cn1.a1', '16.ft1.a1', '16.ha1.a1'], 'contains': ['64.be1.a1', '64.bf1.a1', '64.bg1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1666, -1, 6392, -1, 1666, -1, 6386, -1], 'generators': [205, 18], 'label': '256.30836.32.el1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ft1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.ft1.a1', 'old_label': '32.el1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.el1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878261
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.em1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.hd1.a1', '16.he1.a1', '16.hf1.a1', '16.hf1.b1', '16.hg1.a1', '16.hh1.a1'], 'contains': ['64.f1.a1', '64.bh1.a1', '64.bh1.b1', '64.bu1.a1', '64.bu1.b1', '64.cx1.a1', '64.cx1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8122, -1, 5504, -1, 8126, -1, 5499, -1], 'generators': [2, 8, 160], 'label': '256.30836.32.em1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.em1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.em1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878262
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ct1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.e1', '64.di1.i1', '64.di1.j1', '64.di1.h1', '64.di1.g1', '64.di1.o1', '64.di1.p1', '64.di1.n1', '64.di1.f1', '64.di1.l1', '64.di1.m1', '64.di1.k1', '64.dk1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.d1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.g1', '64.dk1.n1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.i1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.b2', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.f1', '64.do1.e2', '64.do1.f2', '64.do1.e1', '64.do1.g1', '64.do1.h2', '64.do1.g2', '64.do1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '2.q1.a1', '2.y1.a1'], 'contains': ['8.be1.a1', '8.bh1.a1', '8.bj1.a1', '8.dp1.a1', '8.du1.a1', '8.en1.a1', '8.ex1.a1'], 'core': '4.ct1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1053, 5109, 8388, 6197, 1053, 5106, 8381, 6210], 'generators': [17, 66, 4], 'label': '256.30836.4.ct1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ct1.a1', 'normal_contained_in': ['2.q1.a1', '2.h1.a1', '2.y1.a1'], 'normal_contains': ['8.be1.a1', '8.bj1.a1', '8.bh1.a1', '8.dp1.a1', '8.du1.a1', '8.ex1.a1', '8.en1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ct1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878267
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.er1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.hf1.a1', '16.hf1.b1', '16.hj1.a1', '16.hm1.a1', '16.ia1.a1', '16.ib1.a1'], 'contains': ['64.f1.a1', '64.bn1.a1', '64.ca1.a1', '64.dd1.a1', '64.dd1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8574, -1, 5107, -1, 8579, -1, 5102, -1], 'generators': [7, 8, 160], 'label': '256.30836.32.er1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.er1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.er1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878268
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.es1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.hq1.a1', '16.hs1.a1', '16.hs1.b1', '16.hy1.a1', '16.ic1.a1', '16.id1.a1'], 'contains': ['64.f1.a1', '64.bo1.a1', '64.cb1.a1', '64.de1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3917, -1, 7618, -1, 3954, -1, 7611, -1], 'generators': [83, 8, 160], 'label': '256.30836.32.es1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.bc1.a1', 'old_label': '32.es1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.es1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878269
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.et1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.bw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.hk1.a1', '16.hn1.a1', '16.ht1.a1', '16.ht1.b1', '16.ic1.a1', '16.ie1.a1'], 'contains': ['64.f1.a1', '64.bp1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5195, -1, 8247, -1, 5192, -1, 8240, -1], 'generators': [66, 160], 'label': '256.30836.32.et1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.q1.a1', 'old_label': '32.et1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.et1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878270
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.eu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '16.hg1.a1', '16.hu1.a1', '16.hu1.b1', '16.ia1.a1', '16.ic1.a1', '16.if1.a1'], 'contains': ['64.f1.a1', '64.bq1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4880, -1, 7292, -1, 4876, -1, 7286, -1], 'generators': [17, 160], 'label': '256.30836.32.eu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.l1.a1', 'old_label': '32.eu1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.eu1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878271
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ev1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.hh1.a1', '16.hv1.a1', '16.hv1.b1', '16.ia1.a1', '16.ig1.a1', '16.ih1.a1'], 'contains': ['64.f1.a1', '64.cc1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7422, -1, 6653, -1, 7426, -1, 6648, -1], 'generators': [22, 8], 'label': '256.30836.32.ev1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '32.ev1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ev1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878272
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ew1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.ce1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.hk1.a1', '16.ho1.a1', '16.hw1.a1', '16.hw1.b1', '16.ig1.a1', '16.ii1.a1'], 'contains': ['64.f1.a1', '64.br1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5984, -1, 7531, -1, 5988, -1, 7524, -1], 'generators': [67, 160], 'label': '256.30836.32.ew1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.s1.a1', 'old_label': '32.ew1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ew1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878273
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cu1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.di1.i1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.l1', '64.dm1.a1', '64.dm1.a2', '64.dm1.g1', '64.dm1.g2', '64.dm1.c1', '64.dm1.c2', '64.dm1.e1', '64.dm1.e2', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dk1.a1', '64.dk1.c1', '64.dk1.b1', '64.dk1.d1', '64.dk1.m1', '64.dk1.o1', '64.dk1.n1', '64.dk1.p1', '64.dk1.e1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.i1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.do1.a1', '64.do1.c1', '64.do1.a2', '64.do1.c2', '64.do1.d1', '64.do1.b1', '64.do1.d2', '64.do1.b2', '64.do1.e2', '64.do1.g2', '64.do1.e1', '64.do1.g1', '64.do1.h2', '64.do1.f2', '64.do1.h1', '64.do1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '2.p1.a1', '2.y1.a1'], 'contains': ['8.be1.a1', '8.bi1.a1', '8.bk1.a1', '8.dq1.a1', '8.dr1.a1', '8.ep1.a1', '8.ft1.a1', '8.gd1.a1', '8.gd1.b1'], 'core': '4.cu1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1098, 8562, 5463, 261, 1098, 8559, 5458, 261], 'generators': [65, 18, 4, 136], 'label': '256.30836.4.cu1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cu1.a1', 'normal_contained_in': ['2.p1.a1', '2.i1.a1', '2.y1.a1'], 'normal_contains': ['8.be1.a1', '8.bi1.a1', '8.bk1.a1', '8.dq1.a1', '8.dr1.a1', '8.ep1.a1', '8.ft1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cu1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878274
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ex1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.a1', '16.hr1.a1', '16.hx1.a1', '16.hx1.b1', '16.hy1.a1', '16.ih1.a1', '16.ii1.a1'], 'contains': ['64.f1.a1', '64.cd1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6573, -1, 6813, -1, 6577, -1, 6807, -1], 'generators': [80, 8], 'label': '256.30836.32.ex1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.bb1.a1', 'old_label': '32.ex1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ex1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878275
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ey1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.hh1.a1', '16.hu1.a1', '16.hu1.b1', '16.ib1.a1', '16.id1.a1', '16.ie1.a1'], 'contains': ['64.f1.a1', '64.ce1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6264, -1, 6993, -1, 6268, -1, 6987, -1], 'generators': [20, 8], 'label': '256.30836.32.ey1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.l1.a1', 'old_label': '32.ey1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ey1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878276
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ez1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1', '16.hl1.a1', '16.hn1.a1', '16.hw1.a1', '16.hw1.b1', '16.ih1.a1', '16.ij1.a1'], 'contains': ['64.f1.a1', '64.df1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7378, -1, 7485, -1, 7382, -1, 7478, -1], 'generators': [70, 160], 'label': '256.30836.32.ez1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.s1.a1', 'old_label': '32.ez1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ez1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878277
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fa1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ba1.a1', '16.hg1.a1', '16.hv1.a1', '16.hv1.b1', '16.ib1.a1', '16.ii1.a1', '16.ij1.a1'], 'contains': ['64.f1.a1', '64.bs1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6354, -1, 6836, -1, 6356, -1, 6830, -1], 'generators': [19, 160], 'label': '256.30836.32.fa1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.ba1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '32.fa1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fa1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878278
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.eq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bb1.a1', '16.hr1.a1', '16.hs1.a1', '16.hs1.b1', '16.hz1.a1', '16.ie1.a1', '16.if1.a1'], 'contains': ['64.f1.a1', '64.bt1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5150, -1, 7731, -1, 5147, -1, 7724, -1], 'generators': [86, 160], 'label': '256.30836.32.fb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.bc1.a1', 'old_label': '32.fb1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878279
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.ez1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bc1.a1', '16.hq1.a1', '16.hx1.a1', '16.hx1.b1', '16.hz1.a1', '16.ig1.a1', '16.ij1.a1'], 'contains': ['64.f1.a1', '64.dg1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6617, -1, 6947, -1, 6621, -1, 6941, -1], 'generators': [85, 160], 'label': '256.30836.32.fc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.bb1.a1', 'old_label': '32.fc1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878280
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bd1.a1', '16.hl1.a1', '16.ho1.a1', '16.ht1.a1', '16.ht1.b1', '16.id1.a1', '16.if1.a1'], 'contains': ['64.f1.a1', '64.dh1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5611, -1, 8224, -1, 5604, -1, 8217, -1], 'generators': [71, 160], 'label': '256.30836.32.fd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.q1.a1', 'old_label': '32.fd1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878281
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fe1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.co1.a1', '16.eo1.a1', '16.hd1.a1', '16.ik1.a1', '16.ik1.a2', '16.ik1.b1', '16.ik1.b2'], 'contains': ['64.bh1.a1', '64.bi1.a1', '64.bm1.a1', '64.di1.a1', '64.di1.c1', '64.di1.e1', '64.di1.i1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8601, -1, 1952, -1, 8605, -1, 1950, -1], 'generators': [1, 2, 168], 'label': '256.30836.32.fe1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fe1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fe1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878282
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fe1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.co1.a1', '16.eo1.b1', '16.hd1.a1', '16.ik1.c1', '16.ik1.c2', '16.ik1.d1', '16.ik1.d2'], 'contains': ['64.bh1.a1', '64.bi1.b1', '64.bm1.a1', '64.di1.b1', '64.di1.d1', '64.di1.h1', '64.di1.j1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8601, -1, 4036, -1, 8605, -1, 4033, -1], 'generators': [129, 2, 168], 'label': '256.30836.32.fe1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fe1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fe1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878283
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fe1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.co1.b1', '16.eo1.a1', '16.hd1.a1', '16.ik1.e1', '16.ik1.e2', '16.ik1.f1', '16.ik1.f2'], 'contains': ['64.bh1.b1', '64.bi1.a1', '64.bm1.a1', '64.di1.f1', '64.di1.g1', '64.di1.l1', '64.di1.o1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8601, -1, 1200, -1, 8605, -1, 1200, -1], 'generators': [1, 34, 168], 'label': '256.30836.32.fe1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fe1.c1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fe1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878284
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cv1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.m1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.j1', '64.dk1.l1', '64.dk1.k1', '64.dk1.i1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.e1', '64.dm1.a1', '64.dm1.a2', '64.dm1.e1', '64.dm1.e2', '64.dm1.c1', '64.dm1.c2', '64.dm1.g1', '64.dm1.g2', '64.dm1.b1', '64.dm1.b2', '64.dm1.f1', '64.dm1.f2', '64.dm1.d1', '64.dm1.d2', '64.dm1.h1', '64.dm1.h2', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.f2', '64.do1.h2', '64.do1.g1', '64.do1.e1', '64.do1.g2', '64.do1.e2', '64.do1.f1', '64.do1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '2.r1.a1', '2.x1.a1'], 'contains': ['8.bf1.a1', '8.bg1.a1', '8.bn1.a1', '8.dv1.a1', '8.dz1.a1', '8.ee1.a1', '8.fl1.a1', '8.ge1.a1', '8.ge1.b1'], 'core': '4.cv1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7189, 2368, 5432, 3311, 7193, 2367, 5427, 3318], 'generators': [4, 16, 64, 136], 'label': '256.30836.4.cv1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cv1.a1', 'normal_contained_in': ['2.r1.a1', '2.j1.a1', '2.x1.a1'], 'normal_contains': ['8.bg1.a1', '8.bf1.a1', '8.bn1.a1', '8.dv1.a1', '8.ee1.a1', '8.dz1.a1', '8.fl1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cv1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878285
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fe1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.co1.b1', '16.eo1.b1', '16.hd1.a1', '16.ik1.g1', '16.ik1.g2', '16.ik1.h1', '16.ik1.h2'], 'contains': ['64.bh1.b1', '64.bi1.b1', '64.bm1.a1', '64.di1.k1', '64.di1.m1', '64.di1.n1', '64.di1.p1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8601, -1, 3883, -1, 8605, -1, 3880, -1], 'generators': [129, 34, 168], 'label': '256.30836.32.fe1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fe1.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fe1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878286
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ff1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cp1.a1', '16.ep1.a1', '16.he1.a1', '16.ik1.a1', '16.ik1.b1', '16.ik1.c1', '16.ik1.d1'], 'contains': ['64.bh1.a1', '64.bj1.a1', '64.bk1.a1', '64.dj1.a1', '64.dj1.d1', '64.dj1.f1', '64.dj1.g1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8654, -1, 2924, -1, 8658, -1, 2922, -1], 'generators': [2, 4, 168], 'label': '256.30836.32.ff1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ff1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ff1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878287
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ff1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cp1.a1', '16.ep1.a1', '16.he1.a1', '16.ik1.a2', '16.ik1.b2', '16.ik1.c2', '16.ik1.d2'], 'contains': ['64.bh1.a1', '64.bj1.a1', '64.bk1.a1', '64.dj1.b1', '64.dj1.c1', '64.dj1.e1', '64.dj1.h1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8654, -1, 3063, -1, 8658, -1, 3060, -1], 'generators': [130, 4, 168], 'label': '256.30836.32.ff1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ff1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ff1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878288
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ff1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cp1.b1', '16.ep1.a1', '16.he1.a1', '16.ik1.e1', '16.ik1.f1', '16.ik1.g1', '16.ik1.h1'], 'contains': ['64.bh1.b1', '64.bj1.a1', '64.bk1.a1', '64.dj1.j1', '64.dj1.k1', '64.dj1.m1', '64.dj1.p1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8654, -1, 2688, -1, 8658, -1, 2686, -1], 'generators': [34, 4, 168], 'label': '256.30836.32.ff1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ff1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ff1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878289
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ff1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cp1.b1', '16.ep1.a1', '16.he1.a1', '16.ik1.e2', '16.ik1.f2', '16.ik1.g2', '16.ik1.h2'], 'contains': ['64.bh1.b1', '64.bj1.a1', '64.bk1.a1', '64.dj1.i1', '64.dj1.l1', '64.dj1.n1', '64.dj1.o1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8654, -1, 2882, -1, 8658, -1, 2880, -1], 'generators': [162, 4, 168], 'label': '256.30836.32.ff1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ff1.b2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ff1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878290
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cq1.a1', '16.eq1.a1', '16.hf1.a1', '16.ik1.a1', '16.ik1.a2', '16.ik1.c1', '16.ik1.c2'], 'contains': ['64.bh1.a1', '64.bl1.a1', '64.bn1.a1', '64.dk1.a1', '64.dk1.b1', '64.dk1.e1', '64.dk1.f1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8708, -1, 3494, -1, 8712, -1, 3491, -1], 'generators': [5, 2, 168], 'label': '256.30836.32.fg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fg1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878291
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cq1.a1', '16.eq1.a1', '16.hf1.b1', '16.ik1.b1', '16.ik1.b2', '16.ik1.d1', '16.ik1.d2'], 'contains': ['64.bh1.a1', '64.bl1.b1', '64.bn1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.g1', '64.dk1.h1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8708, -1, 1757, -1, 8712, -1, 1755, -1], 'generators': [37, 2, 168], 'label': '256.30836.32.fg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fg1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fg1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878292
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cq1.b1', '16.eq1.a1', '16.hf1.a1', '16.ik1.e1', '16.ik1.e2', '16.ik1.g1', '16.ik1.g2'], 'contains': ['64.bh1.b1', '64.bl1.a1', '64.bn1.a1', '64.dk1.i1', '64.dk1.j1', '64.dk1.m1', '64.dk1.n1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8708, -1, 3355, -1, 8712, -1, 3352, -1], 'generators': [5, 34, 168], 'label': '256.30836.32.fg1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fg1.c1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fg1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878293
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cq1.b1', '16.eq1.a1', '16.hf1.b1', '16.ik1.f1', '16.ik1.f2', '16.ik1.h1', '16.ik1.h2'], 'contains': ['64.bh1.b1', '64.bl1.b1', '64.bn1.a1', '64.dk1.k1', '64.dk1.l1', '64.dk1.o1', '64.dk1.p1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8708, -1, 1076, -1, 8712, -1, 1075, -1], 'generators': [37, 34, 168], 'label': '256.30836.32.fg1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fg1.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fg1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878294
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cu1.a1', '16.es1.a1', '16.hg1.a1'], 'contains': ['64.bh1.a1', '64.bq1.a1', '64.bs1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3081, -1, 7600, -1, 3083, -1, 7593, -1], 'generators': [17, 2], 'label': '256.30836.32.fh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '32.fh1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878295
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cw1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.e1', '64.di1.i1', '64.di1.j1', '64.di1.h1', '64.di1.g1', '64.di1.o1', '64.di1.p1', '64.di1.n1', '64.di1.f1', '64.di1.l1', '64.di1.m1', '64.di1.k1', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.b2', '64.dk1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.d1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.g1', '64.dk1.n1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.i1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.f1', '64.do1.e2', '64.do1.f2', '64.do1.e1', '64.do1.g1', '64.do1.h2', '64.do1.g2', '64.do1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '2.r1.a1', '2.z1.a1'], 'contains': ['8.bf1.a1', '8.bj1.a1', '8.bp1.a1', '8.dw1.a1', '8.eb1.a1', '8.ev1.a1', '8.fo1.a1'], 'core': '4.cw1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5613, 6606, 8169, 8330, 5616, 6604, 8162, 8348], 'generators': [17, 4, 64], 'label': '256.30836.4.cw1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cw1.a1', 'normal_contained_in': ['2.r1.a1', '2.h1.a1', '2.z1.a1'], 'normal_contains': ['8.bj1.a1', '8.bf1.a1', '8.bp1.a1', '8.dw1.a1', '8.ev1.a1', '8.eb1.a1', '8.fo1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cw1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878296
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cu1.b1', '16.es1.a1', '16.hg1.a1'], 'contains': ['64.bh1.b1', '64.bq1.a1', '64.bs1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3081, -1, 7577, -1, 3083, -1, 7570, -1], 'generators': [17, 34], 'label': '256.30836.32.fh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.h1.a1', 'old_label': '32.fh1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fh1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878297
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cx1.a1', '16.et1.a1', '16.hi1.a1', '16.ik1.a1', '16.ik1.a2', '16.ik1.e1', '16.ik1.e2'], 'contains': ['64.bi1.a1', '64.bj1.a1', '64.bl1.a1', '64.dl1.a1', '64.dl1.c1', '64.dl1.i1', '64.dl1.k1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8681, -1, 1993, -1, 8685, -1, 1991, -1], 'generators': [1, 4, 168], 'label': '256.30836.32.fi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fi1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fi1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878298
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cx1.a1', '16.et1.a1', '16.hi1.b1', '16.ik1.b1', '16.ik1.b2', '16.ik1.f1', '16.ik1.f2'], 'contains': ['64.bi1.a1', '64.bj1.a1', '64.bl1.b1', '64.dl1.b1', '64.dl1.d1', '64.dl1.j1', '64.dl1.l1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8681, -1, 200, -1, 8685, -1, 200, -1], 'generators': [33, 4, 168], 'label': '256.30836.32.fi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fi1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fi1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878299
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cx1.a1', '16.et1.b1', '16.hi1.a1', '16.ik1.c1', '16.ik1.c2', '16.ik1.g1', '16.ik1.g2'], 'contains': ['64.bi1.b1', '64.bj1.a1', '64.bl1.a1', '64.dl1.e1', '64.dl1.g1', '64.dl1.m1', '64.dl1.o1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8681, -1, 3411, -1, 8685, -1, 3408, -1], 'generators': [161, 4, 168], 'label': '256.30836.32.fi1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fi1.c1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fi1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878300
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cx1.a1', '16.et1.b1', '16.hi1.b1', '16.ik1.d1', '16.ik1.d2', '16.ik1.h1', '16.ik1.h2'], 'contains': ['64.bi1.b1', '64.bj1.a1', '64.bl1.b1', '64.dl1.f1', '64.dl1.h1', '64.dl1.n1', '64.dl1.p1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8681, -1, 1924, -1, 8685, -1, 1922, -1], 'generators': [129, 4, 168], 'label': '256.30836.32.fi1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fi1.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fi1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878301
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cy1.a1', '16.eu1.a1', '16.hj1.a1', '16.ik1.a1', '16.ik1.b2', '16.ik1.e1', '16.ik1.f2'], 'contains': ['64.bi1.a1', '64.bk1.a1', '64.bn1.a1', '64.dm1.a1', '64.dm1.b1', '64.dm1.e2', '64.dm1.f2'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8734, -1, 1312, -1, 8738, -1, 1311, -1], 'generators': [1, 6, 168], 'label': '256.30836.32.fj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fj1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878302
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cy1.a1', '16.eu1.a1', '16.hj1.a1', '16.ik1.a2', '16.ik1.b1', '16.ik1.e2', '16.ik1.f1'], 'contains': ['64.bi1.a1', '64.bk1.a1', '64.bn1.a1', '64.dm1.a2', '64.dm1.b2', '64.dm1.e1', '64.dm1.f1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8734, -1, 1409, -1, 8738, -1, 1408, -1], 'generators': [33, 6, 168], 'label': '256.30836.32.fj1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fj1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fj1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878303
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cy1.a1', '16.eu1.b1', '16.hj1.a1', '16.ik1.c1', '16.ik1.d2', '16.ik1.g1', '16.ik1.h2'], 'contains': ['64.bi1.b1', '64.bk1.a1', '64.bn1.a1', '64.dm1.c2', '64.dm1.d2', '64.dm1.g1', '64.dm1.h1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8734, -1, 2868, -1, 8738, -1, 2866, -1], 'generators': [161, 6, 168], 'label': '256.30836.32.fj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fj1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fj1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878304
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cy1.a1', '16.eu1.b1', '16.hj1.a1', '16.ik1.c2', '16.ik1.d1', '16.ik1.g2', '16.ik1.h1'], 'contains': ['64.bi1.b1', '64.bk1.a1', '64.bn1.a1', '64.dm1.c1', '64.dm1.d1', '64.dm1.g2', '64.dm1.h2'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8734, -1, 2939, -1, 8738, -1, 2936, -1], 'generators': [129, 6, 168], 'label': '256.30836.32.fj1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fj1.b2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fj1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878305
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.da1.a1', '16.ex1.a1', '16.hk1.a1'], 'contains': ['64.bi1.a1', '64.bp1.a1', '64.br1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4222, -1, 8270, -1, 4224, -1, 8263, -1], 'generators': [1, 66], 'label': '256.30836.32.fk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.fk1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fk1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878385
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cp1.a1', '16.fw1.b1', '16.il1.b1', '16.je1.c1', '16.je1.c2', '16.je1.f1', '16.je1.f2'], 'contains': ['64.h1.b1', '64.cg1.a1', '64.ch1.a1', '64.dj1.e1', '64.dj1.f1', '64.dj1.g1', '64.dj1.h1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2576, -1, 9138, -1, 2574, -1], 'generators': [130, 4, 40], 'label': '256.30836.32.gl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gl1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gl1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878386
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cp1.b1', '16.fw1.a1', '16.il1.b1', '16.je1.d1', '16.je1.d2', '16.je1.g1', '16.je1.g2'], 'contains': ['64.h1.c1', '64.cg1.a1', '64.ch1.a1', '64.dj1.i1', '64.dj1.j1', '64.dj1.k1', '64.dj1.l1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 1938, -1, 9138, -1, 1936, -1], 'generators': [34, 4, 40], 'label': '256.30836.32.gl1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gl1.c1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gl1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878306
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cx1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.c1', '64.di1.b1', '64.di1.f1', '64.di1.m1', '64.di1.l1', '64.di1.k1', '64.di1.e1', '64.di1.j1', '64.di1.i1', '64.di1.h1', '64.di1.g1', '64.di1.p1', '64.di1.o1', '64.di1.n1', '64.dk1.a1', '64.dk1.d1', '64.dk1.c1', '64.dk1.b1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1', '64.dk1.i1', '64.dk1.e1', '64.dk1.h1', '64.dk1.g1', '64.dk1.f1', '64.dk1.n1', '64.dk1.o1', '64.dk1.p1', '64.dk1.m1', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.b2', '64.dm1.h1', '64.dm1.f2', '64.dm1.d1', '64.dm1.d2', '64.dm1.f1', '64.dm1.h2', '64.dm1.b1', '64.do1.a1', '64.do1.c2', '64.do1.d2', '64.do1.b1', '64.do1.d1', '64.do1.b2', '64.do1.a2', '64.do1.c1', '64.do1.e1', '64.do1.g2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.f2', '64.do1.e2', '64.do1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '2.p1.a1', '2.z1.a1'], 'contains': ['8.bf1.a1', '8.bk1.a1', '8.bo1.a1', '8.dx1.a1', '8.ea1.a1', '8.fb1.a1', '8.fn1.a1'], 'core': '4.cx1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7018, 8390, 5923, 2509, 7021, 8387, 5918, 2514], 'generators': [18, 4, 64], 'label': '256.30836.4.cx1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cx1.a1', 'normal_contained_in': ['2.p1.a1', '2.j1.a1', '2.z1.a1'], 'normal_contains': ['8.bf1.a1', '8.bk1.a1', '8.bo1.a1', '8.dx1.a1', '8.ea1.a1', '8.fb1.a1', '8.fn1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cx1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878307
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.da1.a1', '16.ex1.b1', '16.hk1.a1'], 'contains': ['64.bi1.b1', '64.bp1.a1', '64.br1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4222, -1, 8293, -1, 4224, -1, 8286, -1], 'generators': [129, 66], 'label': '256.30836.32.fk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.u1.a1', 'old_label': '32.fk1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fk1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878308
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.db1.a1', '16.fb1.a1', '16.hm1.a1', '16.ik1.a1', '16.ik1.d2', '16.ik1.f1', '16.ik1.g2'], 'contains': ['64.bj1.a1', '64.bm1.a1', '64.bn1.a1', '64.dn1.a1', '64.dn1.d2', '64.dn1.f2', '64.dn1.g1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8787, -1, 2062, -1, 8792, -1, 2061, -1], 'generators': [3, 4, 168], 'label': '256.30836.32.fl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fl1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878309
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.db1.a1', '16.fb1.a1', '16.hm1.a1', '16.ik1.a2', '16.ik1.d1', '16.ik1.f2', '16.ik1.g1'], 'contains': ['64.bj1.a1', '64.bm1.a1', '64.bn1.a1', '64.dn1.b2', '64.dn1.c1', '64.dn1.e1', '64.dn1.h2'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8787, -1, 2035, -1, 8792, -1, 2033, -1], 'generators': [131, 4, 168], 'label': '256.30836.32.fl1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fl1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fl1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878310
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.db1.a1', '16.fb1.a1', '16.hm1.a1', '16.ik1.b1', '16.ik1.c2', '16.ik1.e1', '16.ik1.h2'], 'contains': ['64.bj1.a1', '64.bm1.a1', '64.bn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.f1', '64.dn1.g2'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8787, -1, 1743, -1, 8792, -1, 1741, -1], 'generators': [35, 4, 168], 'label': '256.30836.32.fl1.a3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fl1.a3', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fl1.a3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878311
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.db1.a1', '16.fb1.a1', '16.hm1.a1', '16.ik1.b2', '16.ik1.c1', '16.ik1.e2', '16.ik1.h1'], 'contains': ['64.bj1.a1', '64.bm1.a1', '64.bn1.a1', '64.dn1.b1', '64.dn1.c2', '64.dn1.e2', '64.dn1.h1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8787, -1, 1729, -1, 8792, -1, 1727, -1], 'generators': [163, 4, 168], 'label': '256.30836.32.fl1.a4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fl1.a4', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fl1.a4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878312
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.de1.a1', '16.fe1.a1', '16.hp1.a1', '16.ik1.a1', '16.ik1.c2', '16.ik1.e2', '16.ik1.g1'], 'contains': ['64.bk1.a1', '64.bl1.a1', '64.bm1.a1', '64.do1.a1', '64.do1.b2', '64.do1.e2', '64.do1.f1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8627, -1, 2633, -1, 8632, -1, 2630, -1], 'generators': [5, 6, 168], 'label': '256.30836.32.fm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fm1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878313
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.de1.a1', '16.fe1.a1', '16.hp1.a1', '16.ik1.a2', '16.ik1.c1', '16.ik1.e1', '16.ik1.g2'], 'contains': ['64.bk1.a1', '64.bl1.a1', '64.bm1.a1', '64.do1.a2', '64.do1.b1', '64.do1.e1', '64.do1.f2'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8627, -1, 2646, -1, 8632, -1, 2644, -1], 'generators': [165, 6, 168], 'label': '256.30836.32.fm1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fm1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fm1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878314
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.de1.a1', '16.fe1.a1', '16.hp1.b1', '16.ik1.b1', '16.ik1.d2', '16.ik1.f2', '16.ik1.h1'], 'contains': ['64.bk1.a1', '64.bl1.b1', '64.bm1.a1', '64.do1.c1', '64.do1.d2', '64.do1.g2', '64.do1.h1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8627, -1, 965, -1, 8632, -1, 964, -1], 'generators': [37, 6, 168], 'label': '256.30836.32.fm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fm1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fm1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878315
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.de1.a1', '16.fe1.a1', '16.hp1.b1', '16.ik1.b2', '16.ik1.d1', '16.ik1.f1', '16.ik1.h2'], 'contains': ['64.bk1.a1', '64.bl1.b1', '64.bm1.a1', '64.do1.c2', '64.do1.d1', '64.do1.g1', '64.do1.h2'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8627, -1, 992, -1, 8632, -1, 991, -1], 'generators': [133, 6, 168], 'label': '256.30836.32.fm1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.fm1.b2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fm1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878316
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dh1.a1', '16.fh1.a1', '16.hs1.a1'], 'contains': ['64.bl1.a1', '64.bo1.a1', '64.bt1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3116, -1, 7761, -1, 3117, -1, 7754, -1], 'generators': [5, 86], 'label': '256.30836.32.fn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.cd1.a1', 'old_label': '32.fn1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878387
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cp1.b1', '16.fw1.b1', '16.il1.a1', '16.je1.e1', '16.je1.e2', '16.je1.h1', '16.je1.h2'], 'contains': ['64.h1.d1', '64.cg1.a1', '64.ch1.a1', '64.dj1.m1', '64.dj1.n1', '64.dj1.o1', '64.dj1.p1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 1979, -1, 9138, -1, 1977, -1], 'generators': [162, 4, 40], 'label': '256.30836.32.gl1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gl1.d1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gl1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878388
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cq1.a1', '16.fx1.a1', '16.im1.a1', '16.je1.a1', '16.je1.a2', '16.je1.b1', '16.je1.b2'], 'contains': ['64.h1.a1', '64.ci1.a1', '64.ck1.a1', '64.dk1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.d1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 2104, -1, 9164, -1, 2102, -1], 'generators': [5, 2, 40], 'label': '256.30836.32.gm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gm1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878317
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cy1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.e1', '64.di1.i1', '64.di1.j1', '64.di1.h1', '64.di1.g1', '64.di1.o1', '64.di1.p1', '64.di1.n1', '64.di1.f1', '64.di1.l1', '64.di1.m1', '64.di1.k1', '64.dk1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.d1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.g1', '64.dk1.n1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.i1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.b2', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.f1', '64.do1.e2', '64.do1.f2', '64.do1.e1', '64.do1.g1', '64.do1.h2', '64.do1.g2', '64.do1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '2.q1.a1', '2.ba1.a1'], 'contains': ['8.bg1.a1', '8.bh1.a1', '8.bo1.a1', '8.ec1.a1', '8.ef1.a1', '8.el1.a1', '8.fq1.a1'], 'core': '4.cy1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6581, 549, 6611, 428, 6584, 549, 6605, 429], 'generators': [66, 4, 16], 'label': '256.30836.4.cy1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cy1.a1', 'normal_contained_in': ['2.q1.a1', '2.j1.a1', '2.ba1.a1'], 'normal_contains': ['8.bg1.a1', '8.bh1.a1', '8.bo1.a1', '8.ec1.a1', '8.ef1.a1', '8.el1.a1', '8.fq1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cy1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878318
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dh1.a1', '16.fh1.a1', '16.hs1.b1'], 'contains': ['64.bl1.b1', '64.bo1.a1', '64.bt1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3116, -1, 7748, -1, 3117, -1, 7742, -1], 'generators': [37, 86], 'label': '256.30836.32.fn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.cd1.a1', 'old_label': '32.fn1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fn1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878319
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fo1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.do1.a1', '16.fo1.a1', '16.ic1.a1'], 'contains': ['64.bo1.a1', '64.bp1.a1', '64.bq1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1965, -1, 8376, -1, 1965, -1, 8369, -1], 'generators': [17, 66], 'label': '256.30836.32.fo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dp1.a1', 'old_label': '32.fo1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fo1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878320
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.fo1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.do1.a1', '16.fo1.a1', '16.ic1.a1'], 'contains': ['64.bo1.a1', '64.bp1.a1', '64.bq1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1965, -1, 8399, -1, 1965, -1, 8392, -1], 'generators': [145, 66], 'label': '256.30836.32.fo1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dp1.a1', 'old_label': '32.fo1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fo1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878321
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.il1.a1', '16.il1.b1', '16.ir1.a1', '16.ir1.b1', '16.ix1.a1', '16.ix1.b1'], 'contains': ['64.g1.a1', '64.bw1.a1', '64.bw1.b1', '64.cg1.a1', '64.cq1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9558, -1, 4633, -1, 9564, -1, 4630, -1], 'generators': [4, 136, 160], 'label': '256.30836.32.fp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.fp1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878322
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.il1.a1', '16.il1.b1', '16.is1.a1', '16.is1.b1', '16.iy1.a1', '16.iy1.b1'], 'contains': ['64.g1.a1', '64.bx1.a1', '64.ch1.a1', '64.cr1.a1', '64.cr1.b1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9239, -1, 4662, -1, 9244, -1, 4657, -1], 'generators': [6, 136, 160], 'label': '256.30836.32.fq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.fq1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878323
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fr1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.im1.a1', '16.im1.b1', '16.ir1.a1', '16.ir1.b1', '16.iy1.a1', '16.iy1.b1'], 'contains': ['64.g1.a1', '64.by1.a1', '64.by1.b1', '64.ci1.a1', '64.cs1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9452, -1, 4619, -1, 9457, -1, 4616, -1], 'generators': [5, 136, 160], 'label': '256.30836.32.fr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.fr1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fr1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878324
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.im1.a1', '16.im1.b1', '16.is1.a1', '16.is1.b1', '16.ix1.a1', '16.ix1.b1'], 'contains': ['64.g1.a1', '64.ca1.a1', '64.ck1.a1', '64.cu1.a1', '64.cu1.b1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9666, -1, 4647, -1, 9670, -1, 4644, -1], 'generators': [7, 136, 160], 'label': '256.30836.32.fs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.fs1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fs1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878325
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ft1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.in1.a1', '16.in1.b1', '16.it1.a1', '16.it1.b1', '16.iz1.a1', '16.iz1.b1'], 'contains': ['64.g1.a1', '64.cb1.a1', '64.cl1.a1', '64.cv1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5420, -1, 5328, -1, 5413, -1, 5324, -1], 'generators': [83, 136, 160], 'label': '256.30836.32.ft1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.ft1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ft1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878326
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.io1.a1', '16.io1.b1', '16.iu1.a1', '16.iu1.b1', '16.ja1.a1', '16.ja1.b1'], 'contains': ['64.g1.a1', '64.cc1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7643, -1, 5347, -1, 7647, -1, 5342, -1], 'generators': [22, 136], 'label': '256.30836.32.fu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '32.fu1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fu1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878327
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.ip1.a1', '16.ip1.b1', '16.iu1.a1', '16.iu1.b1', '16.jb1.a1', '16.jb1.b1'], 'contains': ['64.g1.a1', '64.cm1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6971, -1, 5416, -1, 6974, -1, 5411, -1], 'generators': [23, 160], 'label': '256.30836.32.fv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '32.fv1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fv1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878328
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.j1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.d1', '128.i1.c1', '128.i1.b1', '128.m1.a1', '128.m1.b1', '128.l1.a1', '128.l1.b1', '128.n1.a1', '128.n1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.j1.a1', '4.m1.a1', '4.x1.a1', '4.y1.a1', '4.ba1.a1', '4.bh1.a1', '4.cv1.a1', '4.cx1.a1', '4.cy1.a1', '4.da1.a1', '4.dr1.a1', '4.dt1.a1', '4.du1.a1', '4.dw1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7111, 3182, 6040, 3470, 7115, 3180, 6034, 3478], 'generators': [2, 4, 16, 64], 'label': '256.30836.2.j1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.j1.a1', '4.i1.a1', '4.m1.a1', '4.x1.a1', '4.ba1.a1', '4.y1.a1', '4.bh1.a1', '4.cy1.a1', '4.cv1.a1', '4.da1.a1', '4.cx1.a1', '4.du1.a1', '4.dr1.a1', '4.dw1.a1', '4.dt1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878389
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cq1.a1', '16.fx1.b1', '16.im1.b1', '16.je1.c1', '16.je1.c2', '16.je1.f1', '16.je1.f2'], 'contains': ['64.h1.b1', '64.ci1.a1', '64.ck1.a1', '64.dk1.e1', '64.dk1.f1', '64.dk1.g1', '64.dk1.h1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 2313, -1, 9164, -1, 2311, -1], 'generators': [5, 130, 40], 'label': '256.30836.32.gm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gm1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gm1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879501
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ds1.a1', '8.gy1.a1', '8.gy1.b1'], 'contains': ['32.dp1.a1', '32.dr1.a1', '32.ds1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2604, -1, 8724, -1, 2605, -1, 8717, -1], 'generators': [83, 68], 'label': '256.30836.16.gu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ds1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.w1.a1', 'old_label': '16.gu1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878329
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cz1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.di1.i1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.l1', '64.dm1.a1', '64.dm1.a2', '64.dm1.g1', '64.dm1.g2', '64.dm1.c1', '64.dm1.c2', '64.dm1.e1', '64.dm1.e2', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dk1.a1', '64.dk1.c1', '64.dk1.b1', '64.dk1.d1', '64.dk1.m1', '64.dk1.o1', '64.dk1.n1', '64.dk1.p1', '64.dk1.e1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.i1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.do1.a1', '64.do1.c1', '64.do1.a2', '64.do1.c2', '64.do1.d1', '64.do1.b1', '64.do1.d2', '64.do1.b2', '64.do1.e2', '64.do1.g2', '64.do1.e1', '64.do1.g1', '64.do1.h2', '64.do1.f2', '64.do1.h1', '64.do1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '2.r1.a1', '2.ba1.a1'], 'contains': ['8.bg1.a1', '8.bi1.a1', '8.bp1.a1', '8.ed1.a1', '8.eg1.a1', '8.er1.a1', '8.fr1.a1'], 'core': '4.cz1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5311, 2304, 5966, 1088, 5314, 2303, 5961, 1090], 'generators': [65, 4, 16], 'label': '256.30836.4.cz1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cz1.a1', 'normal_contained_in': ['2.r1.a1', '2.i1.a1', '2.ba1.a1'], 'normal_contains': ['8.bg1.a1', '8.bi1.a1', '8.bp1.a1', '8.ed1.a1', '8.eg1.a1', '8.er1.a1', '8.fr1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cz1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878330
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.a1', '16.iq1.a1', '16.iq1.b1', '16.iv1.a1', '16.iv1.b1', '16.iz1.a1', '16.iz1.b1'], 'contains': ['64.g1.a1', '64.cd1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6794, -1, 5263, -1, 6798, -1, 5259, -1], 'generators': [80, 136], 'label': '256.30836.32.fw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.fw1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fw1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878331
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.io1.a1', '16.io1.b1', '16.iw1.a1', '16.iw1.b1', '16.jb1.a1', '16.jb1.b1'], 'contains': ['64.g1.a1', '64.ce1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7599, -1, 5370, -1, 7603, -1, 5365, -1], 'generators': [20, 136], 'label': '256.30836.32.fx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '32.fx1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fx1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878332
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fy1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.ec1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.iq1.a1', '16.iq1.b1', '16.it1.a1', '16.it1.b1', '16.jc1.a1', '16.jc1.b1'], 'contains': ['64.g1.a1', '64.cw1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6529, -1, 5286, -1, 6533, -1, 5282, -1], 'generators': [82, 160], 'label': '256.30836.32.fy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.fy1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fy1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878333
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.fz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1', '16.in1.a1', '16.in1.b1', '16.iv1.a1', '16.iv1.b1', '16.jc1.a1', '16.jc1.b1'], 'contains': ['64.g1.a1', '64.cn1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6485, -1, 5309, -1, 6489, -1, 5305, -1], 'generators': [81, 160], 'label': '256.30836.32.fz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.fz1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.fz1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878334
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ga1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.ip1.a1', '16.ip1.b1', '16.iw1.a1', '16.iw1.b1', '16.ja1.a1', '16.ja1.b1'], 'contains': ['64.g1.a1', '64.co1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7015, -1, 5393, -1, 7018, -1, 5388, -1], 'generators': [21, 160], 'label': '256.30836.32.ga1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '32.ga1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ga1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878335
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.a1', '16.bh1.a1', '16.hd1.a1', '16.jd1.a1', '16.jd1.b1', '16.jd1.c1', '16.jd1.d1'], 'contains': ['64.bu1.a1', '64.bv1.a1', '64.bz1.a1', '64.di1.a1', '64.di1.d1', '64.di1.g1', '64.di1.p1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9479, -1, 4244, -1, 9484, -1, 4241, -1], 'generators': [1, 2, 160], 'label': '256.30836.32.gb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gb1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gb1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878336
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.b1', '16.bh1.a1', '16.hd1.a1', '16.jd1.e1', '16.jd1.f1', '16.jd1.g1', '16.jd1.h1'], 'contains': ['64.bu1.a1', '64.bv1.b1', '64.bz1.b1', '64.di1.b1', '64.di1.c1', '64.di1.n1', '64.di1.o1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9479, -1, 3605, -1, 9484, -1, 3602, -1], 'generators': [129, 2, 160], 'label': '256.30836.32.gb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gb1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gb1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878337
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.c1', '16.bh1.a1', '16.hd1.a1', '16.jd1.i1', '16.jd1.j1', '16.jd1.k1', '16.jd1.l1'], 'contains': ['64.bu1.b1', '64.bv1.a1', '64.bz1.b1', '64.di1.e1', '64.di1.f1', '64.di1.j1', '64.di1.m1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9479, -1, 3438, -1, 9484, -1, 3435, -1], 'generators': [1, 130, 160], 'label': '256.30836.32.gb1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gb1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gb1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878338
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.d1', '16.bh1.a1', '16.hd1.a1', '16.jd1.m1', '16.jd1.n1', '16.jd1.o1', '16.jd1.p1'], 'contains': ['64.bu1.b1', '64.bv1.b1', '64.bz1.a1', '64.di1.h1', '64.di1.i1', '64.di1.k1', '64.di1.l1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9479, -1, 4370, -1, 9484, -1, 4366, -1], 'generators': [129, 130, 160], 'label': '256.30836.32.gb1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gb1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gb1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878339
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.he1.a1', '16.il1.a1', '16.jd1.a1', '16.jd1.b1', '16.jd1.e1', '16.jd1.f1'], 'contains': ['64.bu1.a1', '64.bw1.a1', '64.bx1.a1', '64.dj1.a1', '64.dj1.b1', '64.dj1.m1', '64.dj1.n1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9586, -1, 3133, -1, 9590, -1, 3130, -1], 'generators': [2, 4, 160], 'label': '256.30836.32.gc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gc1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878390
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cq1.b1', '16.fx1.a1', '16.im1.b1', '16.je1.d1', '16.je1.d2', '16.je1.g1', '16.je1.g2'], 'contains': ['64.h1.c1', '64.ci1.a1', '64.ck1.a1', '64.dk1.i1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 1770, -1, 9164, -1, 1769, -1], 'generators': [5, 34, 40], 'label': '256.30836.32.gm1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gm1.c1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gm1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878391
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cq1.b1', '16.fx1.b1', '16.im1.a1', '16.je1.e1', '16.je1.e2', '16.je1.h1', '16.je1.h2'], 'contains': ['64.h1.d1', '64.ci1.a1', '64.ck1.a1', '64.dk1.m1', '64.dk1.n1', '64.dk1.o1', '64.dk1.p1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 1910, -1, 9164, -1, 1908, -1], 'generators': [5, 162, 40], 'label': '256.30836.32.gm1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gm1.d1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gm1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878392
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cr1.a1', '16.fy1.a1', '16.in1.a1'], 'contains': ['64.h1.a1', '64.cl1.a1', '64.cn1.a1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4056, -1, 8584, -1, 4057, -1, 8577, -1], 'generators': [81, 2], 'label': '256.30836.32.gn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '32.gn1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878340
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.da1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.e1', '64.di1.i1', '64.di1.j1', '64.di1.h1', '64.di1.g1', '64.di1.o1', '64.di1.p1', '64.di1.n1', '64.di1.f1', '64.di1.l1', '64.di1.m1', '64.di1.k1', '64.dk1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.d1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.g1', '64.dk1.n1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.i1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.b2', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.f1', '64.do1.e2', '64.do1.f2', '64.do1.e1', '64.do1.g1', '64.do1.h2', '64.do1.g2', '64.do1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '2.s1.a1', '2.y1.a1'], 'contains': ['8.bh1.a1', '8.bk1.a1', '8.bn1.a1', '8.ei1.a1', '8.ek1.a1', '8.fa1.a1', '8.fs1.a1'], 'core': '4.da1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7939, 710, 6013, 2274, 7943, 709, 6008, 2279], 'generators': [66, 4, 80], 'label': '256.30836.4.da1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.da1.a1', 'normal_contained_in': ['2.s1.a1', '2.j1.a1', '2.y1.a1'], 'normal_contains': ['8.bh1.a1', '8.bk1.a1', '8.bn1.a1', '8.ei1.a1', '8.ek1.a1', '8.fa1.a1', '8.fs1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.da1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.da1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878341
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.b1', '16.he1.a1', '16.il1.a1', '16.jd1.c1', '16.jd1.d1', '16.jd1.g1', '16.jd1.h1'], 'contains': ['64.bu1.a1', '64.bw1.b1', '64.bx1.a1', '64.dj1.c1', '64.dj1.d1', '64.dj1.o1', '64.dj1.p1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9586, -1, 4189, -1, 9590, -1, 4185, -1], 'generators': [2, 140, 160], 'label': '256.30836.32.gc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gc1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gc1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878342
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.he1.a1', '16.il1.b1', '16.jd1.i1', '16.jd1.j1', '16.jd1.m1', '16.jd1.n1'], 'contains': ['64.bu1.b1', '64.bw1.a1', '64.bx1.a1', '64.dj1.e1', '64.dj1.f1', '64.dj1.i1', '64.dj1.j1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9586, -1, 3146, -1, 9590, -1, 3144, -1], 'generators': [130, 4, 160], 'label': '256.30836.32.gc1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gc1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gc1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878343
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.b1', '16.he1.a1', '16.il1.b1', '16.jd1.k1', '16.jd1.l1', '16.jd1.o1', '16.jd1.p1'], 'contains': ['64.bu1.b1', '64.bw1.b1', '64.bx1.a1', '64.dj1.g1', '64.dj1.h1', '64.dj1.k1', '64.dj1.l1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9586, -1, 4203, -1, 9590, -1, 4199, -1], 'generators': [130, 140, 160], 'label': '256.30836.32.gc1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gc1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gc1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878344
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.hf1.a1', '16.im1.a1', '16.jd1.a1', '16.jd1.c1', '16.jd1.e1', '16.jd1.g1'], 'contains': ['64.bu1.a1', '64.by1.a1', '64.ca1.a1', '64.dk1.a1', '64.dk1.b1', '64.dk1.m1', '64.dk1.n1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9692, -1, 4147, -1, 9697, -1, 4144, -1], 'generators': [5, 2, 160], 'label': '256.30836.32.gd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gd1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878345
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.hf1.b1', '16.im1.a1', '16.jd1.b1', '16.jd1.d1', '16.jd1.f1', '16.jd1.h1'], 'contains': ['64.bu1.a1', '64.by1.b1', '64.ca1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.o1', '64.dk1.p1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9692, -1, 3119, -1, 9697, -1, 3116, -1], 'generators': [141, 2, 160], 'label': '256.30836.32.gd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gd1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gd1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878346
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.hf1.a1', '16.im1.b1', '16.jd1.i1', '16.jd1.k1', '16.jd1.m1', '16.jd1.o1'], 'contains': ['64.bu1.b1', '64.by1.a1', '64.ca1.a1', '64.dk1.e1', '64.dk1.f1', '64.dk1.i1', '64.dk1.j1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9692, -1, 4175, -1, 9697, -1, 4171, -1], 'generators': [5, 130, 160], 'label': '256.30836.32.gd1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gd1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gd1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878347
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.hf1.b1', '16.im1.b1', '16.jd1.j1', '16.jd1.l1', '16.jd1.n1', '16.jd1.p1'], 'contains': ['64.bu1.b1', '64.by1.b1', '64.ca1.a1', '64.dk1.g1', '64.dk1.h1', '64.dk1.k1', '64.dk1.l1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9692, -1, 3257, -1, 9697, -1, 3255, -1], 'generators': [141, 130, 160], 'label': '256.30836.32.gd1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gd1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gd1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878348
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ge1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bl1.a1', '16.hh1.a1', '16.io1.a1'], 'contains': ['64.bu1.a1', '64.cc1.a1', '64.ce1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7874, -1, 5592, -1, 7878, -1, 5587, -1], 'generators': [2, 20], 'label': '256.30836.32.ge1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.ge1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ge1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878349
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ge1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bl1.a1', '16.hh1.a1', '16.io1.b1'], 'contains': ['64.bu1.b1', '64.cc1.a1', '64.ce1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7874, -1, 5615, -1, 7878, -1, 5610, -1], 'generators': [130, 20], 'label': '256.30836.32.ge1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.i1.a1', 'old_label': '32.ge1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ge1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878350
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1', '16.hi1.a1', '16.ir1.a1', '16.jd1.a1', '16.jd1.i1'], 'contains': ['64.bv1.a1', '64.bw1.a1', '64.by1.a1', '64.dl1.a1', '64.dl1.m1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9612, -1, 4258, -1, 9617, -1, 4255, -1], 'generators': [1, 4, 160], 'label': '256.30836.32.gf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gf1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878393
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cr1.a1', '16.fy1.b1', '16.in1.b1'], 'contains': ['64.h1.b1', '64.cl1.a1', '64.cn1.a1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4056, -1, 8596, -1, 4057, -1, 8589, -1], 'generators': [81, 130], 'label': '256.30836.32.gn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '32.gn1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gn1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878394
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cr1.b1', '16.fy1.a1', '16.in1.b1'], 'contains': ['64.h1.c1', '64.cl1.a1', '64.cn1.a1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [4056, -1, 8572, -1, 4057, -1, 8564, -1], 'generators': [81, 34], 'label': '256.30836.32.gn1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '32.gn1.c1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gn1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878411
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gr1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.db1.a1', '16.gi1.a1', '16.ix1.a1', '16.je1.a2', '16.je1.e1', '16.je1.f2', '16.je1.g1'], 'contains': ['64.cg1.a1', '64.cj1.a1', '64.ck1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.e1', '64.dn1.f2'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9293, -1, 2049, -1, 9298, -1, 2047, -1], 'generators': [163, 4, 40], 'label': '256.30836.32.gr1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gr1.a2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gr1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878351
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.db1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.c1', '64.di1.b1', '64.di1.l1', '64.di1.k1', '64.di1.f1', '64.di1.m1', '64.di1.h1', '64.di1.i1', '64.di1.j1', '64.di1.e1', '64.di1.p1', '64.di1.g1', '64.di1.n1', '64.di1.o1', '64.dk1.a1', '64.dk1.d1', '64.dk1.c1', '64.dk1.b1', '64.dk1.k1', '64.dk1.j1', '64.dk1.i1', '64.dk1.l1', '64.dk1.g1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.n1', '64.do1.a1', '64.do1.c2', '64.do1.d2', '64.do1.b1', '64.do1.d1', '64.do1.b2', '64.do1.a2', '64.do1.c1', '64.do1.g2', '64.do1.e1', '64.do1.f1', '64.do1.h2', '64.do1.f2', '64.do1.h1', '64.do1.g1', '64.do1.e2', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.h1', '64.dm1.b2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dm1.d2', '64.dm1.b1', '64.dm1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '2.s1.a1', '2.ba1.a1'], 'contains': ['8.bh1.a1', '8.bm1.a1', '8.bp1.a1', '8.ej1.a1', '8.em1.a1', '8.fk1.a1', '8.fx1.a1'], 'core': '4.db1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5725, 1247, 8518, 2215, 5728, 1246, 8511, 2220], 'generators': [81, 66, 4], 'label': '256.30836.4.db1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.db1.a1', 'normal_contained_in': ['2.s1.a1', '2.h1.a1', '2.ba1.a1'], 'normal_contains': ['8.bm1.a1', '8.bh1.a1', '8.bp1.a1', '8.ej1.a1', '8.fk1.a1', '8.em1.a1', '8.fx1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.db1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.db1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878352
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1', '16.hi1.b1', '16.ir1.a1', '16.jd1.b1', '16.jd1.j1'], 'contains': ['64.bv1.a1', '64.bw1.a1', '64.by1.b1', '64.dl1.b1', '64.dl1.n1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9612, -1, 4022, -1, 9617, -1, 4019, -1], 'generators': [137, 4, 160], 'label': '256.30836.32.gf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gf1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gf1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878353
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.b1', '16.hi1.a1', '16.ir1.a1', '16.jd1.c1', '16.jd1.k1'], 'contains': ['64.bv1.a1', '64.bw1.b1', '64.by1.a1', '64.dl1.c1', '64.dl1.o1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9612, -1, 4550, -1, 9617, -1, 4546, -1], 'generators': [137, 140, 160], 'label': '256.30836.32.gf1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gf1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gf1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878354
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.b1', '16.hi1.b1', '16.ir1.a1', '16.jd1.d1', '16.jd1.l1'], 'contains': ['64.bv1.a1', '64.bw1.b1', '64.by1.b1', '64.dl1.d1', '64.dl1.p1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9612, -1, 4300, -1, 9617, -1, 4296, -1], 'generators': [1, 140, 160], 'label': '256.30836.32.gf1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gf1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gf1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878355
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1', '16.hi1.a1', '16.ir1.b1', '16.jd1.e1', '16.jd1.m1'], 'contains': ['64.bv1.b1', '64.bw1.a1', '64.by1.a1', '64.dl1.e1', '64.dl1.i1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9612, -1, 4356, -1, 9617, -1, 4352, -1], 'generators': [9, 4, 160], 'label': '256.30836.32.gf1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gf1.e1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gf1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878356
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1', '16.hi1.b1', '16.ir1.b1', '16.jd1.f1', '16.jd1.n1'], 'contains': ['64.bv1.b1', '64.bw1.a1', '64.by1.b1', '64.dl1.f1', '64.dl1.j1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9612, -1, 4092, -1, 9617, -1, 4088, -1], 'generators': [129, 4, 160], 'label': '256.30836.32.gf1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gf1.f1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gf1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878357
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.b1', '16.hi1.a1', '16.ir1.b1', '16.jd1.g1', '16.jd1.o1'], 'contains': ['64.bv1.b1', '64.bw1.b1', '64.by1.a1', '64.dl1.g1', '64.dl1.k1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9612, -1, 4676, -1, 9617, -1, 4671, -1], 'generators': [129, 140, 160], 'label': '256.30836.32.gf1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gf1.g1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gf1.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878358
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.b1', '16.hi1.b1', '16.ir1.b1', '16.jd1.h1', '16.jd1.p1'], 'contains': ['64.bv1.b1', '64.bw1.b1', '64.by1.b1', '64.dl1.h1', '64.dl1.l1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9612, -1, 4384, -1, 9617, -1, 4380, -1], 'generators': [9, 140, 160], 'label': '256.30836.32.gf1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gf1.h1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gf1.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878359
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bn1.a1', '16.hj1.a1', '16.is1.a1', '16.jd1.a1', '16.jd1.d1', '16.jd1.j1', '16.jd1.k1'], 'contains': ['64.bv1.a1', '64.bx1.a1', '64.ca1.a1', '64.dm1.a1', '64.dm1.b2', '64.dm1.g1', '64.dm1.h2'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9719, -1, 3425, -1, 9723, -1, 3422, -1], 'generators': [1, 6, 160], 'label': '256.30836.32.gg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gg1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878360
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bn1.a1', '16.hj1.a1', '16.is1.a1', '16.jd1.b1', '16.jd1.c1', '16.jd1.i1', '16.jd1.l1'], 'contains': ['64.bv1.a1', '64.bx1.a1', '64.ca1.a1', '64.dm1.a2', '64.dm1.b1', '64.dm1.g2', '64.dm1.h1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9719, -1, 3105, -1, 9723, -1, 3102, -1], 'generators': [137, 6, 160], 'label': '256.30836.32.gg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gg1.a2', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gg1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878361
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bn1.a1', '16.hj1.a1', '16.is1.b1', '16.jd1.e1', '16.jd1.h1', '16.jd1.n1', '16.jd1.o1'], 'contains': ['64.bv1.b1', '64.bx1.a1', '64.ca1.a1', '64.dm1.c2', '64.dm1.d1', '64.dm1.e2', '64.dm1.f1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9719, -1, 3286, -1, 9723, -1, 3283, -1], 'generators': [9, 6, 160], 'label': '256.30836.32.gg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gg1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gg1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878407
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gq1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cy1.a1', '16.gf1.a1', '16.is1.a1', '16.je1.a2', '16.je1.c1', '16.je1.d1', '16.je1.e2'], 'contains': ['64.cf1.a1', '64.ch1.a1', '64.ck1.a1', '64.dm1.a2', '64.dm1.b1', '64.dm1.g1', '64.dm1.h2'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1604, -1, 9218, -1, 1602, -1], 'generators': [161, 6, 40], 'label': '256.30836.32.gq1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gq1.a2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gq1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878408
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gq1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cy1.a1', '16.gf1.a1', '16.is1.b1', '16.je1.b1', '16.je1.f2', '16.je1.g2', '16.je1.h1'], 'contains': ['64.cf1.b1', '64.ch1.a1', '64.ck1.a1', '64.dm1.c1', '64.dm1.d2', '64.dm1.e2', '64.dm1.f1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1784, -1, 9218, -1, 1783, -1], 'generators': [129, 6, 40], 'label': '256.30836.32.gq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gq1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gq1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879161
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bp1.a1'], 'contains': ['16.bf1.a1', '16.dz1.a1', '16.eb1.a1', '16.ef1.a1', '16.ei1.a1', '16.ej1.a1', '16.em1.a1'], 'core': '16.bf1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9090, -1, 4460, -1, 9094, -1, 4456, -1], 'generators': [1, 82, 84], 'label': '256.30836.8.gm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '8.gm1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878362
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dc1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.di1.i1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.l1', '64.dm1.a1', '64.dm1.a2', '64.dm1.g1', '64.dm1.g2', '64.dm1.c1', '64.dm1.c2', '64.dm1.e1', '64.dm1.e2', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dk1.a1', '64.dk1.c1', '64.dk1.b1', '64.dk1.d1', '64.dk1.m1', '64.dk1.o1', '64.dk1.n1', '64.dk1.p1', '64.dk1.e1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.i1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.do1.a1', '64.do1.c1', '64.do1.a2', '64.do1.c2', '64.do1.d1', '64.do1.b1', '64.do1.d2', '64.do1.b2', '64.do1.e2', '64.do1.g2', '64.do1.e1', '64.do1.g1', '64.do1.h2', '64.do1.f2', '64.do1.h1', '64.do1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '2.r1.a1', '2.y1.a1'], 'contains': ['8.bi1.a1', '8.bj1.a1', '8.bn1.a1', '8.eo1.a1', '8.es1.a1', '8.ew1.a1', '8.fm1.a1'], 'core': '4.dc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3678, 654, 6473, 5969, 3680, 654, 6467, 5982], 'generators': [65, 4, 80], 'label': '256.30836.4.dc1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dc1.a1', 'normal_contained_in': ['2.r1.a1', '2.k1.a1', '2.y1.a1'], 'normal_contains': ['8.bi1.a1', '8.bj1.a1', '8.bn1.a1', '8.eo1.a1', '8.es1.a1', '8.ew1.a1', '8.fm1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dc1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878363
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bn1.a1', '16.hj1.a1', '16.is1.b1', '16.jd1.f1', '16.jd1.g1', '16.jd1.m1', '16.jd1.p1'], 'contains': ['64.bv1.b1', '64.bx1.a1', '64.ca1.a1', '64.dm1.c1', '64.dm1.d2', '64.dm1.e1', '64.dm1.f2'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9719, -1, 3647, -1, 9723, -1, 3644, -1], 'generators': [129, 6, 160], 'label': '256.30836.32.gg1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gg1.b2', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gg1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878364
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.a1', '16.hm1.a1', '16.ix1.a1', '16.jd1.a1', '16.jd1.b1', '16.jd1.m1', '16.jd1.n1'], 'contains': ['64.bw1.a1', '64.bz1.a1', '64.ca1.a1', '64.dn1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.b2'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 3452, -1, 9750, -1, 3449, -1], 'generators': [3, 4, 160], 'label': '256.30836.32.gh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gh1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878365
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.a1', '16.hm1.a1', '16.ix1.b1', '16.jd1.e1', '16.jd1.f1', '16.jd1.i1', '16.jd1.j1'], 'contains': ['64.bw1.a1', '64.bz1.b1', '64.ca1.a1', '64.dn1.c1', '64.dn1.c2', '64.dn1.d1', '64.dn1.d2'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 576, -1, 9750, -1, 575, -1], 'generators': [131, 4, 160], 'label': '256.30836.32.gh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gh1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gh1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878366
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.b1', '16.hm1.a1', '16.ix1.a1', '16.jd1.c1', '16.jd1.d1', '16.jd1.o1', '16.jd1.p1'], 'contains': ['64.bw1.b1', '64.bz1.a1', '64.ca1.a1', '64.dn1.e1', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 4342, -1, 9750, -1, 4338, -1], 'generators': [3, 140, 160], 'label': '256.30836.32.gh1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gh1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gh1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878367
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.b1', '16.hm1.a1', '16.ix1.b1', '16.jd1.g1', '16.jd1.h1', '16.jd1.k1', '16.jd1.l1'], 'contains': ['64.bw1.b1', '64.bz1.b1', '64.ca1.a1', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 3160, -1, 9750, -1, 3158, -1], 'generators': [131, 140, 160], 'label': '256.30836.32.gh1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gh1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gh1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878368
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.hp1.a1', '16.iy1.a1', '16.jd1.a1', '16.jd1.c1', '16.jd1.m1', '16.jd1.o1'], 'contains': ['64.bx1.a1', '64.by1.a1', '64.bz1.a1', '64.do1.a1', '64.do1.a2', '64.do1.e1', '64.do1.e2'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 4328, -1, 9537, -1, 4324, -1], 'generators': [5, 6, 160], 'label': '256.30836.32.gi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gi1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gi1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878369
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.hp1.a1', '16.iy1.b1', '16.jd1.e1', '16.jd1.g1', '16.jd1.i1', '16.jd1.k1'], 'contains': ['64.bx1.a1', '64.by1.a1', '64.bz1.b1', '64.do1.b1', '64.do1.b2', '64.do1.f1', '64.do1.f2'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 3022, -1, 9537, -1, 3019, -1], 'generators': [13, 6, 160], 'label': '256.30836.32.gi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gi1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gi1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878370
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.hp1.b1', '16.iy1.a1', '16.jd1.b1', '16.jd1.d1', '16.jd1.n1', '16.jd1.p1'], 'contains': ['64.bx1.a1', '64.by1.b1', '64.bz1.a1', '64.do1.c1', '64.do1.c2', '64.do1.g1', '64.do1.g2'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 3619, -1, 9537, -1, 3616, -1], 'generators': [141, 6, 160], 'label': '256.30836.32.gi1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gi1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gi1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878371
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.hp1.b1', '16.iy1.b1', '16.jd1.f1', '16.jd1.h1', '16.jd1.j1', '16.jd1.l1'], 'contains': ['64.bx1.a1', '64.by1.b1', '64.bz1.b1', '64.do1.d1', '64.do1.d2', '64.do1.h1', '64.do1.h2'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 534, -1, 9537, -1, 533, -1], 'generators': [133, 6, 160], 'label': '256.30836.32.gi1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gi1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gi1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878372
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cc1.a1', '16.hy1.a1', '16.iz1.a1'], 'contains': ['64.bz1.a1', '64.cb1.a1', '64.cd1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6143, -1, 6030, -1, 6146, -1, 6026, -1], 'generators': [3, 80], 'label': '256.30836.32.gj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.cp1.a1', 'old_label': '32.gj1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878409
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gq1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cy1.a1', '16.gf1.a1', '16.is1.b1', '16.je1.b2', '16.je1.f1', '16.je1.g1', '16.je1.h2'], 'contains': ['64.cf1.b1', '64.ch1.a1', '64.ck1.a1', '64.dm1.c2', '64.dm1.d1', '64.dm1.e1', '64.dm1.f2'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1563, -1, 9218, -1, 1561, -1], 'generators': [33, 6, 40], 'label': '256.30836.32.gq1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gq1.b2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gq1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878410
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gr1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.db1.a1', '16.gi1.a1', '16.ix1.a1', '16.je1.a1', '16.je1.e2', '16.je1.f1', '16.je1.g2'], 'contains': ['64.cg1.a1', '64.cj1.a1', '64.ck1.a1', '64.dn1.a1', '64.dn1.b2', '64.dn1.e2', '64.dn1.f1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9293, -1, 2118, -1, 9298, -1, 2116, -1], 'generators': [3, 4, 40], 'label': '256.30836.32.gr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gr1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gr1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878373
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dd1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.k1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.dm1.a1', '64.dm1.a2', '64.dm1.g1', '64.dm1.g2', '64.dm1.c1', '64.dm1.c2', '64.dm1.e1', '64.dm1.e2', '64.dm1.h2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.f2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.do1.a1', '64.do1.c1', '64.do1.a2', '64.do1.c2', '64.do1.d1', '64.do1.b1', '64.do1.d2', '64.do1.b2', '64.do1.e1', '64.do1.g1', '64.do1.e2', '64.do1.g2', '64.do1.h1', '64.do1.f1', '64.do1.h2', '64.do1.f2', '64.dk1.a1', '64.dk1.c1', '64.dk1.b1', '64.dk1.d1', '64.dk1.o1', '64.dk1.m1', '64.dk1.p1', '64.dk1.n1', '64.dk1.g1', '64.dk1.e1', '64.dk1.h1', '64.dk1.f1', '64.dk1.i1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '2.p1.a1', '2.ba1.a1'], 'contains': ['8.bi1.a1', '8.bm1.a1', '8.bo1.a1', '8.eq1.a1', '8.et1.a1', '8.fj1.a1', '8.fy1.a1'], 'core': '4.dd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3425, 878, 6656, 701, 3426, 878, 6650, 702], 'generators': [65, 82, 4], 'label': '256.30836.4.dd1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dd1.a1', 'normal_contained_in': ['2.p1.a1', '2.k1.a1', '2.ba1.a1'], 'normal_contains': ['8.bm1.a1', '8.bi1.a1', '8.bo1.a1', '8.eq1.a1', '8.fj1.a1', '8.et1.a1', '8.fy1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dd1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878374
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cc1.a1', '16.hy1.a1', '16.iz1.b1'], 'contains': ['64.bz1.b1', '64.cb1.a1', '64.cd1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6143, -1, 6018, -1, 6146, -1, 6013, -1], 'generators': [131, 80], 'label': '256.30836.32.gj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.cp1.a1', 'old_label': '32.gj1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gj1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878375
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.a1', '16.co1.a1', '16.fv1.a1', '16.je1.a1', '16.je1.a2'], 'contains': ['64.h1.a1', '64.cf1.a1', '64.cj1.a1', '64.di1.a1', '64.di1.d1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8761, -1, 4953, -1, 8765, -1, 4949, -1], 'generators': [1, 2, 40], 'label': '256.30836.32.gk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gk1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gk1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878376
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.b1', '16.co1.a1', '16.fv1.a1', '16.je1.b1', '16.je1.b2'], 'contains': ['64.h1.a1', '64.cf1.b1', '64.cj1.b1', '64.di1.b1', '64.di1.c1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8761, -1, 4884, -1, 8765, -1, 4880, -1], 'generators': [129, 2, 40], 'label': '256.30836.32.gk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gk1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gk1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878377
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.c1', '16.co1.a1', '16.fv1.b1', '16.je1.c1', '16.je1.c2'], 'contains': ['64.h1.b1', '64.cf1.a1', '64.cj1.b1', '64.di1.e1', '64.di1.j1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8761, -1, 4898, -1, 8765, -1, 4893, -1], 'generators': [1, 130, 40], 'label': '256.30836.32.gk1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gk1.c1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gk1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878378
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.c1', '16.co1.b1', '16.fv1.a1', '16.je1.d1', '16.je1.d2'], 'contains': ['64.h1.c1', '64.cf1.a1', '64.cj1.b1', '64.di1.f1', '64.di1.m1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [8761, -1, 4856, -1, 8765, -1, 4852, -1], 'generators': [1, 34, 40], 'label': '256.30836.32.gk1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gk1.d1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gk1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878379
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.a1', '16.co1.b1', '16.fv1.b1', '16.je1.e1', '16.je1.e2'], 'contains': ['64.h1.d1', '64.cf1.a1', '64.cj1.a1', '64.di1.g1', '64.di1.p1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [8761, -1, 4911, -1, 8765, -1, 4907, -1], 'generators': [1, 162, 40], 'label': '256.30836.32.gk1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gk1.e1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gk1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878380
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.d1', '16.co1.a1', '16.fv1.b1', '16.je1.f1', '16.je1.f2'], 'contains': ['64.h1.b1', '64.cf1.b1', '64.cj1.a1', '64.di1.h1', '64.di1.i1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8761, -1, 5009, -1, 8765, -1, 5005, -1], 'generators': [129, 130, 40], 'label': '256.30836.32.gk1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gk1.f1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gk1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878381
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.d1', '16.co1.b1', '16.fv1.a1', '16.je1.g1', '16.je1.g2'], 'contains': ['64.h1.c1', '64.cf1.b1', '64.cj1.a1', '64.di1.k1', '64.di1.l1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [8761, -1, 4939, -1, 8765, -1, 4935, -1], 'generators': [129, 34, 40], 'label': '256.30836.32.gk1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gk1.g1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gk1.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878382
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gk1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.b1', '16.co1.b1', '16.fv1.b1', '16.je1.h1', '16.je1.h2'], 'contains': ['64.h1.d1', '64.cf1.b1', '64.cj1.b1', '64.di1.n1', '64.di1.o1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [8761, -1, 4870, -1, 8765, -1, 4866, -1], 'generators': [129, 162, 40], 'label': '256.30836.32.gk1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gk1.h1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gk1.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878383
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cp1.a1', '16.fw1.a1', '16.il1.a1', '16.je1.a1', '16.je1.a2', '16.je1.b1', '16.je1.b2'], 'contains': ['64.h1.a1', '64.cg1.a1', '64.ch1.a1', '64.dj1.a1', '64.dj1.b1', '64.dj1.c1', '64.dj1.d1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2382, -1, 9138, -1, 2380, -1], 'generators': [2, 4, 40], 'label': '256.30836.32.gl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gl1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878384
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.de1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.do1.a1', '64.do1.b2', '64.do1.d2', '64.do1.c1', '64.do1.d1', '64.do1.c2', '64.do1.a2', '64.do1.b1', '64.do1.f1', '64.do1.e2', '64.do1.g2', '64.do1.h1', '64.do1.g1', '64.do1.h2', '64.do1.f2', '64.do1.e1', '64.dm1.a1', '64.dm1.e2', '64.dm1.e1', '64.dm1.a2', '64.dm1.c1', '64.dm1.g2', '64.dm1.g1', '64.dm1.c2', '64.dm1.b1', '64.dm1.f2', '64.dm1.f1', '64.dm1.b2', '64.dm1.d1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.f1', '64.dk1.e1', '64.dk1.g1', '64.dk1.h1', '64.dk1.j1', '64.dk1.i1', '64.dk1.k1', '64.dk1.l1', '64.dk1.m1', '64.dk1.n1', '64.dk1.p1', '64.dk1.o1'], 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '2.q1.a1', '2.z1.a1'], 'contains': ['8.bj1.a1', '8.bl1.a1', '8.bo1.a1', '8.eu1.a1', '8.ey1.a1', '8.fh1.a1', '8.fw1.a1'], 'core': '4.de1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3174, 5309, 8814, 6135, 3176, 5306, 8806, 6149], 'generators': [17, 82, 4], 'label': '256.30836.4.de1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.de1.a1', 'normal_contained_in': ['2.q1.a1', '2.k1.a1', '2.z1.a1'], 'normal_contains': ['8.bl1.a1', '8.bj1.a1', '8.bo1.a1', '8.eu1.a1', '8.fh1.a1', '8.ey1.a1', '8.fw1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.de1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.de1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878395
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.df1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.p1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.f1', '64.do1.a1', '64.do1.c2', '64.do1.a2', '64.do1.c1', '64.do1.d1', '64.do1.b2', '64.do1.d2', '64.do1.b1', '64.do1.g2', '64.do1.e1', '64.do1.g1', '64.do1.e2', '64.do1.f2', '64.do1.h1', '64.do1.f1', '64.do1.h2', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.m1', '64.dk1.p1', '64.dk1.n1', '64.dk1.o1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.e1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.dk1.i1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '2.s1.a1', '2.z1.a1'], 'contains': ['8.bk1.a1', '8.bl1.a1', '8.bp1.a1', '8.ez1.a1', '8.fc1.a1', '8.fg1.a1', '8.fu1.a1'], 'core': '4.df1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6892, 9444, 7992, 1345, 6896, 9441, 7985, 1349], 'generators': [81, 18, 4], 'label': '256.30836.4.df1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.df1.a1', 'normal_contained_in': ['2.s1.a1', '2.i1.a1', '2.z1.a1'], 'normal_contains': ['8.bl1.a1', '8.bk1.a1', '8.bp1.a1', '8.ez1.a1', '8.fg1.a1', '8.fc1.a1', '8.fu1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.df1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.df1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878396
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cr1.b1', '16.fy1.b1', '16.in1.a1'], 'contains': ['64.h1.d1', '64.cl1.a1', '64.cn1.a1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [4056, -1, 8560, -1, 4057, -1, 8552, -1], 'generators': [81, 162], 'label': '256.30836.32.gn1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '32.gn1.d1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gn1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878397
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.go1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cv1.a1', '16.ga1.a1', '16.ip1.a1'], 'contains': ['64.h1.a1', '64.cm1.a1', '64.co1.a1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4924, -1, 8469, -1, 4921, -1, 8461, -1], 'generators': [21, 2], 'label': '256.30836.32.go1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '32.go1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.go1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878398
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.go1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cv1.a1', '16.ga1.b1', '16.ip1.b1'], 'contains': ['64.h1.b1', '64.cm1.a1', '64.co1.a1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4924, -1, 8492, -1, 4921, -1, 8484, -1], 'generators': [21, 130], 'label': '256.30836.32.go1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '32.go1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.go1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878399
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.go1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cv1.b1', '16.ga1.a1', '16.ip1.b1'], 'contains': ['64.h1.c1', '64.cm1.a1', '64.co1.a1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [4924, -1, 8445, -1, 4921, -1, 8438, -1], 'generators': [21, 34], 'label': '256.30836.32.go1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '32.go1.c1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.go1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878400
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.go1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cv1.b1', '16.ga1.b1', '16.ip1.a1'], 'contains': ['64.h1.d1', '64.cm1.a1', '64.co1.a1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [4924, -1, 8422, -1, 4921, -1, 8415, -1], 'generators': [21, 162], 'label': '256.30836.32.go1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '32.go1.d1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.go1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878401
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cx1.a1', '16.ge1.a1', '16.ir1.a1', '16.je1.a1', '16.je1.c1', '16.je1.d1', '16.je1.e1'], 'contains': ['64.cf1.a1', '64.cg1.a1', '64.ci1.a1', '64.dl1.a1', '64.dl1.d1', '64.dl1.n1', '64.dl1.o1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 1229, -1, 9191, -1, 1227, -1], 'generators': [1, 4, 40], 'label': '256.30836.32.gp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gp1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gp1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878402
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cx1.a1', '16.ge1.a1', '16.ir1.a1', '16.je1.a2', '16.je1.c2', '16.je1.d2', '16.je1.e2'], 'contains': ['64.cf1.a1', '64.cg1.a1', '64.ci1.a1', '64.dl1.b1', '64.dl1.c1', '64.dl1.m1', '64.dl1.p1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 1576, -1, 9191, -1, 1575, -1], 'generators': [161, 4, 40], 'label': '256.30836.32.gp1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gp1.a2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gp1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878403
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cx1.a1', '16.ge1.a1', '16.ir1.b1', '16.je1.b1', '16.je1.f1', '16.je1.g1', '16.je1.h1'], 'contains': ['64.cf1.b1', '64.cg1.a1', '64.ci1.a1', '64.dl1.f1', '64.dl1.g1', '64.dl1.i1', '64.dl1.l1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 1381, -1, 9191, -1, 1380, -1], 'generators': [129, 4, 40], 'label': '256.30836.32.gp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gp1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gp1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878404
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cx1.a1', '16.ge1.a1', '16.ir1.b1', '16.je1.b2', '16.je1.f2', '16.je1.g2', '16.je1.h2'], 'contains': ['64.cf1.b1', '64.cg1.a1', '64.ci1.a1', '64.dl1.e1', '64.dl1.h1', '64.dl1.j1', '64.dl1.k1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 1590, -1, 9191, -1, 1589, -1], 'generators': [33, 4, 40], 'label': '256.30836.32.gp1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gp1.b2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gp1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878405
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gq1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.cy1.a1', '16.gf1.a1', '16.is1.a1', '16.je1.a1', '16.je1.c2', '16.je1.d2', '16.je1.e1'], 'contains': ['64.cf1.a1', '64.ch1.a1', '64.ck1.a1', '64.dm1.a1', '64.dm1.b2', '64.dm1.g2', '64.dm1.h1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1548, -1, 9218, -1, 1547, -1], 'generators': [1, 6, 40], 'label': '256.30836.32.gq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gq1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gq1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878406
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dg1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.i1', '64.di1.e1', '64.di1.h1', '64.di1.j1', '64.di1.p1', '64.di1.n1', '64.di1.g1', '64.di1.o1', '64.di1.k1', '64.di1.m1', '64.di1.l1', '64.di1.f1', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.e2', '64.do1.f1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.g1', '64.do1.h1', '64.do1.g2', '64.dk1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.d1', '64.dk1.e1', '64.dk1.f1', '64.dk1.g1', '64.dk1.h1', '64.dk1.m1', '64.dk1.n1', '64.dk1.o1', '64.dk1.p1', '64.dk1.i1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.f2', '64.dm1.b1', '64.dm1.d2', '64.dm1.h1', '64.dm1.h2', '64.dm1.d1', '64.dm1.b2', '64.dm1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '2.s1.a1', '2.x1.a1'], 'contains': ['8.bl1.a1', '8.bm1.a1', '8.bn1.a1', '8.fd1.a1', '8.fe1.a1', '8.fi1.a1', '8.fv1.a1'], 'core': '4.dg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3884, 1402, 8622, 2158, 3886, 1401, 8614, 2163], 'generators': [67, 4, 80], 'label': '256.30836.4.dg1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dg1.a1', 'normal_contained_in': ['2.s1.a1', '2.k1.a1', '2.x1.a1'], 'normal_contains': ['8.bl1.a1', '8.bm1.a1', '8.bn1.a1', '8.fd1.a1', '8.fe1.a1', '8.fi1.a1', '8.fv1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dg1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878412
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gr1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.db1.a1', '16.gi1.a1', '16.ix1.b1', '16.je1.b1', '16.je1.c1', '16.je1.d2', '16.je1.h2'], 'contains': ['64.cg1.a1', '64.cj1.b1', '64.ck1.a1', '64.dn1.c1', '64.dn1.d2', '64.dn1.g2', '64.dn1.h1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9293, -1, 686, -1, 9298, -1, 686, -1], 'generators': [131, 4, 40], 'label': '256.30836.32.gr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gr1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gr1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878413
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gr1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.db1.a1', '16.gi1.a1', '16.ix1.b1', '16.je1.b2', '16.je1.c2', '16.je1.d1', '16.je1.h1'], 'contains': ['64.cg1.a1', '64.cj1.b1', '64.ck1.a1', '64.dn1.c2', '64.dn1.d1', '64.dn1.g1', '64.dn1.h2'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9293, -1, 756, -1, 9298, -1, 755, -1], 'generators': [35, 4, 40], 'label': '256.30836.32.gr1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gr1.b2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gr1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878414
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.de1.a1', '16.gl1.a1', '16.iy1.a1', '16.je1.a1', '16.je1.e2', '16.je1.f2', '16.je1.g1'], 'contains': ['64.ch1.a1', '64.ci1.a1', '64.cj1.a1', '64.do1.a1', '64.do1.c2', '64.do1.e1', '64.do1.g2'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 2007, -1, 9111, -1, 2005, -1], 'generators': [5, 6, 40], 'label': '256.30836.32.gs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gs1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gs1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878415
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.de1.a1', '16.gl1.a1', '16.iy1.a1', '16.je1.a2', '16.je1.e1', '16.je1.f1', '16.je1.g2'], 'contains': ['64.ch1.a1', '64.ci1.a1', '64.cj1.a1', '64.do1.a2', '64.do1.c1', '64.do1.e2', '64.do1.g1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 2021, -1, 9111, -1, 2019, -1], 'generators': [165, 6, 40], 'label': '256.30836.32.gs1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gs1.a2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gs1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878416
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.de1.a1', '16.gl1.a1', '16.iy1.b1', '16.je1.b1', '16.je1.c2', '16.je1.d1', '16.je1.h2'], 'contains': ['64.ch1.a1', '64.ci1.a1', '64.cj1.b1', '64.do1.b2', '64.do1.d1', '64.do1.f2', '64.do1.h1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 505, -1, 9111, -1, 505, -1], 'generators': [133, 6, 40], 'label': '256.30836.32.gs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gs1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gs1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878417
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dh1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.bb1.a1', '2.bc1.a1'], 'contains': ['8.bq1.a1', '8.br1.a1', '8.by1.a1', '8.cd1.a1', '8.cm1.a1', '8.cp1.a1', '8.da1.a1', '8.hd1.a1', '8.hd1.b1'], 'core': '4.dh1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7082, 1923, 6368, 6047, 7085, 1922, 6363, 6059], 'generators': [5, 6, 80, 128], 'label': '256.30836.4.dh1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dh1.a1', 'normal_contained_in': ['2.a1.a1', '2.bb1.a1', '2.bc1.a1'], 'normal_contains': ['8.bq1.a1', '8.br1.a1', '8.by1.a1', '8.cd1.a1', '8.cm1.a1', '8.cp1.a1', '8.da1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dh1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878418
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.de1.a1', '16.gl1.a1', '16.iy1.b1', '16.je1.b2', '16.je1.c1', '16.je1.d2', '16.je1.h1'], 'contains': ['64.ch1.a1', '64.ci1.a1', '64.cj1.b1', '64.do1.b1', '64.do1.d2', '64.do1.f1', '64.do1.h2'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 700, -1, 9111, -1, 700, -1], 'generators': [37, 6, 40], 'label': '256.30836.32.gs1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gs1.b2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gs1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878419
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gt1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.a1', '16.dv1.a1', '16.eo1.a1', '16.jf1.a1', '16.jf1.b1'], 'contains': ['64.i1.a1', '64.cp1.a1', '64.ct1.a1', '64.di1.a1', '64.di1.g1'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9639, -1, 4704, -1, 9644, -1, 4699, -1], 'generators': [1, 2, 136], 'label': '256.30836.32.gt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.gt1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gt1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878420
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gt1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.b1', '16.dv1.a1', '16.eo1.b1', '16.jf1.c1', '16.jf1.d1'], 'contains': ['64.i1.b1', '64.cp1.a1', '64.ct1.b1', '64.di1.b1', '64.di1.n1'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9639, -1, 4731, -1, 9644, -1, 4727, -1], 'generators': [129, 2, 136], 'label': '256.30836.32.gt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.gt1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gt1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878421
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gt1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.b1', '16.dv1.b1', '16.eo1.a1', '16.jf1.e1', '16.jf1.f1'], 'contains': ['64.i1.c1', '64.cp1.a1', '64.ct1.b1', '64.di1.c1', '64.di1.o1'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9639, -1, 4578, -1, 9644, -1, 4574, -1], 'generators': [33, 2, 136], 'label': '256.30836.32.gt1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.gt1.c1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gt1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878422
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gt1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.a1', '16.dv1.b1', '16.eo1.b1', '16.jf1.g1', '16.jf1.h1'], 'contains': ['64.i1.d1', '64.cp1.a1', '64.ct1.a1', '64.di1.d1', '64.di1.p1'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9639, -1, 4814, -1, 9644, -1, 4810, -1], 'generators': [161, 2, 136], 'label': '256.30836.32.gt1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.gt1.d1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gt1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878423
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gt1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.c1', '16.dv1.a1', '16.eo1.a1', '16.jf1.i1', '16.jf1.j1'], 'contains': ['64.i1.a1', '64.cp1.b1', '64.ct1.b1', '64.di1.e1', '64.di1.f1'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9639, -1, 4564, -1, 9644, -1, 4560, -1], 'generators': [1, 34, 136], 'label': '256.30836.32.gt1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.gt1.e1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gt1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878424
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gt1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.d1', '16.dv1.a1', '16.eo1.b1', '16.jf1.k1', '16.jf1.l1'], 'contains': ['64.i1.b1', '64.cp1.b1', '64.ct1.a1', '64.di1.h1', '64.di1.k1'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9639, -1, 4995, -1, 9644, -1, 4991, -1], 'generators': [129, 34, 136], 'label': '256.30836.32.gt1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.gt1.f1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gt1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878425
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gt1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.d1', '16.dv1.b1', '16.eo1.a1', '16.jf1.m1', '16.jf1.n1'], 'contains': ['64.i1.c1', '64.cp1.b1', '64.ct1.a1', '64.di1.i1', '64.di1.l1'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9639, -1, 4717, -1, 9644, -1, 4713, -1], 'generators': [33, 34, 136], 'label': '256.30836.32.gt1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.gt1.g1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gt1.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878426
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gt1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bg1.c1', '16.dv1.b1', '16.eo1.b1', '16.jf1.o1', '16.jf1.p1'], 'contains': ['64.i1.d1', '64.cp1.b1', '64.ct1.b1', '64.di1.j1', '64.di1.m1'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9639, -1, 4745, -1, 9644, -1, 4741, -1], 'generators': [161, 34, 136], 'label': '256.30836.32.gt1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.gt1.h1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gt1.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878724
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.by1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '32.p1.a1', '32.fr1.a1', '32.gd1.b1', '32.gd1.d1', '32.gf1.b1', '32.gf1.d1', '32.gf1.f1', '32.gf1.h1', '32.gi1.c1', '32.gi1.d1'], 'contains': ['128.d1.a1', '128.l1.b1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8867, -1, 3661, -1, 8871, -1, 3658, -1], 'generators': [141, 160], 'label': '256.30836.64.by1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.by1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.by1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878427
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gu1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dw1.a1', '16.ep1.a1', '16.il1.a1', '16.jf1.a1', '16.jf1.c1', '16.jf1.e1', '16.jf1.g1'], 'contains': ['64.cp1.a1', '64.cq1.a1', '64.cr1.a1', '64.dj1.a1', '64.dj1.c1', '64.dj1.m1', '64.dj1.o1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9798, -1, 3855, -1, 9803, -1, 3852, -1], 'generators': [2, 4, 136], 'label': '256.30836.32.gu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gu1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gu1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878428
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.di1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.bb1.a1', '2.bd1.a1'], 'contains': ['8.bq1.a1', '8.bs1.a1', '8.bx1.a1', '8.ce1.a1', '8.ck1.a1', '8.cq1.a1', '8.cz1.a1'], 'core': '4.di1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7140, 8043, 7033, 5478, 7144, 8041, 7027, 5490], 'generators': [5, 6, 64], 'label': '256.30836.4.di1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.di1.a1', 'normal_contained_in': ['2.b1.a1', '2.bb1.a1', '2.bd1.a1'], 'normal_contains': ['8.bq1.a1', '8.bx1.a1', '8.bs1.a1', '8.ck1.a1', '8.ce1.a1', '8.cq1.a1', '8.cz1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.di1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.di1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878429
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gu1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dw1.b1', '16.ep1.a1', '16.il1.a1', '16.jf1.b1', '16.jf1.d1', '16.jf1.f1', '16.jf1.h1'], 'contains': ['64.cp1.a1', '64.cq1.a1', '64.cr1.b1', '64.dj1.b1', '64.dj1.d1', '64.dj1.n1', '64.dj1.p1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9798, -1, 3661, -1, 9803, -1, 3658, -1], 'generators': [162, 4, 136], 'label': '256.30836.32.gu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gu1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gu1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878430
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gu1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dw1.a1', '16.ep1.a1', '16.il1.b1', '16.jf1.i1', '16.jf1.k1', '16.jf1.m1', '16.jf1.o1'], 'contains': ['64.cp1.b1', '64.cq1.a1', '64.cr1.a1', '64.dj1.e1', '64.dj1.g1', '64.dj1.i1', '64.dj1.k1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9798, -1, 3869, -1, 9803, -1, 3866, -1], 'generators': [130, 4, 136], 'label': '256.30836.32.gu1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gu1.c1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gu1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878431
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gu1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dw1.b1', '16.ep1.a1', '16.il1.b1', '16.jf1.j1', '16.jf1.l1', '16.jf1.n1', '16.jf1.p1'], 'contains': ['64.cp1.b1', '64.cq1.a1', '64.cr1.b1', '64.dj1.f1', '64.dj1.h1', '64.dj1.j1', '64.dj1.l1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9798, -1, 3841, -1, 9803, -1, 3838, -1], 'generators': [34, 4, 136], 'label': '256.30836.32.gu1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gu1.d1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gu1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878432
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gv1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.a1', '16.eq1.a1', '16.im1.a1', '16.jf1.a1', '16.jf1.c1', '16.jf1.f1', '16.jf1.h1'], 'contains': ['64.cp1.a1', '64.cs1.a1', '64.cu1.a1', '64.dk1.a1', '64.dk1.c1', '64.dk1.m1', '64.dk1.o1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 3995, -1, 9910, -1, 3991, -1], 'generators': [5, 2, 136], 'label': '256.30836.32.gv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gv1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gv1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878433
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gv1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.b1', '16.eq1.a1', '16.im1.a1', '16.jf1.b1', '16.jf1.d1', '16.jf1.e1', '16.jf1.g1'], 'contains': ['64.cp1.a1', '64.cs1.a1', '64.cu1.b1', '64.dk1.b1', '64.dk1.d1', '64.dk1.n1', '64.dk1.p1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 2785, -1, 9910, -1, 2783, -1], 'generators': [37, 2, 136], 'label': '256.30836.32.gv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gv1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gv1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878434
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gv1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.a1', '16.eq1.a1', '16.im1.b1', '16.jf1.i1', '16.jf1.k1', '16.jf1.n1', '16.jf1.p1'], 'contains': ['64.cp1.b1', '64.cs1.a1', '64.cu1.a1', '64.dk1.e1', '64.dk1.g1', '64.dk1.i1', '64.dk1.k1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 4064, -1, 9910, -1, 4060, -1], 'generators': [37, 34, 136], 'label': '256.30836.32.gv1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gv1.c1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gv1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878435
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gv1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.b1', '16.eq1.a1', '16.im1.b1', '16.jf1.j1', '16.jf1.l1', '16.jf1.m1', '16.jf1.o1'], 'contains': ['64.cp1.b1', '64.cs1.a1', '64.cu1.b1', '64.dk1.f1', '64.dk1.h1', '64.dk1.j1', '64.dk1.l1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 3271, -1, 9910, -1, 3269, -1], 'generators': [5, 34, 136], 'label': '256.30836.32.gv1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gv1.d1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gv1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878436
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gw1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dy1.a1', '16.et1.a1', '16.ir1.a1', '16.jf1.a1', '16.jf1.b1', '16.jf1.i1', '16.jf1.j1'], 'contains': ['64.i1.a1', '64.cq1.a1', '64.cs1.a1', '64.dl1.a1', '64.dl1.b1', '64.dl1.c1', '64.dl1.d1'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9879, -1, 3230, -1, 9883, -1, 3227, -1], 'generators': [1, 4, 136], 'label': '256.30836.32.gw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gw1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gw1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878437
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gw1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dy1.a1', '16.et1.b1', '16.ir1.b1', '16.jf1.c1', '16.jf1.d1', '16.jf1.k1', '16.jf1.l1'], 'contains': ['64.i1.b1', '64.cq1.a1', '64.cs1.a1', '64.dl1.e1', '64.dl1.f1', '64.dl1.g1', '64.dl1.h1'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9879, -1, 4078, -1, 9883, -1, 4074, -1], 'generators': [129, 4, 136], 'label': '256.30836.32.gw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gw1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gw1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878438
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gw1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dy1.b1', '16.et1.a1', '16.ir1.b1', '16.jf1.e1', '16.jf1.f1', '16.jf1.m1', '16.jf1.n1'], 'contains': ['64.i1.c1', '64.cq1.a1', '64.cs1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.k1', '64.dl1.l1'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9879, -1, 3243, -1, 9883, -1, 3241, -1], 'generators': [33, 4, 136], 'label': '256.30836.32.gw1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gw1.c1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gw1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878439
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.k1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.d1', '128.i1.b1', '128.i1.c1', '128.m1.a1', '128.m1.b1', '128.l1.a1', '128.l1.b1', '128.n1.a1', '128.n1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.k1.a1', '4.l1.a1', '4.m1.a1', '4.bc1.a1', '4.be1.a1', '4.bg1.a1', '4.bi1.a1', '4.dc1.a1', '4.dd1.a1', '4.de1.a1', '4.dg1.a1', '4.dy1.a1', '4.dz1.a1', '4.ea1.a1', '4.eb1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3551, 2994, 7985, 5735, 3553, 2974, 7993, 5747], 'generators': [65, 2, 4, 80], 'label': '256.30836.2.k1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.k1.a1', '4.l1.a1', '4.m1.a1', '4.be1.a1', '4.bc1.a1', '4.bi1.a1', '4.bg1.a1', '4.dg1.a1', '4.de1.a1', '4.dd1.a1', '4.dc1.a1', '4.ea1.a1', '4.eb1.a1', '4.dy1.a1', '4.dz1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.k1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878456
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gz1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ed1.b1', '16.fb1.a1', '16.ix1.a1', '16.jf1.b1', '16.jf1.g1', '16.jf1.l1', '16.jf1.m1'], 'contains': ['64.cq1.a1', '64.ct1.a1', '64.cu1.b1', '64.dn1.b1', '64.dn1.b2', '64.dn1.f1', '64.dn1.f2'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9932, -1, 3300, -1, 9936, -1, 3297, -1], 'generators': [163, 4, 136], 'label': '256.30836.32.gz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gz1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gz1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878440
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dj1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.bb1.a1', '2.be1.a1'], 'contains': ['8.bq1.a1', '8.bt1.a1', '8.cc1.a1', '8.cf1.a1', '8.cj1.a1', '8.cr1.a1', '8.cu1.a1'], 'core': '4.dj1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7438, 3907, 5755, 7306, 7442, 3905, 5750, 7322], 'generators': [5, 6, 16], 'label': '256.30836.4.dj1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dj1.a1', 'normal_contained_in': ['2.c1.a1', '2.bb1.a1', '2.be1.a1'], 'normal_contains': ['8.bq1.a1', '8.bt1.a1', '8.cc1.a1', '8.cf1.a1', '8.cj1.a1', '8.cr1.a1', '8.cu1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dj1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878441
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gw1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dy1.b1', '16.et1.b1', '16.ir1.a1', '16.jf1.g1', '16.jf1.h1', '16.jf1.o1', '16.jf1.p1'], 'contains': ['64.i1.d1', '64.cq1.a1', '64.cs1.a1', '64.dl1.m1', '64.dl1.n1', '64.dl1.o1', '64.dl1.p1'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9879, -1, 4009, -1, 9883, -1, 4005, -1], 'generators': [161, 4, 136], 'label': '256.30836.32.gw1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gw1.d1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gw1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878442
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gx1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.eu1.a1', '16.is1.a1', '16.jf1.a1', '16.jf1.i1'], 'contains': ['64.i1.a1', '64.cr1.a1', '64.cu1.a1', '64.dm1.a1', '64.dm1.a2'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9825, -1, 4522, -1, 9830, -1, 4519, -1], 'generators': [1, 6, 136], 'label': '256.30836.32.gx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gx1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gx1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878443
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gx1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.b1', '16.eu1.a1', '16.is1.a1', '16.jf1.b1', '16.jf1.j1'], 'contains': ['64.i1.a1', '64.cr1.b1', '64.cu1.b1', '64.dm1.b1', '64.dm1.b2'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9825, -1, 4398, -1, 9830, -1, 4394, -1], 'generators': [1, 38, 136], 'label': '256.30836.32.gx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gx1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gx1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878444
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gx1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.eu1.b1', '16.is1.b1', '16.jf1.c1', '16.jf1.k1'], 'contains': ['64.i1.b1', '64.cr1.a1', '64.cu1.a1', '64.dm1.c1', '64.dm1.c2'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9825, -1, 4801, -1, 9830, -1, 4796, -1], 'generators': [129, 6, 136], 'label': '256.30836.32.gx1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gx1.c1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gx1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878445
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gx1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.b1', '16.eu1.b1', '16.is1.b1', '16.jf1.d1', '16.jf1.l1'], 'contains': ['64.i1.b1', '64.cr1.b1', '64.cu1.b1', '64.dm1.d1', '64.dm1.d2'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9825, -1, 4606, -1, 9830, -1, 4602, -1], 'generators': [129, 38, 136], 'label': '256.30836.32.gx1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gx1.d1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gx1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878446
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gx1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.c1', '16.eu1.a1', '16.is1.b1', '16.jf1.e1', '16.jf1.m1'], 'contains': ['64.i1.c1', '64.cr1.a1', '64.cu1.b1', '64.dm1.e1', '64.dm1.e2'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9825, -1, 4425, -1, 9830, -1, 4421, -1], 'generators': [33, 6, 136], 'label': '256.30836.32.gx1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gx1.e1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gx1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878447
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gx1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.d1', '16.eu1.a1', '16.is1.b1', '16.jf1.f1', '16.jf1.n1'], 'contains': ['64.i1.c1', '64.cr1.b1', '64.cu1.a1', '64.dm1.f1', '64.dm1.f2'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9825, -1, 4592, -1, 9830, -1, 4588, -1], 'generators': [33, 38, 136], 'label': '256.30836.32.gx1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gx1.f1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gx1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878448
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gx1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.c1', '16.eu1.b1', '16.is1.a1', '16.jf1.g1', '16.jf1.o1'], 'contains': ['64.i1.d1', '64.cr1.a1', '64.cu1.b1', '64.dm1.g1', '64.dm1.g2'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9825, -1, 4439, -1, 9830, -1, 4435, -1], 'generators': [161, 6, 136], 'label': '256.30836.32.gx1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gx1.g1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gx1.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878449
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gx1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.d1', '16.eu1.b1', '16.is1.a1', '16.jf1.h1', '16.jf1.p1'], 'contains': ['64.i1.d1', '64.cr1.b1', '64.cu1.a1', '64.dm1.h1', '64.dm1.h2'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9825, -1, 4690, -1, 9830, -1, 4685, -1], 'generators': [161, 38, 136], 'label': '256.30836.32.gx1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.gx1.h1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gx1.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878450
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gy1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dz1.a1', '16.ev1.a1', '16.it1.a1'], 'contains': ['64.i1.a1', '64.cv1.a1', '64.cw1.a1'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5446, -1, 5832, -1, 5438, -1, 5827, -1], 'generators': [1, 82], 'label': '256.30836.32.gy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '32.gy1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gy1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878451
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dk1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.bc1.a1', '2.be1.a1'], 'contains': ['8.bq1.a1', '8.bu1.a1', '8.bv1.a1', '8.cg1.a1', '8.ch1.a1', '8.cs1.a1', '8.cw1.a1'], 'core': '4.dk1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6384, 4175, 7207, 2457, 6387, 4173, 7201, 2463], 'generators': [65, 66, 68], 'label': '256.30836.4.dk1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dk1.a1', 'normal_contained_in': ['2.b1.a1', '2.bc1.a1', '2.be1.a1'], 'normal_contains': ['8.bq1.a1', '8.bv1.a1', '8.bu1.a1', '8.ch1.a1', '8.cg1.a1', '8.cs1.a1', '8.cw1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dk1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878452
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gy1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dz1.a1', '16.ev1.b1', '16.it1.b1'], 'contains': ['64.i1.b1', '64.cv1.a1', '64.cw1.a1'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5446, -1, 5868, -1, 5438, -1, 5863, -1], 'generators': [129, 82], 'label': '256.30836.32.gy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '32.gy1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gy1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878453
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gy1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dz1.b1', '16.ev1.a1', '16.it1.b1'], 'contains': ['64.i1.c1', '64.cv1.a1', '64.cw1.a1'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [5446, -1, 5844, -1, 5438, -1, 5839, -1], 'generators': [33, 82], 'label': '256.30836.32.gy1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '32.gy1.c1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gy1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878454
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gy1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dz1.b1', '16.ev1.b1', '16.it1.a1'], 'contains': ['64.i1.d1', '64.cv1.a1', '64.cw1.a1'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [5446, -1, 5856, -1, 5438, -1, 5851, -1], 'generators': [161, 82], 'label': '256.30836.32.gy1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '32.gy1.d1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gy1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878455
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gz1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ed1.a1', '16.fb1.a1', '16.ix1.a1', '16.jf1.a1', '16.jf1.h1', '16.jf1.k1', '16.jf1.n1'], 'contains': ['64.cq1.a1', '64.ct1.a1', '64.cu1.a1', '64.dn1.a1', '64.dn1.a2', '64.dn1.e1', '64.dn1.e2'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9932, -1, 4217, -1, 9936, -1, 4213, -1], 'generators': [3, 4, 136], 'label': '256.30836.32.gz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gz1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gz1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879162
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bp1.a1'], 'contains': ['16.bf1.b1', '16.dz1.a1', '16.eb1.a1', '16.ef1.b1', '16.ei1.b1', '16.ej1.b1', '16.em1.b1'], 'core': '16.bf1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9090, -1, 4372, -1, 9094, -1, 4368, -1], 'generators': [1, 114, 84], 'label': '256.30836.8.gm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '8.gm1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gm1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878457
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gz1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ed1.a1', '16.fb1.a1', '16.ix1.b1', '16.jf1.c1', '16.jf1.f1', '16.jf1.i1', '16.jf1.p1'], 'contains': ['64.cq1.a1', '64.ct1.b1', '64.cu1.a1', '64.dn1.c1', '64.dn1.c2', '64.dn1.g1', '64.dn1.g2'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9932, -1, 2479, -1, 9936, -1, 2477, -1], 'generators': [131, 4, 136], 'label': '256.30836.32.gz1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gz1.c1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gz1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878458
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.gz1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ed1.b1', '16.fb1.a1', '16.ix1.b1', '16.jf1.d1', '16.jf1.e1', '16.jf1.j1', '16.jf1.o1'], 'contains': ['64.cq1.a1', '64.ct1.b1', '64.cu1.b1', '64.dn1.d1', '64.dn1.d2', '64.dn1.h1', '64.dn1.h2'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9932, -1, 1715, -1, 9936, -1, 1714, -1], 'generators': [35, 4, 136], 'label': '256.30836.32.gz1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.gz1.d1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.gz1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878459
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ha1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ee1.a1', '16.fe1.a1', '16.iy1.a1', '16.jf1.a1', '16.jf1.g1', '16.jf1.k1', '16.jf1.m1'], 'contains': ['64.cr1.a1', '64.cs1.a1', '64.ct1.a1', '64.do1.a1', '64.do1.a2', '64.do1.c1', '64.do1.c2'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9772, -1, 3938, -1, 9777, -1, 3935, -1], 'generators': [5, 6, 136], 'label': '256.30836.32.ha1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ha1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ha1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878460
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ha1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ee1.a1', '16.fe1.a1', '16.iy1.b1', '16.jf1.c1', '16.jf1.e1', '16.jf1.i1', '16.jf1.o1'], 'contains': ['64.cr1.a1', '64.cs1.a1', '64.ct1.b1', '64.do1.b1', '64.do1.b2', '64.do1.d1', '64.do1.d2'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9772, -1, 2215, -1, 9777, -1, 2213, -1], 'generators': [37, 6, 136], 'label': '256.30836.32.ha1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ha1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ha1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878461
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ha1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ee1.b1', '16.fe1.a1', '16.iy1.a1', '16.jf1.b1', '16.jf1.h1', '16.jf1.l1', '16.jf1.n1'], 'contains': ['64.cr1.b1', '64.cs1.a1', '64.ct1.a1', '64.do1.e1', '64.do1.e2', '64.do1.g1', '64.do1.g2'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9772, -1, 3924, -1, 9777, -1, 3921, -1], 'generators': [37, 38, 136], 'label': '256.30836.32.ha1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ha1.c1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ha1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878462
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dl1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.bc1.a1', '2.bd1.a1'], 'contains': ['8.bq1.a1', '8.bw1.a1', '8.bz1.a1', '8.ci1.a1', '8.cl1.a1', '8.ct1.a1', '8.cv1.a1'], 'core': '4.dl1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5530, 9552, 6541, 6831, 5532, 9548, 6536, 6845], 'generators': [17, 18, 20], 'label': '256.30836.4.dl1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dl1.a1', 'normal_contained_in': ['2.c1.a1', '2.bc1.a1', '2.bd1.a1'], 'normal_contains': ['8.bq1.a1', '8.bw1.a1', '8.bz1.a1', '8.cl1.a1', '8.ci1.a1', '8.cv1.a1', '8.ct1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dl1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878463
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ha1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ee1.b1', '16.fe1.a1', '16.iy1.b1', '16.jf1.d1', '16.jf1.f1', '16.jf1.j1', '16.jf1.p1'], 'contains': ['64.cr1.b1', '64.cs1.a1', '64.ct1.b1', '64.do1.f1', '64.do1.f2', '64.do1.h1', '64.do1.h2'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9772, -1, 1895, -1, 9777, -1, 1894, -1], 'generators': [5, 38, 136], 'label': '256.30836.32.ha1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ha1.d1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ha1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878464
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dv1.a1', '16.fv1.a1', '16.hd1.a1', '16.jg1.a1', '16.jg1.b1', '16.jg1.c1', '16.jg1.d1'], 'contains': ['64.cx1.a1', '64.cy1.a1', '64.dc1.a1', '64.di1.a1', '64.di1.b1', '64.di1.f1', '64.di1.k1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9320, -1, 3731, -1, 9324, -1, 3727, -1], 'generators': [1, 2, 8], 'label': '256.30836.32.hb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hb1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hb1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878465
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dv1.b1', '16.fv1.a1', '16.hd1.a1', '16.jg1.e1', '16.jg1.f1', '16.jg1.g1', '16.jg1.h1'], 'contains': ['64.cx1.a1', '64.cy1.b1', '64.dc1.a1', '64.di1.c1', '64.di1.d1', '64.di1.l1', '64.di1.m1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9320, -1, 3717, -1, 9324, -1, 3713, -1], 'generators': [33, 2, 8], 'label': '256.30836.32.hb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hb1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hb1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878466
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dv1.a1', '16.fv1.b1', '16.hd1.a1', '16.jg1.i1', '16.jg1.j1', '16.jg1.k1', '16.jg1.l1'], 'contains': ['64.cx1.b1', '64.cy1.a1', '64.dc1.a1', '64.di1.e1', '64.di1.g1', '64.di1.h1', '64.di1.n1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9320, -1, 3758, -1, 9324, -1, 3755, -1], 'generators': [1, 130, 8], 'label': '256.30836.32.hb1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hb1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hb1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878467
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hb1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dv1.b1', '16.fv1.b1', '16.hd1.a1', '16.jg1.m1', '16.jg1.n1', '16.jg1.o1', '16.jg1.p1'], 'contains': ['64.cx1.b1', '64.cy1.b1', '64.dc1.a1', '64.di1.i1', '64.di1.j1', '64.di1.o1', '64.di1.p1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9320, -1, 3744, -1, 9324, -1, 3741, -1], 'generators': [33, 130, 8], 'label': '256.30836.32.hb1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hb1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hb1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878468
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dw1.a1', '16.fw1.a1', '16.he1.a1', '16.jg1.a1', '16.jg1.b1', '16.jg1.e1', '16.jg1.f1'], 'contains': ['64.cx1.a1', '64.cz1.a1', '64.da1.a1', '64.dj1.a1', '64.dj1.c1', '64.dj1.i1', '64.dj1.k1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9346, -1, 3675, -1, 9351, -1, 3671, -1], 'generators': [2, 4, 8], 'label': '256.30836.32.hc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hc1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878469
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dw1.b1', '16.fw1.a1', '16.he1.a1', '16.jg1.c1', '16.jg1.d1', '16.jg1.g1', '16.jg1.h1'], 'contains': ['64.cx1.a1', '64.cz1.a1', '64.da1.b1', '64.dj1.b1', '64.dj1.d1', '64.dj1.j1', '64.dj1.l1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9346, -1, 3522, -1, 9351, -1, 3519, -1], 'generators': [34, 4, 8], 'label': '256.30836.32.hc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hc1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hc1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878470
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dw1.a1', '16.fw1.b1', '16.he1.a1', '16.jg1.i1', '16.jg1.j1', '16.jg1.m1', '16.jg1.n1'], 'contains': ['64.cx1.b1', '64.cz1.a1', '64.da1.a1', '64.dj1.e1', '64.dj1.g1', '64.dj1.m1', '64.dj1.o1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9346, -1, 3689, -1, 9351, -1, 3685, -1], 'generators': [130, 4, 8], 'label': '256.30836.32.hc1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hc1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hc1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878725
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.q1.a1', '32.eq1.a1', '32.gb1.a1', '32.gb1.d1', '32.gh1.a1', '32.gh1.c1', '32.gi1.a1', '32.gi1.c1', '32.gj1.a1'], 'contains': ['128.d1.a1', '128.m1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8654, -1, 4735, -1, 8658, -1, 4736, -1], 'generators': [3, 160], 'label': '256.30836.64.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.bz1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878471
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hc1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dw1.b1', '16.fw1.b1', '16.he1.a1', '16.jg1.k1', '16.jg1.l1', '16.jg1.o1', '16.jg1.p1'], 'contains': ['64.cx1.b1', '64.cz1.a1', '64.da1.b1', '64.dj1.f1', '64.dj1.h1', '64.dj1.n1', '64.dj1.p1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9346, -1, 3535, -1, 9351, -1, 3533, -1], 'generators': [162, 4, 8], 'label': '256.30836.32.hc1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hc1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hc1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878472
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.a1', '16.fx1.a1', '16.hf1.a1', '16.jg1.a1', '16.jg1.g1'], 'contains': ['64.cx1.a1', '64.db1.a1', '64.dd1.a1', '64.dk1.a1', '64.dk1.i1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9426, -1, 4412, -1, 9431, -1, 4407, -1], 'generators': [5, 2, 8], 'label': '256.30836.32.hd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.hd1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878473
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dm1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.bd1.a1', '2.be1.a1'], 'contains': ['8.bq1.a1', '8.ca1.a1', '8.cb1.a1', '8.cn1.a1', '8.co1.a1', '8.cx1.a1', '8.cy1.a1'], 'core': '4.dm1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6622, 3950, 5797, 9370, 6625, 3948, 5792, 9391], 'generators': [81, 82, 84], 'label': '256.30836.4.dm1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dm1.a1', 'normal_contained_in': ['2.a1.a1', '2.bd1.a1', '2.be1.a1'], 'normal_contains': ['8.bq1.a1', '8.ca1.a1', '8.cb1.a1', '8.cn1.a1', '8.co1.a1', '8.cx1.a1', '8.cy1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dm1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878474
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.b1', '16.fx1.a1', '16.hf1.a1', '16.jg1.c1', '16.jg1.e1'], 'contains': ['64.cx1.a1', '64.db1.a1', '64.dd1.b1', '64.dk1.b1', '64.dk1.j1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9426, -1, 4133, -1, 9431, -1, 4130, -1], 'generators': [165, 2, 8], 'label': '256.30836.32.hd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.hd1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hd1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878475
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.a1', '16.fx1.a1', '16.hf1.b1', '16.jg1.b1', '16.jg1.h1'], 'contains': ['64.cx1.a1', '64.db1.b1', '64.dd1.a1', '64.dk1.c1', '64.dk1.k1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9426, -1, 4106, -1, 9431, -1, 4102, -1], 'generators': [133, 2, 8], 'label': '256.30836.32.hd1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.hd1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hd1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878476
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.b1', '16.fx1.a1', '16.hf1.b1', '16.jg1.d1', '16.jg1.f1'], 'contains': ['64.cx1.a1', '64.db1.b1', '64.dd1.b1', '64.dk1.d1', '64.dk1.l1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9426, -1, 2771, -1, 9431, -1, 2769, -1], 'generators': [37, 2, 8], 'label': '256.30836.32.hd1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.hd1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hd1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878477
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.a1', '16.fx1.b1', '16.hf1.a1', '16.jg1.i1', '16.jg1.o1'], 'contains': ['64.cx1.b1', '64.db1.a1', '64.dd1.a1', '64.dk1.e1', '64.dk1.m1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9426, -1, 4453, -1, 9431, -1, 4449, -1], 'generators': [5, 130, 8], 'label': '256.30836.32.hd1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.hd1.e1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hd1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878478
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.b1', '16.fx1.b1', '16.hf1.a1', '16.jg1.k1', '16.jg1.m1'], 'contains': ['64.cx1.b1', '64.db1.a1', '64.dd1.b1', '64.dk1.f1', '64.dk1.n1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9426, -1, 4161, -1, 9431, -1, 4158, -1], 'generators': [165, 130, 8], 'label': '256.30836.32.hd1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.hd1.f1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hd1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878479
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.a1', '16.fx1.b1', '16.hf1.b1', '16.jg1.j1', '16.jg1.p1'], 'contains': ['64.cx1.b1', '64.db1.b1', '64.dd1.a1', '64.dk1.g1', '64.dk1.o1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9426, -1, 4120, -1, 9431, -1, 4116, -1], 'generators': [133, 130, 8], 'label': '256.30836.32.hd1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.hd1.g1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hd1.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878480
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hd1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dx1.b1', '16.fx1.b1', '16.hf1.b1', '16.jg1.l1', '16.jg1.n1'], 'contains': ['64.cx1.b1', '64.db1.b1', '64.dd1.b1', '64.dk1.h1', '64.dk1.p1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9426, -1, 2799, -1, 9431, -1, 2797, -1], 'generators': [37, 130, 8], 'label': '256.30836.32.hd1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.hd1.h1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hd1.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878481
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.he1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dy1.a1', '16.ge1.a1', '16.hi1.a1', '16.jg1.a1', '16.jg1.c1', '16.jg1.i1', '16.jg1.k1'], 'contains': ['64.cy1.a1', '64.cz1.a1', '64.db1.a1', '64.dl1.a1', '64.dl1.c1', '64.dl1.e1', '64.dl1.g1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9373, -1, 3633, -1, 9377, -1, 3630, -1], 'generators': [1, 4, 8], 'label': '256.30836.32.he1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.he1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.he1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878482
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.he1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dy1.a1', '16.ge1.a1', '16.hi1.b1', '16.jg1.b1', '16.jg1.d1', '16.jg1.j1', '16.jg1.l1'], 'contains': ['64.cy1.a1', '64.cz1.a1', '64.db1.b1', '64.dl1.b1', '64.dl1.d1', '64.dl1.f1', '64.dl1.h1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9373, -1, 1215, -1, 9377, -1, 1214, -1], 'generators': [129, 4, 8], 'label': '256.30836.32.he1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.he1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.he1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878483
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.he1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dy1.b1', '16.ge1.a1', '16.hi1.a1', '16.jg1.e1', '16.jg1.g1', '16.jg1.m1', '16.jg1.o1'], 'contains': ['64.cy1.b1', '64.cz1.a1', '64.db1.a1', '64.dl1.i1', '64.dl1.k1', '64.dl1.m1', '64.dl1.o1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9373, -1, 3549, -1, 9377, -1, 3547, -1], 'generators': [161, 4, 8], 'label': '256.30836.32.he1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.he1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.he1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878550
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.l1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.c1', '128.i1.d1', '128.i1.b1', '128.m1.a1', '128.m1.b1', '128.j1.a1', '128.j1.b1', '128.k1.a1', '128.k1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.n1.a1', '4.o1.a1', '4.r1.a1', '4.t1.a1', '4.v1.a1', '4.y1.a1', '4.bg1.a1', '4.ed1.a1', '4.ef1.a1', '4.ei1.a1', '4.em1.a1', '4.fj1.a1', '4.fl1.a1', '4.fo1.a1', '4.ft1.a1'], 'core': '2.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3749, 4538, 8030, 3001, 3736, 4536, 8038, 3008], 'generators': [17, 2, 20, 64], 'label': '256.30836.2.l1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.l1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.n1.a1', '4.r1.a1', '4.o1.a1', '4.t1.a1', '4.v1.a1', '4.bg1.a1', '4.y1.a1', '4.ef1.a1', '4.ed1.a1', '4.ei1.a1', '4.em1.a1', '4.fl1.a1', '4.fj1.a1', '4.fo1.a1', '4.ft1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.l1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.l1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878726
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.b1', '32.q1.a1', '32.eq1.a1', '32.gb1.b1', '32.gb1.c1', '32.gh1.b1', '32.gh1.d1', '32.gi1.b1', '32.gi1.d1', '32.gj1.b1'], 'contains': ['128.d1.a1', '128.m1.b1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8654, -1, 3459, -1, 8658, -1, 3456, -1], 'generators': [131, 160], 'label': '256.30836.64.bz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.bz1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bz1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878484
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dn1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.n1', '64.dk1.o1', '64.dk1.m1', '64.dk1.p1', '64.dk1.e1', '64.dk1.h1', '64.dk1.f1', '64.dk1.g1', '64.dk1.j1', '64.dk1.k1', '64.dk1.i1', '64.dk1.l1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.f1', '64.dn1.e2', '64.dn1.e1', '64.dn1.f2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.h2', '64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.p1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '2.t1.a1', '2.bb1.a1'], 'contains': ['8.br1.a1', '8.bs1.a1', '8.cc1.a1', '8.dn1.a1', '8.du1.a1', '8.eb1.a1', '8.fx1.a1'], 'core': '4.dn1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5667, 7230, 8242, 9308, 5670, 7228, 8235, 9328], 'generators': [21, 6, 64], 'label': '256.30836.4.dn1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dn1.a1', 'normal_contained_in': ['2.t1.a1', '2.h1.a1', '2.bb1.a1'], 'normal_contains': ['8.br1.a1', '8.bs1.a1', '8.cc1.a1', '8.dn1.a1', '8.du1.a1', '8.eb1.a1', '8.fx1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dn1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878485
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.he1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.dy1.b1', '16.ge1.a1', '16.hi1.b1', '16.jg1.f1', '16.jg1.h1', '16.jg1.n1', '16.jg1.p1'], 'contains': ['64.cy1.b1', '64.cz1.a1', '64.db1.b1', '64.dl1.j1', '64.dl1.l1', '64.dl1.n1', '64.dl1.p1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9373, -1, 1368, -1, 9377, -1, 1366, -1], 'generators': [33, 4, 8], 'label': '256.30836.32.he1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.he1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.he1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878486
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.gf1.a1', '16.hj1.a1', '16.jg1.a1', '16.jg1.b1', '16.jg1.i1', '16.jg1.j1'], 'contains': ['64.cy1.a1', '64.da1.a1', '64.dd1.a1', '64.dm1.a1', '64.dm1.a2', '64.dm1.c1', '64.dm1.c2'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9399, -1, 3397, -1, 9404, -1, 3394, -1], 'generators': [1, 6, 8], 'label': '256.30836.32.hf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hf1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878487
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.b1', '16.gf1.a1', '16.hj1.a1', '16.jg1.c1', '16.jg1.d1', '16.jg1.k1', '16.jg1.l1'], 'contains': ['64.cy1.a1', '64.da1.b1', '64.dd1.b1', '64.dm1.b1', '64.dm1.b2', '64.dm1.d1', '64.dm1.d2'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9399, -1, 2257, -1, 9404, -1, 2255, -1], 'generators': [1, 38, 8], 'label': '256.30836.32.hf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hf1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hf1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878488
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.c1', '16.gf1.a1', '16.hj1.a1', '16.jg1.e1', '16.jg1.f1', '16.jg1.m1', '16.jg1.n1'], 'contains': ['64.cy1.b1', '64.da1.a1', '64.dd1.b1', '64.dm1.e1', '64.dm1.e2', '64.dm1.g1', '64.dm1.g2'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9399, -1, 2396, -1, 9404, -1, 2394, -1], 'generators': [33, 6, 8], 'label': '256.30836.32.hf1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hf1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hf1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878489
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hf1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.d1', '16.gf1.a1', '16.hj1.a1', '16.jg1.g1', '16.jg1.h1', '16.jg1.o1', '16.jg1.p1'], 'contains': ['64.cy1.b1', '64.da1.b1', '64.dd1.a1', '64.dm1.f1', '64.dm1.f2', '64.dm1.h1', '64.dm1.h2'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9399, -1, 3383, -1, 9404, -1, 3380, -1], 'generators': [33, 38, 8], 'label': '256.30836.32.hf1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hf1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hf1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878490
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ec1.a1', '16.gh1.a1', '16.hl1.a1'], 'contains': ['64.cy1.a1', '64.df1.a1', '64.dh1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7466, -1, 7779, -1, 7470, -1, 7772, -1], 'generators': [1, 70], 'label': '256.30836.32.hg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1.a1', 'old_label': '32.hg1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878491
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hg1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ec1.b1', '16.gh1.a1', '16.hl1.a1'], 'contains': ['64.cy1.b1', '64.df1.a1', '64.dh1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7466, -1, 7994, -1, 7470, -1, 7987, -1], 'generators': [33, 70], 'label': '256.30836.32.hg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.bb1.a1', 'old_label': '32.hg1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hg1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878492
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ed1.a1', '16.gi1.a1', '16.hm1.a1', '16.jg1.a1', '16.jg1.h1', '16.jg1.j1', '16.jg1.o1'], 'contains': ['64.cz1.a1', '64.dc1.a1', '64.dd1.a1', '64.dn1.a1', '64.dn1.c2', '64.dn1.e1', '64.dn1.g2'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9506, -1, 3216, -1, 9510, -1, 3213, -1], 'generators': [3, 4, 8], 'label': '256.30836.32.hh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hh1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878493
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ed1.a1', '16.gi1.a1', '16.hm1.a1', '16.jg1.b1', '16.jg1.g1', '16.jg1.i1', '16.jg1.p1'], 'contains': ['64.cz1.a1', '64.dc1.a1', '64.dd1.a1', '64.dn1.a2', '64.dn1.c1', '64.dn1.e2', '64.dn1.g1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9506, -1, 3202, -1, 9510, -1, 3199, -1], 'generators': [131, 4, 8], 'label': '256.30836.32.hh1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hh1.a2', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hh1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878494
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ed1.b1', '16.gi1.a1', '16.hm1.a1', '16.jg1.c1', '16.jg1.f1', '16.jg1.l1', '16.jg1.m1'], 'contains': ['64.cz1.a1', '64.dc1.a1', '64.dd1.b1', '64.dn1.b2', '64.dn1.d1', '64.dn1.f2', '64.dn1.h1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9506, -1, 2201, -1, 9510, -1, 2200, -1], 'generators': [35, 4, 8], 'label': '256.30836.32.hh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hh1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hh1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878649
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '64.e1', 'aut_quo_index': 1152, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.h1.a1', '32.h1.b1', '32.dj1.a1', '32.dk1.a1', '32.dl1.a1', '32.dm1.a1', '32.dn1.a1', '32.do1.a1', '32.dp1.a1', '32.dq1.a1', '32.dr1.a1', '32.ds1.a1', '32.dt1.a1', '32.du1.a1', '32.dv1.a1', '32.dw1.a1', '32.dx1.a1', '32.dy1.a1', '32.dz1.a1', '32.ea1.a1'], 'contains': ['128.b1.a1', '128.e1.a1', '128.g1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5820, 4715, 6613, 6128, 5813, 4695, 6607, 6142], 'generators': [8, 32], 'label': '256.30836.64.e1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.e1.a1', 'normal_contained_in': ['32.a1.a1', '32.h1.a1', '32.h1.b1'], 'normal_contains': ['128.e1.a1', '128.b1.a1', '128.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.e1.a1', 'projective_image': '64.264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.264', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879163
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bp1.a1'], 'contains': ['16.bf1.c1', '16.dz1.b1', '16.eb1.b1', '16.ef1.a1', '16.ei1.a1', '16.ej1.b1', '16.em1.b1'], 'core': '16.bf1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9090, -1, 4402, -1, 9094, -1, 4397, -1], 'generators': [33, 82, 84], 'label': '256.30836.8.gm1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '8.gm1.c1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gm1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878495
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.do1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.b1', '64.dl1.j1', '64.dl1.i1', '64.dl1.f1', '64.dl1.e1', '64.dl1.m1', '64.dl1.n1', '64.dl1.c1', '64.dl1.d1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dl1.g1', '64.dl1.o1', '64.dl1.p1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.m1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.j1', '64.dk1.l1', '64.dk1.k1', '64.dk1.i1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.e1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '2.u1.a1', '2.bb1.a1'], 'contains': ['8.br1.a1', '8.bt1.a1', '8.bx1.a1', '8.do1.a1', '8.dr1.a1', '8.eg1.a1', '8.ez1.a1'], 'core': '4.do1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3117, 8252, 6302, 1502, 3118, 8249, 6297, 1506], 'generators': [69, 6, 16], 'label': '256.30836.4.do1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.do1.a1', 'normal_contained_in': ['2.u1.a1', '2.i1.a1', '2.bb1.a1'], 'normal_contains': ['8.br1.a1', '8.bx1.a1', '8.bt1.a1', '8.do1.a1', '8.dr1.a1', '8.ez1.a1', '8.eg1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.do1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.do1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878496
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hh1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ed1.b1', '16.gi1.a1', '16.hm1.a1', '16.jg1.d1', '16.jg1.e1', '16.jg1.k1', '16.jg1.n1'], 'contains': ['64.cz1.a1', '64.dc1.a1', '64.dd1.b1', '64.dn1.b1', '64.dn1.d2', '64.dn1.f1', '64.dn1.h2'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9506, -1, 2187, -1, 9510, -1, 2186, -1], 'generators': [163, 4, 8], 'label': '256.30836.32.hh1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hh1.b2', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hh1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878497
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ee1.a1', '16.gl1.a1', '16.hp1.a1', '16.jg1.a1', '16.jg1.e1', '16.jg1.i1', '16.jg1.m1'], 'contains': ['64.da1.a1', '64.db1.a1', '64.dc1.a1', '64.do1.a1', '64.do1.a2', '64.do1.b1', '64.do1.b2'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 3563, -1, 9271, -1, 3560, -1], 'generators': [5, 6, 8], 'label': '256.30836.32.hi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hi1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hi1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878498
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ee1.a1', '16.gl1.a1', '16.hp1.b1', '16.jg1.b1', '16.jg1.f1', '16.jg1.j1', '16.jg1.n1'], 'contains': ['64.da1.a1', '64.db1.b1', '64.dc1.a1', '64.do1.c1', '64.do1.c2', '64.do1.d1', '64.do1.d2'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 1186, -1, 9271, -1, 1186, -1], 'generators': [37, 6, 8], 'label': '256.30836.32.hi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hi1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hi1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878499
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ee1.b1', '16.gl1.a1', '16.hp1.a1', '16.jg1.c1', '16.jg1.g1', '16.jg1.k1', '16.jg1.o1'], 'contains': ['64.da1.b1', '64.db1.a1', '64.dc1.a1', '64.do1.e1', '64.do1.e2', '64.do1.f1', '64.do1.f2'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 3466, -1, 9271, -1, 3463, -1], 'generators': [5, 38, 8], 'label': '256.30836.32.hi1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hi1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hi1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878500
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hi1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ee1.b1', '16.gl1.a1', '16.hp1.b1', '16.jg1.d1', '16.jg1.h1', '16.jg1.l1', '16.jg1.p1'], 'contains': ['64.da1.b1', '64.db1.b1', '64.dc1.a1', '64.do1.g1', '64.do1.g2', '64.do1.h1', '64.do1.h2'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 1062, -1, 9271, -1, 1061, -1], 'generators': [37, 38, 8], 'label': '256.30836.32.hi1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hi1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hi1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878501
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ef1.a1', '16.gm1.a1', '16.hq1.a1'], 'contains': ['64.da1.a1', '64.de1.a1', '64.dg1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6044, -1, 6636, -1, 6047, -1, 6630, -1], 'generators': [85, 6], 'label': '256.30836.32.hj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.br1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.br1.a1', 'old_label': '32.hj1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878502
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.hj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ef1.b1', '16.gm1.a1', '16.hq1.a1'], 'contains': ['64.da1.b1', '64.de1.a1', '64.dg1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6044, -1, 6624, -1, 6047, -1, 6618, -1], 'generators': [85, 38], 'label': '256.30836.32.hj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.br1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.br1.a1', 'old_label': '32.hj1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hj1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878503
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.a1', '16.hc1.a1', '16.ik1.a1', '16.jd1.a1', '16.je1.a1', '16.jf1.a1', '16.jg1.a1'], 'contains': ['64.di1.a1', '64.dj1.a1', '64.dk1.a1', '64.dl1.a1', '64.dm1.a1', '64.dn1.a1', '64.do1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1826, -1, 9856, -1, 1825, -1], 'generators': [1, 2, 4], 'label': '256.30836.32.hk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878504
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.a1', '16.hc1.a2', '16.ik1.b1', '16.jd1.b1', '16.je1.a2', '16.jf1.a1', '16.jg1.b1'], 'contains': ['64.di1.a1', '64.dj1.a1', '64.dk1.c1', '64.dl1.b1', '64.dm1.a2', '64.dn1.a2', '64.do1.c1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 673, -1, 9856, -1, 672, -1], 'generators': [137, 2, 4], 'label': '256.30836.32.hk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878505
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.b1', '16.hc1.a2', '16.ik1.a2', '16.jd1.a1', '16.je1.a1', '16.jf1.b1', '16.jg1.c1'], 'contains': ['64.di1.a1', '64.dj1.b1', '64.dk1.b1', '64.dl1.a1', '64.dm1.b2', '64.dn1.b2', '64.do1.e1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1492, -1, 9856, -1, 1491, -1], 'generators': [1, 42, 4], 'label': '256.30836.32.hk1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.c1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878660
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.i1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '32.g1.b1', '32.k1.a1', '32.gt1.d1', '32.gt1.h1', '32.gw1.d1', '32.gx1.g1', '32.gx1.h1', '32.gy1.d1'], 'contains': ['128.f1.a1', '128.i1.d1'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8946, 6962, 4776, 7405, 8951, 6959, 4777, 7422], 'generators': [161, 136], 'label': '256.30836.64.i1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.i1.d1', 'normal_contained_in': ['32.k1.a1', '32.g1.b1', '32.d1.b1'], 'normal_contains': ['128.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.i1.d1', 'projective_image': '128.2201', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.22', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.i1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878727
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.ca1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.r1.a1', '32.er1.a1', '32.fs1.a1', '32.gd1.a1', '32.gd1.b1', '32.gd1.c1', '32.gd1.d1', '32.gg1.a1', '32.gg1.a2', '32.gg1.b1', '32.gg1.b2', '32.gh1.a1', '32.gh1.b1', '32.gh1.c1', '32.gh1.d1'], 'contains': ['128.d1.a1', '128.n1.a1', '128.n1.b1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9186, -1, 3445, -1, 9191, -1, 3442, -1], 'generators': [7, 160], 'label': '256.30836.64.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.ca1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878506
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dp1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.e1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.k1', '64.dk1.l1', '64.dk1.j1', '64.dk1.i1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.m1', '64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.dn1.g2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '2.u1.a1', '2.bc1.a1'], 'contains': ['8.br1.a1', '8.bu1.a1', '8.bw1.a1', '8.dp1.a1', '8.ds1.a1', '8.ej1.a1', '8.ev1.a1'], 'core': '4.dp1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1761, 7919, 8190, 2956, 1762, 7916, 8182, 2962], 'generators': [17, 66, 68], 'label': '256.30836.4.dp1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dp1.a1', 'normal_contained_in': ['2.u1.a1', '2.h1.a1', '2.bc1.a1'], 'normal_contains': ['8.br1.a1', '8.bw1.a1', '8.bu1.a1', '8.ds1.a1', '8.dp1.a1', '8.ej1.a1', '8.ev1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dp1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878507
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.b1', '16.hc1.a1', '16.ik1.b2', '16.jd1.b1', '16.je1.a2', '16.jf1.b1', '16.jg1.d1'], 'contains': ['64.di1.a1', '64.dj1.b1', '64.dk1.d1', '64.dl1.b1', '64.dm1.b1', '64.dn1.b1', '64.do1.g1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 284, -1, 9856, -1, 283, -1], 'generators': [137, 42, 4], 'label': '256.30836.32.hk1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.d1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878508
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.c1', '16.hc1.b1', '16.ik1.a2', '16.jd1.c1', '16.je1.a2', '16.jf1.a1', '16.jg1.a1'], 'contains': ['64.di1.a1', '64.dj1.c1', '64.dk1.a1', '64.dl1.c1', '64.dm1.a2', '64.dn1.e1', '64.do1.a2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3174, -1, 9856, -1, 3172, -1], 'generators': [137, 2, 140], 'label': '256.30836.32.hk1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.e1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878509
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.c1', '16.hc1.b2', '16.ik1.b2', '16.jd1.d1', '16.je1.a1', '16.jf1.a1', '16.jg1.b1'], 'contains': ['64.di1.a1', '64.dj1.c1', '64.dk1.c1', '64.dl1.d1', '64.dm1.a1', '64.dn1.e2', '64.do1.c2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1660, -1, 9856, -1, 1658, -1], 'generators': [1, 2, 140], 'label': '256.30836.32.hk1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.f1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878510
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.d1', '16.hc1.b2', '16.ik1.a1', '16.jd1.c1', '16.je1.a2', '16.jf1.b1', '16.jg1.c1'], 'contains': ['64.di1.a1', '64.dj1.d1', '64.dk1.b1', '64.dl1.c1', '64.dm1.b1', '64.dn1.f2', '64.do1.e2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2132, -1, 9856, -1, 2130, -1], 'generators': [137, 42, 140], 'label': '256.30836.32.hk1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.g1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878511
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.d1', '16.hc1.b1', '16.ik1.b1', '16.jd1.d1', '16.je1.a1', '16.jf1.b1', '16.jg1.d1'], 'contains': ['64.di1.a1', '64.dj1.d1', '64.dk1.d1', '64.dl1.d1', '64.dm1.b2', '64.dn1.f1', '64.do1.g2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 979, -1, 9856, -1, 977, -1], 'generators': [1, 42, 140], 'label': '256.30836.32.hk1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.h1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878512
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.a1', '16.hc1.c2', '16.ik1.c1', '16.jd1.e1', '16.je1.b2', '16.jf1.c1', '16.jg1.a1'], 'contains': ['64.di1.b1', '64.dj1.a1', '64.dk1.a1', '64.dl1.e1', '64.dm1.c2', '64.dn1.c2', '64.do1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1618, -1, 9856, -1, 1616, -1], 'generators': [9, 2, 4], 'label': '256.30836.32.hk1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.i1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878513
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.a1', '16.hc1.c1', '16.ik1.d1', '16.jd1.f1', '16.je1.b1', '16.jf1.c1', '16.jg1.b1'], 'contains': ['64.di1.b1', '64.dj1.a1', '64.dk1.c1', '64.dl1.f1', '64.dm1.c1', '64.dn1.c1', '64.do1.d1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 548, -1, 9856, -1, 547, -1], 'generators': [129, 2, 4], 'label': '256.30836.32.hk1.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.j1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878514
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.b1', '16.hc1.c1', '16.ik1.c2', '16.jd1.e1', '16.je1.b2', '16.jf1.d1', '16.jg1.c1'], 'contains': ['64.di1.b1', '64.dj1.b1', '64.dk1.b1', '64.dl1.e1', '64.dm1.d1', '64.dn1.d1', '64.do1.f1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1145, -1, 9856, -1, 1144, -1], 'generators': [9, 42, 4], 'label': '256.30836.32.hk1.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.k1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878515
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.b1', '16.hc1.c2', '16.ik1.d2', '16.jd1.f1', '16.je1.b1', '16.jf1.d1', '16.jg1.d1'], 'contains': ['64.di1.b1', '64.dj1.b1', '64.dk1.d1', '64.dl1.f1', '64.dm1.d2', '64.dn1.d2', '64.do1.h1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 297, -1, 9856, -1, 297, -1], 'generators': [129, 42, 4], 'label': '256.30836.32.hk1.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.l1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878516
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.c1', '16.hc1.d2', '16.ik1.c2', '16.jd1.g1', '16.je1.b1', '16.jf1.c1', '16.jg1.a1'], 'contains': ['64.di1.b1', '64.dj1.c1', '64.dk1.a1', '64.dl1.g1', '64.dm1.c1', '64.dn1.g2', '64.do1.b2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3091, -1, 9856, -1, 3088, -1], 'generators': [129, 2, 140], 'label': '256.30836.32.hk1.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.m1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878685
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.cs1.a1', '32.dk1.a1', '32.ec1.a1', '32.ec1.c1', '32.ef1.a1', '32.ef1.c1', '32.ei1.a1', '32.ei1.a2', '32.ej1.a1'], 'contains': ['128.b1.a1', '128.j1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7989, -1, 1582, -1, 7993, -1, 1582, -1], 'generators': [4, 32], 'label': '256.30836.64.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.w1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879502
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.du1.a1', '8.gy1.a1', '8.gy1.b1'], 'contains': ['32.dp1.a1', '32.du1.a1', '32.dx1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3079, -1, 8743, -1, 3081, -1, 8736, -1], 'generators': [21, 70], 'label': '256.30836.16.gv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.du1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.w1.a1', 'old_label': '16.gv1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878517
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dq1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.di1.i1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.l1', '64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.d1', '64.dl1.o1', '64.dl1.p1', '64.dl1.c1', '64.dl1.g1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.m1', '64.dk1.p1', '64.dk1.n1', '64.dk1.o1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.e1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.dk1.i1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2', '64.dn1.e1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2', '64.dn1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '2.t1.a1', '2.bc1.a1'], 'contains': ['8.br1.a1', '8.bv1.a1', '8.bz1.a1', '8.dq1.a1', '8.dt1.a1', '8.er1.a1', '8.fu1.a1'], 'core': '4.dq1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5097, 9024, 7513, 1617, 5100, 9021, 7506, 1621], 'generators': [65, 18, 20], 'label': '256.30836.4.dq1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dq1.a1', 'normal_contained_in': ['2.t1.a1', '2.i1.a1', '2.bc1.a1'], 'normal_contains': ['8.br1.a1', '8.bv1.a1', '8.bz1.a1', '8.dq1.a1', '8.dt1.a1', '8.er1.a1', '8.fu1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dq1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878518
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.c1', '16.hc1.d1', '16.ik1.d2', '16.jd1.h1', '16.je1.b2', '16.jf1.c1', '16.jg1.b1'], 'contains': ['64.di1.b1', '64.dj1.c1', '64.dk1.c1', '64.dl1.h1', '64.dm1.c2', '64.dn1.g1', '64.do1.d2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1798, -1, 9856, -1, 1797, -1], 'generators': [9, 2, 140], 'label': '256.30836.32.hk1.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.n1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878519
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.d1', '16.hc1.d1', '16.ik1.c1', '16.jd1.g1', '16.je1.b1', '16.jf1.d1', '16.jg1.c1'], 'contains': ['64.di1.b1', '64.dj1.d1', '64.dk1.b1', '64.dl1.g1', '64.dm1.d2', '64.dn1.h1', '64.do1.f2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2341, -1, 9856, -1, 2338, -1], 'generators': [129, 42, 140], 'label': '256.30836.32.hk1.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.o1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878520
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.d1', '16.hc1.d2', '16.ik1.d1', '16.jd1.h1', '16.je1.b2', '16.jf1.d1', '16.jg1.d1'], 'contains': ['64.di1.b1', '64.dj1.d1', '64.dk1.d1', '64.dl1.h1', '64.dm1.d1', '64.dn1.h2', '64.do1.h2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1159, -1, 9856, -1, 1158, -1], 'generators': [9, 42, 140], 'label': '256.30836.32.hk1.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.p1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878521
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.e1', '16.hc1.a2', '16.ik1.a1', '16.jd1.e1', '16.je1.b1', '16.jf1.e1', '16.jg1.e1'], 'contains': ['64.di1.c1', '64.dj1.a1', '64.dk1.b1', '64.dl1.i1', '64.dm1.e2', '64.dn1.d2', '64.do1.b2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 381, -1, 9856, -1, 380, -1], 'generators': [169, 2, 4], 'label': '256.30836.32.hk1.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.q1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878522
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.e1', '16.hc1.a1', '16.ik1.b1', '16.jd1.f1', '16.je1.b2', '16.jf1.e1', '16.jg1.f1'], 'contains': ['64.di1.c1', '64.dj1.a1', '64.dk1.d1', '64.dl1.j1', '64.dm1.e1', '64.dn1.d1', '64.do1.d2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 89, -1, 9856, -1, 89, -1], 'generators': [33, 2, 4], 'label': '256.30836.32.hk1.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.r1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878523
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.f1', '16.hc1.a1', '16.ik1.a2', '16.jd1.e1', '16.je1.b1', '16.jf1.f1', '16.jg1.g1'], 'contains': ['64.di1.c1', '64.dj1.b1', '64.dk1.a1', '64.dl1.i1', '64.dm1.f1', '64.dn1.c1', '64.do1.f2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 589, -1, 9856, -1, 589, -1], 'generators': [169, 42, 4], 'label': '256.30836.32.hk1.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.s1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878524
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.f1', '16.hc1.a2', '16.ik1.b2', '16.jd1.f1', '16.je1.b2', '16.jf1.f1', '16.jg1.h1'], 'contains': ['64.di1.c1', '64.dj1.b1', '64.dk1.c1', '64.dl1.j1', '64.dm1.f2', '64.dn1.c2', '64.do1.h2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 102, -1, 9856, -1, 103, -1], 'generators': [33, 42, 4], 'label': '256.30836.32.hk1.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.t1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878525
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.g1', '16.hc1.b2', '16.ik1.a2', '16.jd1.g1', '16.je1.b2', '16.jf1.e1', '16.jg1.e1'], 'contains': ['64.di1.c1', '64.dj1.c1', '64.dk1.b1', '64.dl1.k1', '64.dm1.e1', '64.dn1.h2', '64.do1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1423, -1, 9856, -1, 1422, -1], 'generators': [33, 2, 140], 'label': '256.30836.32.hk1.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.u1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.u1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878526
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.g1', '16.hc1.b1', '16.ik1.b2', '16.jd1.h1', '16.je1.b1', '16.jf1.e1', '16.jg1.f1'], 'contains': ['64.di1.c1', '64.dj1.c1', '64.dk1.d1', '64.dl1.l1', '64.dm1.e2', '64.dn1.h1', '64.do1.d1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 325, -1, 9856, -1, 325, -1], 'generators': [169, 2, 140], 'label': '256.30836.32.hk1.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.v1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.v1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878527
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.h1', '16.hc1.b1', '16.ik1.a1', '16.jd1.g1', '16.je1.b2', '16.jf1.f1', '16.jg1.g1'], 'contains': ['64.di1.c1', '64.dj1.d1', '64.dk1.a1', '64.dl1.k1', '64.dm1.f2', '64.dn1.g1', '64.do1.f1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1632, -1, 9856, -1, 1630, -1], 'generators': [33, 42, 140], 'label': '256.30836.32.hk1.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.w1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878686
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '32.cs1.a1', '32.dk1.a1', '32.ec1.b1', '32.ec1.d1', '32.ef1.b1', '32.ef1.d1', '32.ei1.b1', '32.ei1.b2', '32.ej1.b1'], 'contains': ['128.b1.a1', '128.j1.b1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7989, -1, 3501, -1, 7993, -1, 3498, -1], 'generators': [140, 32], 'label': '256.30836.64.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.w1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.w1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879547
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.by1.a1', '8.hd1.a1', '8.hd1.b1'], 'contains': ['32.ep1.a1', '32.ex1.a1', '32.fb1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6829, -1, 6980, -1, 6832, -1, 6974, -1], 'generators': [6, 80], 'label': '256.30836.16.hr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.by1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.dh1.a1', 'old_label': '16.hr1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hr1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878528
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dr1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.b1', '64.dl1.j1', '64.dl1.i1', '64.dl1.f1', '64.dl1.e1', '64.dl1.m1', '64.dl1.n1', '64.dl1.d1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e1', '64.dn1.e2', '64.dn1.h1', '64.dn1.h2', '64.dn1.g1', '64.dn1.g2', '64.dn1.f1', '64.dn1.f2', '64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.o1', '64.dk1.m1', '64.dk1.n1', '64.dk1.p1', '64.dk1.k1', '64.dk1.i1', '64.dk1.j1', '64.dk1.l1', '64.dk1.e1', '64.dk1.g1', '64.dk1.h1', '64.dk1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '2.v1.a1', '2.bb1.a1'], 'contains': ['8.bs1.a1', '8.bt1.a1', '8.by1.a1', '8.dv1.a1', '8.dx1.a1', '8.ef1.a1', '8.fa1.a1'], 'core': '4.dr1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8021, 1997, 6633, 5235, 8025, 1996, 6628, 5246], 'generators': [6, 16, 64], 'label': '256.30836.4.dr1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dr1.a1', 'normal_contained_in': ['2.v1.a1', '2.j1.a1', '2.bb1.a1'], 'normal_contains': ['8.bt1.a1', '8.bs1.a1', '8.by1.a1', '8.dv1.a1', '8.ef1.a1', '8.dx1.a1', '8.fa1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dr1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878529
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.h1', '16.hc1.b2', '16.ik1.b1', '16.jd1.h1', '16.je1.b1', '16.jf1.f1', '16.jg1.h1'], 'contains': ['64.di1.c1', '64.dj1.d1', '64.dk1.c1', '64.dl1.l1', '64.dm1.f1', '64.dn1.g2', '64.do1.h1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 464, -1, 9856, -1, 464, -1], 'generators': [169, 42, 140], 'label': '256.30836.32.hk1.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.x1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.x1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878530
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.e1', '16.hc1.c1', '16.ik1.c1', '16.jd1.a1', '16.je1.a2', '16.jf1.g1', '16.jg1.e1'], 'contains': ['64.di1.d1', '64.dj1.a1', '64.dk1.b1', '64.dl1.m1', '64.dm1.g1', '64.dn1.b1', '64.do1.a2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2299, -1, 9856, -1, 2297, -1], 'generators': [161, 2, 4], 'label': '256.30836.32.hk1.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.y1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878531
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.e1', '16.hc1.c2', '16.ik1.d1', '16.jd1.b1', '16.je1.a1', '16.jf1.g1', '16.jg1.f1'], 'contains': ['64.di1.d1', '64.dj1.a1', '64.dk1.d1', '64.dl1.n1', '64.dm1.g2', '64.dn1.b2', '64.do1.c2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1117, -1, 9856, -1, 1116, -1], 'generators': [41, 2, 4], 'label': '256.30836.32.hk1.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.z1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.z1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878532
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.f1', '16.hc1.c2', '16.ik1.c2', '16.jd1.a1', '16.je1.a2', '16.jf1.h1', '16.jg1.g1'], 'contains': ['64.di1.d1', '64.dj1.b1', '64.dk1.a1', '64.dl1.m1', '64.dm1.h2', '64.dn1.a2', '64.do1.e2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2674, -1, 9856, -1, 2672, -1], 'generators': [161, 42, 4], 'label': '256.30836.32.hk1.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ba1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878533
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.f1', '16.hc1.c1', '16.ik1.d2', '16.jd1.b1', '16.je1.a1', '16.jf1.h1', '16.jg1.h1'], 'contains': ['64.di1.d1', '64.dj1.b1', '64.dk1.c1', '64.dl1.n1', '64.dm1.h1', '64.dn1.a1', '64.do1.g2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1437, -1, 9856, -1, 1436, -1], 'generators': [41, 42, 4], 'label': '256.30836.32.hk1.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bb1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878534
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.g1', '16.hc1.d1', '16.ik1.c2', '16.jd1.c1', '16.je1.a1', '16.jf1.g1', '16.jg1.e1'], 'contains': ['64.di1.d1', '64.dj1.c1', '64.dk1.b1', '64.dl1.o1', '64.dm1.g2', '64.dn1.f1', '64.do1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2952, -1, 9856, -1, 2949, -1], 'generators': [41, 2, 140], 'label': '256.30836.32.hk1.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bc1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878535
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.g1', '16.hc1.d2', '16.ik1.d2', '16.jd1.d1', '16.je1.a2', '16.jf1.g1', '16.jg1.f1'], 'contains': ['64.di1.d1', '64.dj1.c1', '64.dk1.d1', '64.dl1.p1', '64.dm1.g1', '64.dn1.f2', '64.do1.c1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2355, -1, 9856, -1, 2352, -1], 'generators': [161, 2, 140], 'label': '256.30836.32.hk1.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bd1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878536
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.h1', '16.hc1.d2', '16.ik1.c1', '16.jd1.c1', '16.je1.a1', '16.jf1.h1', '16.jg1.g1'], 'contains': ['64.di1.d1', '64.dj1.d1', '64.dk1.a1', '64.dl1.o1', '64.dm1.h1', '64.dn1.e2', '64.do1.e1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3508, -1, 9856, -1, 3505, -1], 'generators': [41, 42, 140], 'label': '256.30836.32.hk1.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.be1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.be1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878537
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.h1', '16.hc1.d1', '16.ik1.d1', '16.jd1.d1', '16.je1.a2', '16.jf1.h1', '16.jg1.h1'], 'contains': ['64.di1.d1', '64.dj1.d1', '64.dk1.c1', '64.dl1.p1', '64.dm1.h2', '64.dn1.e1', '64.do1.g1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2716, -1, 9856, -1, 2713, -1], 'generators': [161, 42, 140], 'label': '256.30836.32.hk1.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bf1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878538
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.a1', '16.hc1.e2', '16.ik1.a2', '16.jd1.i1', '16.je1.c1', '16.jf1.i1', '16.jg1.i1'], 'contains': ['64.di1.e1', '64.dj1.e1', '64.dk1.e1', '64.dl1.a1', '64.dm1.a2', '64.dn1.c1', '64.do1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 603, -1, 9856, -1, 603, -1], 'generators': [1, 130, 4], 'label': '256.30836.32.hk1.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bg1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878687
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.ct1.a1', '32.dl1.a1', '32.ec1.a1', '32.ec1.b1', '32.ec1.c1', '32.ec1.d1', '32.eg1.a1', '32.eg1.a2', '32.eg1.b1', '32.eg1.b2', '32.ek1.a1', '32.ek1.a2', '32.ek1.a3', '32.ek1.a4'], 'contains': ['128.b1.a1', '128.k1.a1', '128.k1.b1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8015, -1, 1817, -1, 8019, -1, 1818, -1], 'generators': [6, 32], 'label': '256.30836.64.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.x1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.x1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878539
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ds1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.dn1.g2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.e2', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.e1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.k1', '64.dk1.l1', '64.dk1.j1', '64.dk1.i1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.m1'], 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '2.v1.a1', '2.bd1.a1'], 'contains': ['8.bs1.a1', '8.bw1.a1', '8.cb1.a1', '8.dw1.a1', '8.dy1.a1', '8.ex1.a1', '8.fk1.a1'], 'core': '4.ds1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4414, 6998, 8599, 9016, 4416, 6995, 8592, 9036], 'generators': [17, 6, 64], 'label': '256.30836.4.ds1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ds1.a1', 'normal_contained_in': ['2.v1.a1', '2.h1.a1', '2.bd1.a1'], 'normal_contains': ['8.bw1.a1', '8.bs1.a1', '8.cb1.a1', '8.dy1.a1', '8.fk1.a1', '8.dw1.a1', '8.ex1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ds1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878540
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.a1', '16.hc1.e1', '16.ik1.b2', '16.jd1.j1', '16.je1.c2', '16.jf1.i1', '16.jg1.j1'], 'contains': ['64.di1.e1', '64.dj1.e1', '64.dk1.g1', '64.dl1.b1', '64.dm1.a1', '64.dn1.c2', '64.do1.d1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 130, -1, 9856, -1, 130, -1], 'generators': [137, 130, 4], 'label': '256.30836.32.hk1.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bh1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878541
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.b1', '16.hc1.e1', '16.ik1.a1', '16.jd1.i1', '16.je1.c1', '16.jf1.j1', '16.jg1.k1'], 'contains': ['64.di1.e1', '64.dj1.f1', '64.dk1.f1', '64.dl1.a1', '64.dm1.b1', '64.dn1.d2', '64.do1.f1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 353, -1, 9856, -1, 353, -1], 'generators': [1, 170, 4], 'label': '256.30836.32.hk1.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bi1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878542
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.b1', '16.hc1.e2', '16.ik1.b1', '16.jd1.j1', '16.je1.c2', '16.jf1.j1', '16.jg1.l1'], 'contains': ['64.di1.e1', '64.dj1.f1', '64.dk1.h1', '64.dl1.b1', '64.dm1.b2', '64.dn1.d1', '64.do1.h1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 61, -1, 9856, -1, 61, -1], 'generators': [137, 170, 4], 'label': '256.30836.32.hk1.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bj1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878543
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.c1', '16.hc1.f2', '16.ik1.a1', '16.jd1.k1', '16.je1.c2', '16.jf1.i1', '16.jg1.i1'], 'contains': ['64.di1.e1', '64.dj1.g1', '64.dk1.e1', '64.dl1.c1', '64.dm1.a1', '64.dn1.g1', '64.do1.b2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1673, -1, 9856, -1, 1672, -1], 'generators': [137, 130, 140], 'label': '256.30836.32.hk1.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bk1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878544
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.c1', '16.hc1.f1', '16.ik1.b1', '16.jd1.l1', '16.je1.c1', '16.jf1.i1', '16.jg1.j1'], 'contains': ['64.di1.e1', '64.dj1.g1', '64.dk1.g1', '64.dl1.d1', '64.dm1.a2', '64.dn1.g2', '64.do1.d2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 478, -1, 9856, -1, 478, -1], 'generators': [1, 130, 140], 'label': '256.30836.32.hk1.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bl1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878545
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.d1', '16.hc1.f1', '16.ik1.a2', '16.jd1.k1', '16.je1.c2', '16.jf1.j1', '16.jg1.k1'], 'contains': ['64.di1.e1', '64.dj1.h1', '64.dk1.f1', '64.dl1.c1', '64.dm1.b2', '64.dn1.h2', '64.do1.f2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1395, -1, 9856, -1, 1394, -1], 'generators': [137, 170, 140], 'label': '256.30836.32.hk1.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bm1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878546
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.d1', '16.hc1.f2', '16.ik1.b2', '16.jd1.l1', '16.je1.c1', '16.jf1.j1', '16.jg1.l1'], 'contains': ['64.di1.e1', '64.dj1.h1', '64.dk1.h1', '64.dl1.d1', '64.dm1.b1', '64.dn1.h1', '64.do1.h2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 228, -1, 9856, -1, 228, -1], 'generators': [1, 170, 140], 'label': '256.30836.32.hk1.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bn1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878547
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.i1', '16.hc1.a2', '16.ik1.e2', '16.jd1.i1', '16.je1.d1', '16.jf1.i1', '16.jg1.a1'], 'contains': ['64.di1.f1', '64.dj1.i1', '64.dk1.i1', '64.dl1.a1', '64.dm1.a2', '64.dn1.c2', '64.do1.b2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 256, -1, 9856, -1, 255, -1], 'generators': [1, 10, 4], 'label': '256.30836.32.hk1.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bo1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878548
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.i1', '16.hc1.a1', '16.ik1.f2', '16.jd1.j1', '16.je1.d2', '16.jf1.i1', '16.jg1.b1'], 'contains': ['64.di1.f1', '64.dj1.i1', '64.dk1.k1', '64.dl1.b1', '64.dm1.a1', '64.dn1.c1', '64.do1.d2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 33, -1, 9856, -1, 33, -1], 'generators': [137, 10, 4], 'label': '256.30836.32.hk1.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bp1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878549
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.j1', '16.hc1.a1', '16.ik1.e1', '16.jd1.i1', '16.je1.d1', '16.jf1.j1', '16.jg1.c1'], 'contains': ['64.di1.f1', '64.dj1.j1', '64.dk1.j1', '64.dl1.a1', '64.dm1.b1', '64.dn1.d1', '64.do1.f2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 158, -1, 9856, -1, 158, -1], 'generators': [1, 34, 4], 'label': '256.30836.32.hk1.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bq1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878688
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1.a1', '32.cu1.a1', '32.dm1.a1', '32.ed1.a1', '32.ed1.a2', '32.ed1.b1', '32.ed1.b2', '32.ef1.a1', '32.ef1.b1', '32.ef1.c1', '32.ef1.d1', '32.ek1.a1', '32.ek1.a2', '32.ek1.a3', '32.ek1.a4'], 'contains': ['128.b1.a1', '128.l1.a1', '128.l1.b1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8068, -1, 2165, -1, 8073, -1, 2165, -1], 'generators': [5, 32], 'label': '256.30836.64.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.y1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.y1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878551
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dt1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.c1', '64.di1.b1', '64.di1.f1', '64.di1.m1', '64.di1.l1', '64.di1.k1', '64.di1.e1', '64.di1.j1', '64.di1.i1', '64.di1.h1', '64.di1.g1', '64.di1.p1', '64.di1.o1', '64.di1.n1', '64.dk1.a1', '64.dk1.d1', '64.dk1.c1', '64.dk1.b1', '64.dk1.k1', '64.dk1.j1', '64.dk1.i1', '64.dk1.l1', '64.dk1.g1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.n1', '64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.d1', '64.dl1.o1', '64.dl1.k1', '64.dl1.h1', '64.dl1.g1', '64.dl1.l1', '64.dl1.p1', '64.dl1.c1', '64.dn1.a1', '64.dn1.b2', '64.dn1.d1', '64.dn1.c2', '64.dn1.c1', '64.dn1.d2', '64.dn1.b1', '64.dn1.a2', '64.dn1.e2', '64.dn1.f1', '64.dn1.h2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.f2', '64.dn1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '2.t1.a1', '2.bd1.a1'], 'contains': ['8.bs1.a1', '8.bz1.a1', '8.ca1.a1', '8.dz1.a1', '8.ea1.a1', '8.fq1.a1', '8.fs1.a1'], 'core': '4.dt1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7634, 8915, 6827, 8385, 7637, 8911, 6821, 8403], 'generators': [18, 20, 64], 'label': '256.30836.4.dt1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dt1.a1', 'normal_contained_in': ['2.t1.a1', '2.j1.a1', '2.bd1.a1'], 'normal_contains': ['8.bs1.a1', '8.bz1.a1', '8.ca1.a1', '8.dz1.a1', '8.ea1.a1', '8.fq1.a1', '8.fs1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dt1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878552
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.j1', '16.hc1.a2', '16.ik1.f1', '16.jd1.j1', '16.je1.d2', '16.jf1.j1', '16.jg1.d1'], 'contains': ['64.di1.f1', '64.dj1.j1', '64.dk1.l1', '64.dl1.b1', '64.dm1.b2', '64.dn1.d2', '64.do1.h2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 5, -1, 9856, -1, 5, -1], 'generators': [137, 34, 4], 'label': '256.30836.32.hk1.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.br1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.br1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878553
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.k1', '16.hc1.b2', '16.ik1.e1', '16.jd1.k1', '16.je1.d2', '16.jf1.i1', '16.jg1.a1'], 'contains': ['64.di1.f1', '64.dj1.k1', '64.dk1.i1', '64.dl1.c1', '64.dm1.a1', '64.dn1.g2', '64.do1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1354, -1, 9856, -1, 1352, -1], 'generators': [137, 10, 140], 'label': '256.30836.32.hk1.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bs1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878554
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.k1', '16.hc1.b1', '16.ik1.f1', '16.jd1.l1', '16.je1.d1', '16.jf1.i1', '16.jg1.b1'], 'contains': ['64.di1.f1', '64.dj1.k1', '64.dk1.k1', '64.dl1.d1', '64.dm1.a2', '64.dn1.g1', '64.do1.d1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 270, -1, 9856, -1, 269, -1], 'generators': [1, 10, 140], 'label': '256.30836.32.hk1.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bt1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bt1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878555
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.l1', '16.hc1.b1', '16.ik1.e2', '16.jd1.k1', '16.je1.d2', '16.jf1.j1', '16.jg1.c1'], 'contains': ['64.di1.f1', '64.dj1.l1', '64.dk1.j1', '64.dl1.c1', '64.dm1.b2', '64.dn1.h1', '64.do1.f1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 797, -1, 9856, -1, 797, -1], 'generators': [137, 34, 140], 'label': '256.30836.32.hk1.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bu1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878556
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.l1', '16.hc1.b2', '16.ik1.f2', '16.jd1.l1', '16.je1.d1', '16.jf1.j1', '16.jg1.d1'], 'contains': ['64.di1.f1', '64.dj1.l1', '64.dk1.l1', '64.dl1.d1', '64.dm1.b1', '64.dn1.h2', '64.do1.h1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 116, -1, 9856, -1, 117, -1], 'generators': [1, 34, 140], 'label': '256.30836.32.hk1.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bv1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878557
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.i1', '16.hc1.e1', '16.ik1.e1', '16.jd1.a1', '16.je1.e1', '16.jf1.a1', '16.jg1.i1'], 'contains': ['64.di1.g1', '64.dj1.m1', '64.dk1.m1', '64.dl1.a1', '64.dm1.a1', '64.dn1.a2', '64.do1.a2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1326, -1, 9856, -1, 1325, -1], 'generators': [1, 138, 4], 'label': '256.30836.32.hk1.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bw1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878558
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.i1', '16.hc1.e2', '16.ik1.f1', '16.jd1.b1', '16.je1.e2', '16.jf1.a1', '16.jg1.j1'], 'contains': ['64.di1.g1', '64.dj1.m1', '64.dk1.o1', '64.dl1.b1', '64.dm1.a2', '64.dn1.a1', '64.do1.c2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 617, -1, 9856, -1, 616, -1], 'generators': [137, 138, 4], 'label': '256.30836.32.hk1.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bx1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878559
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.j1', '16.hc1.e2', '16.ik1.e2', '16.jd1.a1', '16.je1.e1', '16.jf1.b1', '16.jg1.k1'], 'contains': ['64.di1.g1', '64.dj1.n1', '64.dk1.n1', '64.dl1.a1', '64.dm1.b2', '64.dn1.b1', '64.do1.e2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 783, -1, 9856, -1, 783, -1], 'generators': [1, 162, 4], 'label': '256.30836.32.hk1.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.by1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.by1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878560
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.j1', '16.hc1.e1', '16.ik1.f2', '16.jd1.b1', '16.je1.e2', '16.jf1.b1', '16.jg1.l1'], 'contains': ['64.di1.g1', '64.dj1.n1', '64.dk1.p1', '64.dl1.b1', '64.dm1.b1', '64.dn1.b2', '64.do1.g2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 173, -1, 9856, -1, 172, -1], 'generators': [137, 162, 4], 'label': '256.30836.32.hk1.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.bz1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.bz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878561
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.k1', '16.hc1.f1', '16.ik1.e2', '16.jd1.c1', '16.je1.e2', '16.jf1.a1', '16.jg1.i1'], 'contains': ['64.di1.g1', '64.dj1.o1', '64.dk1.m1', '64.dl1.c1', '64.dm1.a2', '64.dn1.e2', '64.do1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3036, -1, 9856, -1, 3033, -1], 'generators': [137, 138, 140], 'label': '256.30836.32.hk1.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ca1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ca1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878689
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.q1.a1', '32.cv1.a1', '32.dn1.a1', '32.eb1.a1', '32.eb1.b1', '32.eb1.c1', '32.eb1.d1', '32.ei1.a1', '32.ei1.a2', '32.ei1.b1', '32.ei1.b2', '32.ek1.a1', '32.ek1.a2', '32.ek1.a3', '32.ek1.a4'], 'contains': ['128.b1.a1', '128.m1.a1', '128.m1.b1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7962, -1, 1831, -1, 7966, -1, 1832, -1], 'generators': [3, 32], 'label': '256.30836.64.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.z1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.z1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878562
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.du1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.e1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.k1', '64.dk1.l1', '64.dk1.j1', '64.dk1.i1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.m1', '64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.dn1.g2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '2.u1.a1', '2.be1.a1'], 'contains': ['8.bt1.a1', '8.bu1.a1', '8.ca1.a1', '8.ec1.a1', '8.ee1.a1', '8.ei1.a1', '8.fb1.a1'], 'core': '4.du1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5447, 4127, 5776, 3089, 5449, 4126, 5771, 3096], 'generators': [66, 68, 16], 'label': '256.30836.4.du1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.du1.a1', 'normal_contained_in': ['2.u1.a1', '2.j1.a1', '2.be1.a1'], 'normal_contains': ['8.bt1.a1', '8.bu1.a1', '8.ca1.a1', '8.ec1.a1', '8.ee1.a1', '8.ei1.a1', '8.fb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.du1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.du1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878563
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.k1', '16.hc1.f2', '16.ik1.f2', '16.jd1.d1', '16.je1.e1', '16.jf1.a1', '16.jg1.j1'], 'contains': ['64.di1.g1', '64.dj1.o1', '64.dk1.o1', '64.dl1.d1', '64.dm1.a1', '64.dn1.e1', '64.do1.c1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1298, -1, 9856, -1, 1297, -1], 'generators': [1, 138, 140], 'label': '256.30836.32.hk1.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cb1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878564
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.l1', '16.hc1.f2', '16.ik1.e1', '16.jd1.c1', '16.je1.e2', '16.jf1.b1', '16.jg1.k1'], 'contains': ['64.di1.g1', '64.dj1.p1', '64.dk1.n1', '64.dl1.c1', '64.dm1.b1', '64.dn1.f1', '64.do1.e1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1965, -1, 9856, -1, 1963, -1], 'generators': [137, 162, 140], 'label': '256.30836.32.hk1.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cc1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878565
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.l1', '16.hc1.f1', '16.ik1.f1', '16.jd1.d1', '16.je1.e1', '16.jf1.b1', '16.jg1.l1'], 'contains': ['64.di1.g1', '64.dj1.p1', '64.dk1.p1', '64.dl1.d1', '64.dm1.b2', '64.dn1.f2', '64.do1.g1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 770, -1, 9856, -1, 769, -1], 'generators': [1, 162, 140], 'label': '256.30836.32.hk1.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cd1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878566
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.a1', '16.hc1.g1', '16.ik1.c2', '16.jd1.m1', '16.je1.f2', '16.jf1.k1', '16.jg1.i1'], 'contains': ['64.di1.h1', '64.dj1.e1', '64.dk1.e1', '64.dl1.e1', '64.dm1.c1', '64.dn1.a2', '64.do1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2896, -1, 9856, -1, 2894, -1], 'generators': [9, 130, 4], 'label': '256.30836.32.hk1.ce1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ce1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ce1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878567
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.a1', '16.hc1.g2', '16.ik1.d2', '16.jd1.n1', '16.je1.f1', '16.jf1.k1', '16.jg1.j1'], 'contains': ['64.di1.h1', '64.dj1.e1', '64.dk1.g1', '64.dl1.f1', '64.dm1.c2', '64.dn1.a1', '64.do1.c1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1478, -1, 9856, -1, 1477, -1], 'generators': [129, 130, 4], 'label': '256.30836.32.hk1.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cf1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878568
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.b1', '16.hc1.g2', '16.ik1.c1', '16.jd1.m1', '16.je1.f2', '16.jf1.l1', '16.jg1.k1'], 'contains': ['64.di1.h1', '64.dj1.f1', '64.dk1.f1', '64.dl1.e1', '64.dm1.d2', '64.dn1.b1', '64.do1.e1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2173, -1, 9856, -1, 2172, -1], 'generators': [9, 170, 4], 'label': '256.30836.32.hk1.cg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cg1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878569
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.b1', '16.hc1.g1', '16.ik1.d1', '16.jd1.n1', '16.je1.f1', '16.jf1.l1', '16.jg1.l1'], 'contains': ['64.di1.h1', '64.dj1.f1', '64.dk1.h1', '64.dl1.f1', '64.dm1.d1', '64.dn1.b2', '64.do1.g1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1131, -1, 9856, -1, 1130, -1], 'generators': [129, 170, 4], 'label': '256.30836.32.hk1.ch1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ch1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ch1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878570
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.c1', '16.hc1.h1', '16.ik1.c1', '16.jd1.o1', '16.je1.f1', '16.jf1.k1', '16.jg1.i1'], 'contains': ['64.di1.h1', '64.dj1.g1', '64.dk1.e1', '64.dl1.g1', '64.dm1.c2', '64.dn1.e2', '64.do1.a2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3591, -1, 9856, -1, 3588, -1], 'generators': [129, 130, 140], 'label': '256.30836.32.hk1.ci1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ci1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ci1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878571
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.c1', '16.hc1.h2', '16.ik1.d1', '16.jd1.p1', '16.je1.f2', '16.jf1.k1', '16.jg1.j1'], 'contains': ['64.di1.h1', '64.dj1.g1', '64.dk1.g1', '64.dl1.h1', '64.dm1.c1', '64.dn1.e1', '64.do1.c2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2730, -1, 9856, -1, 2727, -1], 'generators': [9, 130, 140], 'label': '256.30836.32.hk1.cj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cj1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878572
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.d1', '16.hc1.h2', '16.ik1.c2', '16.jd1.o1', '16.je1.f1', '16.jf1.l1', '16.jg1.k1'], 'contains': ['64.di1.h1', '64.dj1.h1', '64.dk1.f1', '64.dl1.g1', '64.dm1.d1', '64.dn1.f1', '64.do1.e2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2966, -1, 9856, -1, 2963, -1], 'generators': [129, 170, 140], 'label': '256.30836.32.hk1.ck1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ck1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ck1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878690
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.r1.a1', '32.cw1.a1', '32.do1.a1', '32.ed1.a1', '32.ed1.a2', '32.ed1.b1', '32.ed1.b2', '32.eg1.a1', '32.eg1.a2', '32.eg1.b1', '32.eg1.b2', '32.ei1.a1', '32.ei1.a2', '32.ei1.b1', '32.ei1.b2'], 'contains': ['128.b1.a1', '128.n1.a1', '128.n1.b1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8122, -1, 2472, -1, 8126, -1, 2477, -1], 'generators': [7, 32], 'label': '256.30836.64.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.ba1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878573
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dv1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.b1', '64.dl1.j1', '64.dl1.i1', '64.dl1.f1', '64.dl1.e1', '64.dl1.m1', '64.dl1.n1', '64.dl1.d1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e1', '64.dn1.e2', '64.dn1.h1', '64.dn1.h2', '64.dn1.g1', '64.dn1.g2', '64.dn1.f1', '64.dn1.f2', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.o1', '64.dk1.m1', '64.dk1.n1', '64.dk1.p1', '64.dk1.k1', '64.dk1.i1', '64.dk1.j1', '64.dk1.l1', '64.dk1.e1', '64.dk1.g1', '64.dk1.h1', '64.dk1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '2.v1.a1', '2.be1.a1'], 'contains': ['8.bt1.a1', '8.bv1.a1', '8.cb1.a1', '8.ed1.a1', '8.eh1.a1', '8.ep1.a1', '8.fc1.a1'], 'core': '4.dv1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5402, 3998, 6896, 5581, 5405, 3996, 6890, 5593], 'generators': [65, 6, 16], 'label': '256.30836.4.dv1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dv1.a1', 'normal_contained_in': ['2.v1.a1', '2.i1.a1', '2.be1.a1'], 'normal_contains': ['8.bt1.a1', '8.bv1.a1', '8.cb1.a1', '8.ed1.a1', '8.eh1.a1', '8.ep1.a1', '8.fc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dv1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878574
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.d1', '16.hc1.h1', '16.ik1.d2', '16.jd1.p1', '16.je1.f2', '16.jf1.l1', '16.jg1.l1'], 'contains': ['64.di1.h1', '64.dj1.h1', '64.dk1.h1', '64.dl1.h1', '64.dm1.d2', '64.dn1.f2', '64.do1.g2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2285, -1, 9856, -1, 2283, -1], 'generators': [9, 170, 140], 'label': '256.30836.32.hk1.cl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cl1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878575
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.e1', '16.hc1.e1', '16.ik1.a2', '16.jd1.m1', '16.je1.f1', '16.jf1.m1', '16.jg1.m1'], 'contains': ['64.di1.i1', '64.dj1.e1', '64.dk1.f1', '64.dl1.i1', '64.dm1.e1', '64.dn1.b2', '64.do1.a2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1701, -1, 9856, -1, 1700, -1], 'generators': [169, 130, 4], 'label': '256.30836.32.hk1.cm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cm1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878576
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.e1', '16.hc1.e2', '16.ik1.b2', '16.jd1.n1', '16.je1.f2', '16.jf1.m1', '16.jg1.n1'], 'contains': ['64.di1.i1', '64.dj1.e1', '64.dk1.h1', '64.dl1.j1', '64.dm1.e2', '64.dn1.b1', '64.do1.c2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 491, -1, 9856, -1, 491, -1], 'generators': [33, 130, 4], 'label': '256.30836.32.hk1.cn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cn1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878577
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.f1', '16.hc1.e2', '16.ik1.a1', '16.jd1.m1', '16.je1.f1', '16.jf1.n1', '16.jg1.o1'], 'contains': ['64.di1.i1', '64.dj1.f1', '64.dk1.e1', '64.dl1.i1', '64.dm1.f2', '64.dn1.a1', '64.do1.e2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1840, -1, 9856, -1, 1838, -1], 'generators': [169, 170, 4], 'label': '256.30836.32.hk1.co1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.co1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.co1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878578
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.f1', '16.hc1.e1', '16.ik1.b1', '16.jd1.n1', '16.je1.f2', '16.jf1.n1', '16.jg1.p1'], 'contains': ['64.di1.i1', '64.dj1.f1', '64.dk1.g1', '64.dl1.j1', '64.dm1.f1', '64.dn1.a2', '64.do1.g2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 742, -1, 9856, -1, 741, -1], 'generators': [33, 170, 4], 'label': '256.30836.32.hk1.cp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cp1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878579
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.g1', '16.hc1.f1', '16.ik1.a1', '16.jd1.o1', '16.je1.f2', '16.jf1.m1', '16.jg1.m1'], 'contains': ['64.di1.i1', '64.dj1.g1', '64.dk1.f1', '64.dl1.k1', '64.dm1.e2', '64.dn1.f2', '64.do1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2327, -1, 9856, -1, 2325, -1], 'generators': [33, 130, 140], 'label': '256.30836.32.hk1.cq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cq1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878580
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.g1', '16.hc1.f2', '16.ik1.b1', '16.jd1.p1', '16.je1.f1', '16.jf1.m1', '16.jg1.n1'], 'contains': ['64.di1.i1', '64.dj1.g1', '64.dk1.h1', '64.dl1.l1', '64.dm1.e1', '64.dn1.f1', '64.do1.c1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1506, -1, 9856, -1, 1505, -1], 'generators': [169, 130, 140], 'label': '256.30836.32.hk1.cr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cr1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878581
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.h1', '16.hc1.f2', '16.ik1.a2', '16.jd1.o1', '16.je1.f2', '16.jf1.n1', '16.jg1.o1'], 'contains': ['64.di1.i1', '64.dj1.h1', '64.dk1.e1', '64.dl1.k1', '64.dm1.f1', '64.dn1.e1', '64.do1.e1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3188, -1, 9856, -1, 3185, -1], 'generators': [33, 170, 140], 'label': '256.30836.32.hk1.cs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cs1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878582
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.h1', '16.hc1.f1', '16.ik1.b2', '16.jd1.p1', '16.je1.f1', '16.jf1.n1', '16.jg1.p1'], 'contains': ['64.di1.i1', '64.dj1.h1', '64.dk1.g1', '64.dl1.l1', '64.dm1.f2', '64.dn1.e2', '64.do1.g1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1854, -1, 9856, -1, 1852, -1], 'generators': [169, 170, 140], 'label': '256.30836.32.hk1.ct1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ct1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ct1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878583
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.e1', '16.hc1.g2', '16.ik1.c2', '16.jd1.i1', '16.je1.c2', '16.jf1.o1', '16.jg1.m1'], 'contains': ['64.di1.j1', '64.dj1.e1', '64.dk1.f1', '64.dl1.m1', '64.dm1.g2', '64.dn1.d1', '64.do1.b2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1520, -1, 9856, -1, 1519, -1], 'generators': [161, 130, 4], 'label': '256.30836.32.hk1.cu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cu1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878691
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.s1.a1', '32.cx1.a1', '32.dp1.a1', '32.ej1.a1', '32.ej1.b1'], 'contains': ['128.b1.a1', '128.o1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3282, -1, 6210, -1, 3284, -1, 6204, -1], 'generators': [83, 32], 'label': '256.30836.64.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ct1.a1', 'old_label': '64.bb1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878692
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.u1.a1', '32.cy1.a1', '32.dq1.a1', '32.ee1.a1', '32.ee1.b1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4557, -1, 6503, -1, 4560, -1, 6497, -1], 'generators': [16], 'label': '256.30836.64.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.x1.a1', 'old_label': '64.bc1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878584
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dw1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.e1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.k1', '64.dk1.l1', '64.dk1.j1', '64.dk1.i1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.m1', '64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.dn1.g2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '2.w1.a1', '2.bc1.a1'], 'contains': ['8.bu1.a1', '8.by1.a1', '8.bz1.a1', '8.ek1.a1', '8.el1.a1', '8.fl1.a1', '8.fn1.a1'], 'core': '4.dw1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4367, 2607, 6276, 2017, 4369, 2606, 6271, 2022], 'generators': [66, 68, 80], 'label': '256.30836.4.dw1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dw1.a1', 'normal_contained_in': ['2.w1.a1', '2.j1.a1', '2.bc1.a1'], 'normal_contains': ['8.bu1.a1', '8.bz1.a1', '8.by1.a1', '8.el1.a1', '8.ek1.a1', '8.fl1.a1', '8.fn1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dw1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878585
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.e1', '16.hc1.g1', '16.ik1.d2', '16.jd1.j1', '16.je1.c1', '16.jf1.o1', '16.jg1.n1'], 'contains': ['64.di1.j1', '64.dj1.e1', '64.dk1.h1', '64.dl1.n1', '64.dm1.g1', '64.dn1.d2', '64.do1.d2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 520, -1, 9856, -1, 519, -1], 'generators': [41, 130, 4], 'label': '256.30836.32.hk1.cv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cv1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878586
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.f1', '16.hc1.g1', '16.ik1.c1', '16.jd1.i1', '16.je1.c2', '16.jf1.p1', '16.jg1.o1'], 'contains': ['64.di1.j1', '64.dj1.f1', '64.dk1.e1', '64.dl1.m1', '64.dm1.h1', '64.dn1.c2', '64.do1.f2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1646, -1, 9856, -1, 1644, -1], 'generators': [161, 170, 4], 'label': '256.30836.32.hk1.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cw1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878587
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.f1', '16.hc1.g2', '16.ik1.d1', '16.jd1.j1', '16.je1.c1', '16.jf1.p1', '16.jg1.p1'], 'contains': ['64.di1.j1', '64.dj1.f1', '64.dk1.g1', '64.dl1.n1', '64.dm1.h2', '64.dn1.c1', '64.do1.h2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 714, -1, 9856, -1, 714, -1], 'generators': [41, 170, 4], 'label': '256.30836.32.hk1.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cx1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878588
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.g1', '16.hc1.h2', '16.ik1.c1', '16.jd1.k1', '16.je1.c1', '16.jf1.o1', '16.jg1.m1'], 'contains': ['64.di1.j1', '64.dj1.g1', '64.dk1.f1', '64.dl1.o1', '64.dm1.g1', '64.dn1.h1', '64.do1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2410, -1, 9856, -1, 2408, -1], 'generators': [41, 130, 140], 'label': '256.30836.32.hk1.cy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cy1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cy1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878589
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.g1', '16.hc1.h1', '16.ik1.d1', '16.jd1.l1', '16.je1.c2', '16.jf1.o1', '16.jg1.n1'], 'contains': ['64.di1.j1', '64.dj1.g1', '64.dk1.h1', '64.dl1.p1', '64.dm1.g2', '64.dn1.h2', '64.do1.d1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1534, -1, 9856, -1, 1533, -1], 'generators': [161, 130, 140], 'label': '256.30836.32.hk1.cz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.cz1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.cz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878590
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.h1', '16.hc1.h1', '16.ik1.c2', '16.jd1.k1', '16.je1.c1', '16.jf1.p1', '16.jg1.o1'], 'contains': ['64.di1.j1', '64.dj1.h1', '64.dk1.e1', '64.dl1.o1', '64.dm1.h2', '64.dn1.g2', '64.do1.f1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3077, -1, 9856, -1, 3074, -1], 'generators': [41, 170, 140], 'label': '256.30836.32.hk1.da1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.da1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.da1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878591
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.h1', '16.hc1.h2', '16.ik1.d2', '16.jd1.l1', '16.je1.c2', '16.jf1.p1', '16.jg1.p1'], 'contains': ['64.di1.j1', '64.dj1.h1', '64.dk1.g1', '64.dl1.p1', '64.dm1.h1', '64.dn1.g1', '64.do1.h1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1812, -1, 9856, -1, 1811, -1], 'generators': [161, 170, 140], 'label': '256.30836.32.hk1.db1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.db1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.db1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878592
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.i1', '16.hc1.c1', '16.ik1.g2', '16.jd1.m1', '16.je1.g2', '16.jf1.k1', '16.jg1.a1'], 'contains': ['64.di1.k1', '64.dj1.i1', '64.dk1.i1', '64.dl1.e1', '64.dm1.c1', '64.dn1.a1', '64.do1.a2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2702, -1, 9856, -1, 2699, -1], 'generators': [9, 10, 4], 'label': '256.30836.32.hk1.dc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dc1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878593
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.i1', '16.hc1.c2', '16.ik1.h2', '16.jd1.n1', '16.je1.g1', '16.jf1.k1', '16.jg1.b1'], 'contains': ['64.di1.k1', '64.dj1.i1', '64.dk1.k1', '64.dl1.f1', '64.dm1.c2', '64.dn1.a2', '64.do1.c2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1103, -1, 9856, -1, 1102, -1], 'generators': [129, 10, 4], 'label': '256.30836.32.hk1.dd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dd1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878594
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.j1', '16.hc1.c2', '16.ik1.g1', '16.jd1.m1', '16.je1.g2', '16.jf1.l1', '16.jg1.c1'], 'contains': ['64.di1.k1', '64.dj1.j1', '64.dk1.j1', '64.dl1.e1', '64.dm1.d2', '64.dn1.b2', '64.do1.e2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2076, -1, 9856, -1, 2075, -1], 'generators': [9, 34, 4], 'label': '256.30836.32.hk1.de1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.de1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.de1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878693
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.y1.a1', '32.dc1.a1', '32.ds1.a1', '32.eh1.a1', '32.eh1.b1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4773, -1, 6296, -1, 4782, -1, 6296, -1], 'generators': [68], 'label': '256.30836.64.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ci1.a1', 'old_label': '64.bd1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878694
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.be1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ba1.a1', '32.dd1.a1', '32.dt1.a1', '32.ee1.a1', '32.ee1.b1', '32.el1.a1', '32.el1.a2'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3307, -1, 6442, -1, 3309, -1, 6436, -1], 'generators': [18], 'label': '256.30836.64.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '64.be1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.be1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878595
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dx1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.c1', '64.di1.b1', '64.di1.l1', '64.di1.k1', '64.di1.f1', '64.di1.m1', '64.di1.h1', '64.di1.i1', '64.di1.j1', '64.di1.e1', '64.di1.p1', '64.di1.g1', '64.di1.n1', '64.di1.o1', '64.dk1.a1', '64.dk1.d1', '64.dk1.c1', '64.dk1.b1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1', '64.dk1.i1', '64.dk1.e1', '64.dk1.h1', '64.dk1.g1', '64.dk1.f1', '64.dk1.n1', '64.dk1.o1', '64.dk1.p1', '64.dk1.m1', '64.dn1.a1', '64.dn1.b2', '64.dn1.d1', '64.dn1.c2', '64.dn1.c1', '64.dn1.d2', '64.dn1.b1', '64.dn1.a2', '64.dn1.f1', '64.dn1.e2', '64.dn1.g1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.e1', '64.dn1.f2', '64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.o1', '64.dl1.d1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.c1', '64.dl1.p1'], 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '2.w1.a1', '2.be1.a1'], 'contains': ['8.bu1.a1', '8.cb1.a1', '8.cc1.a1', '8.em1.a1', '8.en1.a1', '8.fo1.a1', '8.fp1.a1'], 'core': '4.dx1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1805, 3799, 7143, 7016, 1806, 3798, 7136, 7031], 'generators': [81, 66, 68], 'label': '256.30836.4.dx1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dx1.a1', 'normal_contained_in': ['2.w1.a1', '2.h1.a1', '2.be1.a1'], 'normal_contains': ['8.bu1.a1', '8.cc1.a1', '8.cb1.a1', '8.en1.a1', '8.em1.a1', '8.fo1.a1', '8.fp1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dx1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dx1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878596
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.j1', '16.hc1.c1', '16.ik1.h1', '16.jd1.n1', '16.je1.g1', '16.jf1.l1', '16.jg1.d1'], 'contains': ['64.di1.k1', '64.dj1.j1', '64.dk1.l1', '64.dl1.f1', '64.dm1.d1', '64.dn1.b1', '64.do1.g2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 562, -1, 9856, -1, 561, -1], 'generators': [129, 34, 4], 'label': '256.30836.32.hk1.df1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.df1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.df1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878597
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.k1', '16.hc1.d1', '16.ik1.g1', '16.jd1.o1', '16.je1.g1', '16.jf1.k1', '16.jg1.a1'], 'contains': ['64.di1.k1', '64.dj1.k1', '64.dk1.i1', '64.dl1.g1', '64.dm1.c2', '64.dn1.e1', '64.do1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3577, -1, 9856, -1, 3574, -1], 'generators': [129, 10, 140], 'label': '256.30836.32.hk1.dg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dg1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878598
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.k1', '16.hc1.d2', '16.ik1.h1', '16.jd1.p1', '16.je1.g2', '16.jf1.k1', '16.jg1.b1'], 'contains': ['64.di1.k1', '64.dj1.k1', '64.dk1.k1', '64.dl1.h1', '64.dm1.c1', '64.dn1.e2', '64.do1.c1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3008, -1, 9856, -1, 3005, -1], 'generators': [9, 10, 140], 'label': '256.30836.32.hk1.dh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dh1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878599
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.l1', '16.hc1.d2', '16.ik1.g2', '16.jd1.o1', '16.je1.g1', '16.jf1.l1', '16.jg1.c1'], 'contains': ['64.di1.k1', '64.dj1.l1', '64.dk1.j1', '64.dl1.g1', '64.dm1.d1', '64.dn1.f2', '64.do1.e1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2854, -1, 9856, -1, 2852, -1], 'generators': [129, 34, 140], 'label': '256.30836.32.hk1.di1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.di1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.di1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878600
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.l1', '16.hc1.d1', '16.ik1.h2', '16.jd1.p1', '16.je1.g2', '16.jf1.l1', '16.jg1.d1'], 'contains': ['64.di1.k1', '64.dj1.l1', '64.dk1.l1', '64.dl1.h1', '64.dm1.d2', '64.dn1.f1', '64.do1.g1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2146, -1, 9856, -1, 2144, -1], 'generators': [9, 34, 140], 'label': '256.30836.32.hk1.dj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dj1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878601
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.m1', '16.hc1.a1', '16.ik1.e2', '16.jd1.m1', '16.je1.g1', '16.jf1.m1', '16.jg1.e1'], 'contains': ['64.di1.l1', '64.dj1.i1', '64.dk1.j1', '64.dl1.i1', '64.dm1.e1', '64.dn1.b1', '64.do1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 951, -1, 9856, -1, 950, -1], 'generators': [169, 10, 4], 'label': '256.30836.32.hk1.dk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dk1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878602
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.m1', '16.hc1.a2', '16.ik1.f2', '16.jd1.n1', '16.je1.g2', '16.jf1.m1', '16.jg1.f1'], 'contains': ['64.di1.l1', '64.dj1.i1', '64.dk1.l1', '64.dl1.j1', '64.dm1.e2', '64.dn1.b2', '64.do1.c1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 187, -1, 9856, -1, 186, -1], 'generators': [33, 10, 4], 'label': '256.30836.32.hk1.dl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dl1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878603
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.n1', '16.hc1.a2', '16.ik1.e1', '16.jd1.m1', '16.je1.g1', '16.jf1.n1', '16.jg1.g1'], 'contains': ['64.di1.l1', '64.dj1.j1', '64.dk1.i1', '64.dl1.i1', '64.dm1.f2', '64.dn1.a2', '64.do1.e1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1465, -1, 9856, -1, 1464, -1], 'generators': [169, 34, 4], 'label': '256.30836.32.hk1.dm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dm1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878604
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.n1', '16.hc1.a1', '16.ik1.f1', '16.jd1.n1', '16.je1.g2', '16.jf1.n1', '16.jg1.h1'], 'contains': ['64.di1.l1', '64.dj1.j1', '64.dk1.k1', '64.dl1.j1', '64.dm1.f1', '64.dn1.a1', '64.do1.g1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 408, -1, 9856, -1, 408, -1], 'generators': [33, 34, 4], 'label': '256.30836.32.hk1.dn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dn1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878605
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.o1', '16.hc1.b1', '16.ik1.e1', '16.jd1.o1', '16.je1.g2', '16.jf1.m1', '16.jg1.e1'], 'contains': ['64.di1.l1', '64.dj1.k1', '64.dk1.j1', '64.dl1.k1', '64.dm1.e2', '64.dn1.f1', '64.do1.a2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2159, -1, 9856, -1, 2158, -1], 'generators': [33, 10, 140], 'label': '256.30836.32.hk1.do1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.do1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.do1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878718
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.a1', '32.n1.a1', '32.en1.a1', '32.gb1.a1', '32.gb1.c1', '32.gf1.a1', '32.gf1.b1', '32.gf1.c1', '32.gf1.d1', '32.gg1.a1', '32.gg1.a2'], 'contains': ['128.d1.a1', '128.i1.a1', '128.i1.d1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8893, -1, 4217, -1, 8898, -1, 4213, -1], 'generators': [1, 160], 'label': '256.30836.64.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.bv1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879567
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.id1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dt1.a1', '8.he1.a1', '8.he1.b1'], 'contains': ['32.es1.a1', '32.ey1.a1', '32.fd1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3808, -1, 8391, -1, 3810, -1, 8384, -1], 'generators': [83, 20], 'label': '256.30836.16.id1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dt1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ef1.a1', 'old_label': '16.id1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.id1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878606
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dy1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.b1', '64.dl1.m1', '64.dl1.n1', '64.dl1.f1', '64.dl1.e1', '64.dl1.j1', '64.dl1.i1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.di1.i1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.l1', '64.dn1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.b2', '64.dn1.c1', '64.dn1.c2', '64.dn1.d1', '64.dn1.d2', '64.dn1.e1', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2', '64.dk1.a1', '64.dk1.c1', '64.dk1.b1', '64.dk1.d1', '64.dk1.o1', '64.dk1.m1', '64.dk1.p1', '64.dk1.n1', '64.dk1.g1', '64.dk1.e1', '64.dk1.h1', '64.dk1.f1', '64.dk1.i1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '2.v1.a1', '2.bc1.a1'], 'contains': ['8.bv1.a1', '8.bw1.a1', '8.by1.a1', '8.eo1.a1', '8.eq1.a1', '8.ey1.a1', '8.fi1.a1'], 'core': '4.dy1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4457, 1693, 8543, 5429, 4459, 1693, 8535, 5441], 'generators': [65, 6, 80], 'label': '256.30836.4.dy1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dy1.a1', 'normal_contained_in': ['2.v1.a1', '2.k1.a1', '2.bc1.a1'], 'normal_contains': ['8.bw1.a1', '8.bv1.a1', '8.by1.a1', '8.eq1.a1', '8.fi1.a1', '8.eo1.a1', '8.ey1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dy1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dy1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878607
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.o1', '16.hc1.b2', '16.ik1.f1', '16.jd1.p1', '16.je1.g1', '16.jf1.m1', '16.jg1.f1'], 'contains': ['64.di1.l1', '64.dj1.k1', '64.dk1.l1', '64.dl1.l1', '64.dm1.e1', '64.dn1.f2', '64.do1.c2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 853, -1, 9856, -1, 853, -1], 'generators': [169, 10, 140], 'label': '256.30836.32.hk1.dp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dp1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878608
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.p1', '16.hc1.b2', '16.ik1.e2', '16.jd1.o1', '16.je1.g2', '16.jf1.n1', '16.jg1.g1'], 'contains': ['64.di1.l1', '64.dj1.l1', '64.dk1.i1', '64.dl1.k1', '64.dm1.f1', '64.dn1.e2', '64.do1.e2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3049, -1, 9856, -1, 3047, -1], 'generators': [33, 34, 140], 'label': '256.30836.32.hk1.dq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dq1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878609
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.p1', '16.hc1.b1', '16.ik1.f2', '16.jd1.p1', '16.je1.g1', '16.jf1.n1', '16.jg1.h1'], 'contains': ['64.di1.l1', '64.dj1.l1', '64.dk1.k1', '64.dl1.l1', '64.dm1.f2', '64.dn1.e1', '64.do1.g2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1340, -1, 9856, -1, 1339, -1], 'generators': [169, 34, 140], 'label': '256.30836.32.hk1.dr1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dr1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dr1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878610
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.m1', '16.hc1.c2', '16.ik1.g2', '16.jd1.i1', '16.je1.d2', '16.jf1.o1', '16.jg1.e1'], 'contains': ['64.di1.m1', '64.dj1.i1', '64.dk1.j1', '64.dl1.m1', '64.dm1.g2', '64.dn1.d2', '64.do1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1020, -1, 9856, -1, 1019, -1], 'generators': [161, 10, 4], 'label': '256.30836.32.hk1.ds1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ds1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ds1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878611
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.m1', '16.hc1.c1', '16.ik1.h2', '16.jd1.j1', '16.je1.d1', '16.jf1.o1', '16.jg1.f1'], 'contains': ['64.di1.m1', '64.dj1.i1', '64.dk1.l1', '64.dl1.n1', '64.dm1.g1', '64.dn1.d1', '64.do1.d1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 144, -1, 9856, -1, 144, -1], 'generators': [41, 10, 4], 'label': '256.30836.32.hk1.dt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dt1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dt1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878612
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.n1', '16.hc1.c1', '16.ik1.g1', '16.jd1.i1', '16.je1.d2', '16.jf1.p1', '16.jg1.g1'], 'contains': ['64.di1.m1', '64.dj1.j1', '64.dk1.i1', '64.dl1.m1', '64.dm1.h1', '64.dn1.c1', '64.do1.f1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1257, -1, 9856, -1, 1255, -1], 'generators': [161, 34, 4], 'label': '256.30836.32.hk1.du1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.du1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.du1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878613
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.n1', '16.hc1.c2', '16.ik1.h1', '16.jd1.j1', '16.je1.d1', '16.jf1.p1', '16.jg1.h1'], 'contains': ['64.di1.m1', '64.dj1.j1', '64.dk1.k1', '64.dl1.n1', '64.dm1.h2', '64.dn1.c2', '64.do1.h1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 242, -1, 9856, -1, 241, -1], 'generators': [41, 34, 4], 'label': '256.30836.32.hk1.dv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dv1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dv1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878614
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.o1', '16.hc1.d2', '16.ik1.g1', '16.jd1.k1', '16.je1.d1', '16.jf1.o1', '16.jg1.e1'], 'contains': ['64.di1.m1', '64.dj1.k1', '64.dk1.j1', '64.dl1.o1', '64.dm1.g1', '64.dn1.h2', '64.do1.b2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2368, -1, 9856, -1, 2366, -1], 'generators': [41, 10, 140], 'label': '256.30836.32.hk1.dw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dw1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dw1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878615
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.o1', '16.hc1.d1', '16.ik1.h1', '16.jd1.l1', '16.je1.d2', '16.jf1.o1', '16.jg1.f1'], 'contains': ['64.di1.m1', '64.dj1.k1', '64.dk1.l1', '64.dl1.p1', '64.dm1.g2', '64.dn1.h1', '64.do1.d2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1034, -1, 9856, -1, 1033, -1], 'generators': [161, 10, 140], 'label': '256.30836.32.hk1.dx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dx1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dx1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878616
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.p1', '16.hc1.d1', '16.ik1.g2', '16.jd1.k1', '16.je1.d1', '16.jf1.p1', '16.jg1.g1'], 'contains': ['64.di1.m1', '64.dj1.l1', '64.dk1.i1', '64.dl1.o1', '64.dm1.h2', '64.dn1.g1', '64.do1.f2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2980, -1, 9856, -1, 2977, -1], 'generators': [41, 34, 140], 'label': '256.30836.32.hk1.dy1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dy1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dy1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878719
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.b1', '32.n1.a1', '32.en1.a1', '32.gb1.b1', '32.gb1.d1', '32.gf1.e1', '32.gf1.f1', '32.gf1.g1', '32.gf1.h1', '32.gg1.b1', '32.gg1.b2'], 'contains': ['128.d1.a1', '128.i1.b1', '128.i1.c1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8893, -1, 4325, -1, 8898, -1, 4321, -1], 'generators': [129, 160], 'label': '256.30836.64.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.bv1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bv1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879568
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ie1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.el1.a1', '8.he1.a1', '8.he1.b1'], 'contains': ['32.et1.a1', '32.ey1.a1', '32.fb1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3922, -1, 8408, -1, 3924, -1, 8401, -1], 'generators': [66, 20], 'label': '256.30836.16.ie1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.el1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ef1.a1', 'old_label': '16.ie1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ie1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 30878617
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.dz1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.k1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.dl1.a1', '64.dl1.b1', '64.dl1.m1', '64.dl1.n1', '64.dl1.f1', '64.dl1.e1', '64.dl1.j1', '64.dl1.i1', '64.dl1.c1', '64.dl1.d1', '64.dl1.o1', '64.dl1.p1', '64.dl1.h1', '64.dl1.g1', '64.dl1.l1', '64.dl1.k1', '64.dn1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.b2', '64.dn1.c1', '64.dn1.c2', '64.dn1.d1', '64.dn1.d2', '64.dn1.e2', '64.dn1.e1', '64.dn1.f2', '64.dn1.f1', '64.dn1.g2', '64.dn1.g1', '64.dn1.h2', '64.dn1.h1', '64.dk1.a1', '64.dk1.c1', '64.dk1.b1', '64.dk1.d1', '64.dk1.m1', '64.dk1.o1', '64.dk1.n1', '64.dk1.p1', '64.dk1.e1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.i1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '2.t1.a1', '2.be1.a1'], 'contains': ['8.bv1.a1', '8.ca1.a1', '8.cc1.a1', '8.es1.a1', '8.et1.a1', '8.fv1.a1', '8.fw1.a1'], 'core': '4.dz1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4924, 3857, 8096, 8548, 4926, 3855, 8089, 8567], 'generators': [65, 82, 84], 'label': '256.30836.4.dz1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.dz1.a1', 'normal_contained_in': ['2.t1.a1', '2.k1.a1', '2.be1.a1'], 'normal_contains': ['8.bv1.a1', '8.cc1.a1', '8.ca1.a1', '8.es1.a1', '8.et1.a1', '8.fw1.a1', '8.fv1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.dz1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.dz1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878618
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.p1', '16.hc1.d2', '16.ik1.h2', '16.jd1.l1', '16.je1.d2', '16.jf1.p1', '16.jg1.h1'], 'contains': ['64.di1.m1', '64.dj1.l1', '64.dk1.k1', '64.dl1.p1', '64.dm1.h1', '64.dn1.g2', '64.do1.h2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1173, -1, 9856, -1, 1172, -1], 'generators': [161, 34, 140], 'label': '256.30836.32.hk1.dz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.dz1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.dz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878619
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.i1', '16.hc1.g2', '16.ik1.g1', '16.jd1.e1', '16.je1.h2', '16.jf1.c1', '16.jg1.i1'], 'contains': ['64.di1.n1', '64.dj1.m1', '64.dk1.m1', '64.dl1.e1', '64.dm1.c2', '64.dn1.c1', '64.do1.b2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1270, -1, 9856, -1, 1269, -1], 'generators': [9, 138, 4], 'label': '256.30836.32.hk1.ea1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ea1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ea1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878620
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.i1', '16.hc1.g1', '16.ik1.h1', '16.jd1.f1', '16.je1.h1', '16.jf1.c1', '16.jg1.j1'], 'contains': ['64.di1.n1', '64.dj1.m1', '64.dk1.o1', '64.dl1.f1', '64.dm1.c1', '64.dn1.c2', '64.do1.d2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 450, -1, 9856, -1, 450, -1], 'generators': [129, 138, 4], 'label': '256.30836.32.hk1.eb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.eb1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.eb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878621
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.j1', '16.hc1.g1', '16.ik1.g2', '16.jd1.e1', '16.je1.h2', '16.jf1.d1', '16.jg1.k1'], 'contains': ['64.di1.n1', '64.dj1.n1', '64.dk1.n1', '64.dl1.e1', '64.dm1.d1', '64.dn1.d2', '64.do1.f2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 937, -1, 9856, -1, 936, -1], 'generators': [9, 162, 4], 'label': '256.30836.32.hk1.ec1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ec1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ec1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878622
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.j1', '16.hc1.g2', '16.ik1.h2', '16.jd1.f1', '16.je1.h1', '16.jf1.d1', '16.jg1.l1'], 'contains': ['64.di1.n1', '64.dj1.n1', '64.dk1.p1', '64.dl1.f1', '64.dm1.d2', '64.dn1.d1', '64.do1.h2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 214, -1, 9856, -1, 214, -1], 'generators': [129, 162, 4], 'label': '256.30836.32.hk1.ed1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ed1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ed1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878623
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.k1', '16.hc1.h2', '16.ik1.g2', '16.jd1.g1', '16.je1.h1', '16.jf1.c1', '16.jg1.i1'], 'contains': ['64.di1.n1', '64.dj1.o1', '64.dk1.m1', '64.dl1.g1', '64.dm1.c1', '64.dn1.g1', '64.do1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2994, -1, 9856, -1, 2991, -1], 'generators': [129, 138, 140], 'label': '256.30836.32.hk1.ee1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ee1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ee1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878624
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.k1', '16.hc1.h1', '16.ik1.h2', '16.jd1.h1', '16.je1.h2', '16.jf1.c1', '16.jg1.j1'], 'contains': ['64.di1.n1', '64.dj1.o1', '64.dk1.o1', '64.dl1.h1', '64.dm1.c2', '64.dn1.g2', '64.do1.d1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1451, -1, 9856, -1, 1450, -1], 'generators': [9, 138, 140], 'label': '256.30836.32.hk1.ef1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ef1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ef1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878625
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.l1', '16.hc1.h1', '16.ik1.g1', '16.jd1.g1', '16.je1.h1', '16.jf1.d1', '16.jg1.k1'], 'contains': ['64.di1.n1', '64.dj1.p1', '64.dk1.n1', '64.dl1.g1', '64.dm1.d2', '64.dn1.h2', '64.do1.f1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2244, -1, 9856, -1, 2241, -1], 'generators': [129, 162, 140], 'label': '256.30836.32.hk1.eg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.eg1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.eg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878626
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.l1', '16.hc1.h2', '16.ik1.h1', '16.jd1.h1', '16.je1.h2', '16.jf1.d1', '16.jg1.l1'], 'contains': ['64.di1.n1', '64.dj1.p1', '64.dk1.p1', '64.dl1.h1', '64.dm1.d1', '64.dn1.h1', '64.do1.h1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 839, -1, 9856, -1, 839, -1], 'generators': [9, 162, 140], 'label': '256.30836.32.hk1.eh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.eh1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.eh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878627
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.m1', '16.hc1.e2', '16.ik1.e1', '16.jd1.e1', '16.je1.h1', '16.jf1.e1', '16.jg1.m1'], 'contains': ['64.di1.o1', '64.dj1.m1', '64.dk1.n1', '64.dl1.i1', '64.dm1.e2', '64.dn1.d1', '64.do1.b1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 339, -1, 9856, -1, 339, -1], 'generators': [169, 138, 4], 'label': '256.30836.32.hk1.ei1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ei1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ei1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878720
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.eo1.a1', '32.fp1.a1', '32.gc1.a1', '32.gc1.c1', '32.gf1.a1', '32.gf1.b1', '32.gf1.e1', '32.gf1.f1', '32.gh1.a1', '32.gh1.b1'], 'contains': ['128.d1.a1', '128.j1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9001, -1, 3563, -1, 9005, -1, 3560, -1], 'generators': [4, 160], 'label': '256.30836.64.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.bw1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879569
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.if1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ey1.a1', '8.he1.a1', '8.he1.b1'], 'contains': ['32.eu1.a1', '32.fb1.a1', '32.fd1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3585, -1, 8443, -1, 3587, -1, 8436, -1], 'generators': [17, 86], 'label': '256.30836.16.if1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ey1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ef1.a1', 'old_label': '16.if1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.if1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 30878628
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ea1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.dn1.g2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.e2', '64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.e1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.k1', '64.dk1.l1', '64.dk1.j1', '64.dk1.i1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.m1'], 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '2.u1.a1', '2.bd1.a1'], 'contains': ['8.bw1.a1', '8.bx1.a1', '8.ca1.a1', '8.eu1.a1', '8.ew1.a1', '8.fd1.a1', '8.fj1.a1'], 'core': '4.ea1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2290, 7724, 7401, 6353, 2290, 7721, 7395, 6366], 'generators': [17, 82, 84], 'label': '256.30836.4.ea1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ea1.a1', 'normal_contained_in': ['2.u1.a1', '2.k1.a1', '2.bd1.a1'], 'normal_contains': ['8.bx1.a1', '8.bw1.a1', '8.ca1.a1', '8.fd1.a1', '8.eu1.a1', '8.fj1.a1', '8.ew1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ea1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ea1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878629
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.m1', '16.hc1.e1', '16.ik1.f1', '16.jd1.f1', '16.je1.h2', '16.jf1.e1', '16.jg1.n1'], 'contains': ['64.di1.o1', '64.dj1.m1', '64.dk1.p1', '64.dl1.j1', '64.dm1.e1', '64.dn1.d2', '64.do1.d1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 19, -1, 9856, -1, 19, -1], 'generators': [33, 138, 4], 'label': '256.30836.32.hk1.ej1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ej1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ej1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878630
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.n1', '16.hc1.e1', '16.ik1.e2', '16.jd1.e1', '16.je1.h1', '16.jf1.f1', '16.jg1.o1'], 'contains': ['64.di1.o1', '64.dj1.n1', '64.dk1.m1', '64.dl1.i1', '64.dm1.f1', '64.dn1.c2', '64.do1.f1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 367, -1, 9856, -1, 366, -1], 'generators': [169, 162, 4], 'label': '256.30836.32.hk1.ek1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ek1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ek1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878631
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.n1', '16.hc1.e2', '16.ik1.f2', '16.jd1.f1', '16.je1.h2', '16.jf1.f1', '16.jg1.p1'], 'contains': ['64.di1.o1', '64.dj1.n1', '64.dk1.o1', '64.dl1.j1', '64.dm1.f2', '64.dn1.c1', '64.do1.h1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 75, -1, 9856, -1, 75, -1], 'generators': [33, 162, 4], 'label': '256.30836.32.hk1.el1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.el1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.el1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878632
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.o1', '16.hc1.f2', '16.ik1.e2', '16.jd1.g1', '16.je1.h2', '16.jf1.e1', '16.jg1.m1'], 'contains': ['64.di1.o1', '64.dj1.o1', '64.dk1.n1', '64.dl1.k1', '64.dm1.e1', '64.dn1.h1', '64.do1.b2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1048, -1, 9856, -1, 1047, -1], 'generators': [33, 138, 140], 'label': '256.30836.32.hk1.em1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.em1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.em1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878633
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.o1', '16.hc1.f1', '16.ik1.f2', '16.jd1.h1', '16.je1.h1', '16.jf1.e1', '16.jg1.n1'], 'contains': ['64.di1.o1', '64.dj1.o1', '64.dk1.p1', '64.dl1.l1', '64.dm1.e2', '64.dn1.h2', '64.do1.d2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 311, -1, 9856, -1, 311, -1], 'generators': [169, 138, 140], 'label': '256.30836.32.hk1.en1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.en1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.en1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878634
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.p1', '16.hc1.f1', '16.ik1.e1', '16.jd1.g1', '16.je1.h2', '16.jf1.f1', '16.jg1.o1'], 'contains': ['64.di1.o1', '64.dj1.p1', '64.dk1.m1', '64.dl1.k1', '64.dm1.f2', '64.dn1.g2', '64.do1.f2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1284, -1, 9856, -1, 1283, -1], 'generators': [33, 162, 140], 'label': '256.30836.32.hk1.eo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.eo1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.eo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878635
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.p1', '16.hc1.f2', '16.ik1.f1', '16.jd1.h1', '16.je1.h1', '16.jf1.f1', '16.jg1.p1'], 'contains': ['64.di1.o1', '64.dj1.p1', '64.dk1.o1', '64.dl1.l1', '64.dm1.f1', '64.dn1.g1', '64.do1.h2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 436, -1, 9856, -1, 436, -1], 'generators': [169, 162, 140], 'label': '256.30836.32.hk1.ep1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ep1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ep1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878636
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.m1', '16.hc1.g1', '16.ik1.g1', '16.jd1.a1', '16.je1.e2', '16.jf1.g1', '16.jg1.m1'], 'contains': ['64.di1.p1', '64.dj1.m1', '64.dk1.n1', '64.dl1.m1', '64.dm1.g1', '64.dn1.b2', '64.do1.a1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2271, -1, 9856, -1, 2269, -1], 'generators': [161, 138, 4], 'label': '256.30836.32.hk1.eq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.eq1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.eq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878637
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.m1', '16.hc1.g2', '16.ik1.h1', '16.jd1.b1', '16.je1.e1', '16.jf1.g1', '16.jg1.n1'], 'contains': ['64.di1.p1', '64.dj1.m1', '64.dk1.p1', '64.dl1.n1', '64.dm1.g2', '64.dn1.b1', '64.do1.c1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 728, -1, 9856, -1, 728, -1], 'generators': [41, 138, 4], 'label': '256.30836.32.hk1.er1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.er1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.er1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878638
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.n1', '16.hc1.g2', '16.ik1.g2', '16.jd1.a1', '16.je1.e2', '16.jf1.h1', '16.jg1.o1'], 'contains': ['64.di1.p1', '64.dj1.n1', '64.dk1.m1', '64.dl1.m1', '64.dm1.h2', '64.dn1.a1', '64.do1.e1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2660, -1, 9856, -1, 2658, -1], 'generators': [161, 162, 4], 'label': '256.30836.32.hk1.es1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.es1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.es1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878721
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '32.eo1.a1', '32.fp1.a1', '32.gc1.b1', '32.gc1.d1', '32.gf1.c1', '32.gf1.d1', '32.gf1.g1', '32.gf1.h1', '32.gh1.c1', '32.gh1.d1'], 'contains': ['128.d1.a1', '128.j1.b1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9001, -1, 4394, -1, 9005, -1, 4390, -1], 'generators': [140, 160], 'label': '256.30836.64.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.bw1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879617
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.hi1.a1', '8.hi1.c1'], 'contains': ['32.k1.a1', '32.fx1.a1', '32.ga1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8402, -1, 4633, -1, 8406, -1, 4629, -1], 'generators': [1, 20], 'label': '256.30836.16.iw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.iw1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878639
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.eb1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.b1', '64.dl1.j1', '64.dl1.i1', '64.dl1.f1', '64.dl1.e1', '64.dl1.m1', '64.dl1.n1', '64.dl1.c1', '64.dl1.d1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dl1.g1', '64.dl1.o1', '64.dl1.p1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.m1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.j1', '64.dk1.l1', '64.dk1.k1', '64.dk1.i1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.e1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '2.w1.a1', '2.bb1.a1'], 'contains': ['8.bx1.a1', '8.by1.a1', '8.cc1.a1', '8.fe1.a1', '8.fh1.a1', '8.fm1.a1', '8.fy1.a1'], 'core': '4.eb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2554, 2968, 6924, 5302, 2555, 2966, 6918, 5313], 'generators': [69, 6, 80], 'label': '256.30836.4.eb1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.eb1.a1', 'normal_contained_in': ['2.w1.a1', '2.k1.a1', '2.bb1.a1'], 'normal_contains': ['8.bx1.a1', '8.cc1.a1', '8.by1.a1', '8.fh1.a1', '8.fe1.a1', '8.fm1.a1', '8.fy1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.eb1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.eb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878640
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.n1', '16.hc1.g1', '16.ik1.h2', '16.jd1.b1', '16.je1.e1', '16.jf1.h1', '16.jg1.p1'], 'contains': ['64.di1.p1', '64.dj1.n1', '64.dk1.o1', '64.dl1.n1', '64.dm1.h1', '64.dn1.a2', '64.do1.g1'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 1089, -1, 9856, -1, 1089, -1], 'generators': [41, 162, 4], 'label': '256.30836.32.hk1.et1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.et1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.et1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878641
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.o1', '16.hc1.h1', '16.ik1.g2', '16.jd1.c1', '16.je1.e1', '16.jf1.g1', '16.jg1.m1'], 'contains': ['64.di1.p1', '64.dj1.o1', '64.dk1.n1', '64.dl1.o1', '64.dm1.g2', '64.dn1.f2', '64.do1.a2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2841, -1, 9856, -1, 2838, -1], 'generators': [41, 138, 140], 'label': '256.30836.32.hk1.eu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.eu1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.eu1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878642
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.o1', '16.hc1.h2', '16.ik1.h2', '16.jd1.d1', '16.je1.e2', '16.jf1.g1', '16.jg1.n1'], 'contains': ['64.di1.p1', '64.dj1.o1', '64.dk1.p1', '64.dl1.p1', '64.dm1.g1', '64.dn1.f1', '64.do1.c2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2229, -1, 9856, -1, 2227, -1], 'generators': [161, 138, 140], 'label': '256.30836.32.hk1.ev1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ev1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ev1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878643
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.p1', '16.hc1.h2', '16.ik1.g1', '16.jd1.c1', '16.je1.e1', '16.jf1.h1', '16.jg1.o1'], 'contains': ['64.di1.p1', '64.dj1.p1', '64.dk1.m1', '64.dl1.o1', '64.dm1.h1', '64.dn1.e1', '64.do1.e2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 3480, -1, 9856, -1, 3477, -1], 'generators': [41, 162, 140], 'label': '256.30836.32.hk1.ew1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ew1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ew1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878644
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '32.hk1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.en1.p1', '16.hc1.h1', '16.ik1.h1', '16.jd1.d1', '16.je1.e2', '16.jf1.h1', '16.jg1.p1'], 'contains': ['64.di1.p1', '64.dj1.p1', '64.dk1.o1', '64.dl1.p1', '64.dm1.h2', '64.dn1.e2', '64.do1.g2'], 'core': '256.a1.a1', 'coset_action_label': '32T3549', 'count': 4, 'diagramx': [9851, -1, 2562, -1, 9856, -1, 2561, -1], 'generators': [161, 162, 140], 'label': '256.30836.32.hk1.ex1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.hk1.ex1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.hk1.ex1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878645
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '64.a1', 'aut_quo_index': 1152, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '32.m1.a1', '32.n1.a1', '32.o1.a1', '32.p1.a1', '32.q1.a1', '32.r1.a1', '32.s1.a1', '32.t1.a1', '32.u1.a1', '32.v1.a1', '32.w1.a1', '32.x1.a1', '32.y1.a1', '32.z1.a1', '32.ba1.a1', '32.bb1.a1', '32.bc1.a1', '32.bd1.a1'], 'contains': ['128.a1.a1', '128.b1.a1', '128.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6676, 4647, 5692, 5971, 6679, 4628, 5686, 6037], 'generators': [32, 128], 'label': '256.30836.64.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.b1', '32.b1.a1'], 'normal_contains': ['128.d1.a1', '128.b1.a1', '128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.264', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878646
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '64.b1', 'aut_quo_index': 1152, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.c1.a1', '32.c1.b1', '32.be1.a1', '32.bf1.a1', '32.bg1.a1', '32.bh1.a1', '32.bi1.a1', '32.bj1.a1', '32.bk1.a1', '32.bl1.a1', '32.bm1.a1', '32.bn1.a1', '32.bo1.a1', '32.bp1.a1', '32.bq1.a1', '32.br1.a1', '32.bs1.a1', '32.bt1.a1', '32.bu1.a1', '32.bv1.a1'], 'contains': ['128.a1.a1', '128.c1.a1', '128.e1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5420, 4779, 8616, 6160, 5413, 4759, 8609, 6174], 'generators': [168, 128], 'label': '256.30836.64.b1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1', '32.c1.a1', '32.c1.b1'], 'normal_contains': ['128.e1.a1', '128.c1.a1', '128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '64.264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.264', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878647
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '64.c1', 'aut_quo_index': 2304, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.d1.a1', '32.d1.b1', '32.e1.a1', '32.e1.b1', '32.f1.a1', '32.f1.b1', '32.bw1.a1', '32.bx1.a1', '32.by1.a1', '32.bz1.a1', '32.ca1.a1', '32.cb1.a1', '32.cc1.a1', '32.cd1.a1', '32.ce1.a1', '32.cf1.a1', '32.cg1.a1', '32.ch1.a1'], 'contains': ['128.a1.a1', '128.f1.a1', '128.g1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7909, 4747, 5761, 7162, 7913, 4727, 5756, 7177], 'generators': [136, 128], 'label': '256.30836.64.c1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.a1.a1', '32.d1.a1', '32.d1.b1', '32.e1.a1', '32.e1.b1', '32.f1.b1', '32.f1.a1'], 'normal_contains': ['128.f1.a1', '128.g1.a1', '128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': '64.263', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.263', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878648
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '64.d1', 'aut_quo_index': 1152, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.g1.a1', '32.g1.b1', '32.cr1.a1', '32.cs1.a1', '32.ct1.a1', '32.cu1.a1', '32.cv1.a1', '32.cw1.a1', '32.cx1.a1', '32.cy1.a1', '32.cz1.a1', '32.da1.a1', '32.db1.a1', '32.dc1.a1', '32.dd1.a1', '32.de1.a1', '32.df1.a1', '32.dg1.a1', '32.dh1.a1', '32.di1.a1'], 'contains': ['128.b1.a1', '128.c1.a1', '128.f1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3355, 4810, 6352, 7210, 3357, 4790, 6344, 7226], 'generators': [136, 32], 'label': '256.30836.64.d1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.d1.a1', 'normal_contained_in': ['32.a1.a1', '32.g1.b1', '32.g1.a1'], 'normal_contains': ['128.b1.a1', '128.c1.a1', '128.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.d1.a1', 'projective_image': '64.264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.264', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879618
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.y1.a1', '8.hi1.b1', '8.hi1.d1'], 'contains': ['32.k1.b1', '32.fx1.a1', '32.ga1.a1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8402, -1, 4767, -1, 8406, -1, 4763, -1], 'generators': [129, 20], 'label': '256.30836.16.iw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.iw1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iw1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878650
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ec1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.p1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.f1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.f1', '64.dn1.e2', '64.dn1.e1', '64.dn1.f2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.h2', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.n1', '64.dk1.o1', '64.dk1.m1', '64.dk1.p1', '64.dk1.e1', '64.dk1.h1', '64.dk1.f1', '64.dk1.g1', '64.dk1.j1', '64.dk1.k1', '64.dk1.i1', '64.dk1.l1', '64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1'], 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '2.w1.a1', '2.bd1.a1'], 'contains': ['8.bx1.a1', '8.bz1.a1', '8.cb1.a1', '8.ff1.a1', '8.fg1.a1', '8.fr1.a1', '8.ft1.a1'], 'core': '4.ec1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2941, 9805, 6496, 4052, 2942, 9801, 6490, 4061], 'generators': [81, 18, 20], 'label': '256.30836.4.ec1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ec1.a1', 'normal_contained_in': ['2.w1.a1', '2.i1.a1', '2.bd1.a1'], 'normal_contains': ['8.bx1.a1', '8.bz1.a1', '8.cb1.a1', '8.ff1.a1', '8.fg1.a1', '8.fr1.a1', '8.ft1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ec1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ec1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878651
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '64.f1', 'aut_quo_index': 1152, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.i1.a1', '32.i1.b1', '32.em1.a1', '32.en1.a1', '32.eo1.a1', '32.ep1.a1', '32.eq1.a1', '32.er1.a1', '32.es1.a1', '32.et1.a1', '32.eu1.a1', '32.ev1.a1', '32.ew1.a1', '32.ex1.a1', '32.ey1.a1', '32.ez1.a1', '32.fa1.a1', '32.fb1.a1', '32.fc1.a1', '32.fd1.a1'], 'contains': ['128.c1.a1', '128.d1.a1', '128.g1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7103, 4679, 6672, 6034, 7107, 4659, 6666, 6101], 'generators': [8, 160], 'label': '256.30836.64.f1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.f1.a1', 'normal_contained_in': ['32.a1.a1', '32.i1.b1', '32.i1.a1'], 'normal_contains': ['128.d1.a1', '128.c1.a1', '128.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.f1.a1', 'projective_image': '64.264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.264', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878652
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '64.g1', 'aut_quo_index': 2304, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.j1.a1', '32.j1.b1', '32.k1.a1', '32.k1.b1', '32.l1.a1', '32.l1.b1', '32.fp1.a1', '32.fq1.a1', '32.fr1.a1', '32.fs1.a1', '32.ft1.a1', '32.fu1.a1', '32.fv1.a1', '32.fw1.a1', '32.fx1.a1', '32.fy1.a1', '32.fz1.a1', '32.ga1.a1'], 'contains': ['128.d1.a1', '128.e1.a1', '128.f1.a1'], 'core': '64.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7936, 4842, 5190, 7275, 7940, 4822, 5185, 7291], 'generators': [136, 160], 'label': '256.30836.64.g1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.g1.a1', 'normal_contained_in': ['32.a1.a1', '32.k1.b1', '32.k1.a1', '32.j1.a1', '32.j1.b1', '32.l1.b1', '32.l1.a1'], 'normal_contains': ['128.e1.a1', '128.d1.a1', '128.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.g1.a1', 'projective_image': '64.263', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.263', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878653
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.h1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.h1.a1', '32.j1.a1', '32.gk1.a1', '32.gk1.b1', '32.gl1.a1', '32.gm1.a1', '32.gn1.a1', '32.go1.a1'], 'contains': ['128.e1.a1', '128.h1.a1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7883, 5222, 5231, 6258, 7886, 5216, 5227, 6272], 'generators': [2, 40], 'label': '256.30836.64.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.h1.a1', 'normal_contained_in': ['32.j1.a1', '32.h1.a1', '32.c1.a1'], 'normal_contains': ['128.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.h1.a1', 'projective_image': '128.2182', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.27', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878654
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.h1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.h1.b1', '32.j1.b1', '32.gk1.c1', '32.gk1.f1', '32.gl1.b1', '32.gm1.b1', '32.gn1.b1', '32.go1.b1'], 'contains': ['128.e1.a1', '128.h1.b1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7883, 5222, 5245, 6290, 7886, 5216, 5241, 6304], 'generators': [130, 40], 'label': '256.30836.64.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.h1.b1', 'normal_contained_in': ['32.j1.b1', '32.h1.b1', '32.c1.a1'], 'normal_contains': ['128.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.h1.b1', 'projective_image': '128.2182', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.27', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878655
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.h1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '32.h1.a1', '32.j1.b1', '32.gk1.d1', '32.gk1.g1', '32.gl1.c1', '32.gm1.c1', '32.gn1.c1', '32.go1.c1'], 'contains': ['128.e1.a1', '128.h1.c1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [7883, 5222, 5217, 6225, 7886, 5216, 5213, 6239], 'generators': [34, 40], 'label': '256.30836.64.h1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.h1.c1', 'normal_contained_in': ['32.j1.b1', '32.h1.a1', '32.c1.b1'], 'normal_contains': ['128.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.h1.c1', 'projective_image': '128.2182', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.27', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.h1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878656
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.h1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '32.h1.b1', '32.j1.a1', '32.gk1.e1', '32.gk1.h1', '32.gl1.d1', '32.gm1.d1', '32.gn1.d1', '32.go1.d1'], 'contains': ['128.e1.a1', '128.h1.d1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7883, 5222, 5203, 6193, 7886, 5216, 5199, 6206], 'generators': [162, 40], 'label': '256.30836.64.h1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.h1.d1', 'normal_contained_in': ['32.j1.a1', '32.h1.b1', '32.c1.b1'], 'normal_contains': ['128.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.h1.d1', 'projective_image': '128.2182', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.27', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.h1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878657
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.i1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.g1.a1', '32.k1.a1', '32.gt1.a1', '32.gt1.e1', '32.gw1.a1', '32.gx1.a1', '32.gx1.b1', '32.gy1.a1'], 'contains': ['128.f1.a1', '128.i1.a1'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8946, 6962, 4749, 7308, 8951, 6959, 4749, 7324], 'generators': [1, 136], 'label': '256.30836.64.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.i1.a1', 'normal_contained_in': ['32.k1.a1', '32.g1.a1', '32.d1.a1'], 'normal_contains': ['128.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.i1.a1', 'projective_image': '128.2201', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.22', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878658
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.i1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.g1.b1', '32.k1.b1', '32.gt1.b1', '32.gt1.f1', '32.gw1.b1', '32.gx1.c1', '32.gx1.d1', '32.gy1.b1'], 'contains': ['128.f1.a1', '128.i1.b1'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8946, 6962, 4801, 7373, 8951, 6959, 4796, 7389], 'generators': [129, 136], 'label': '256.30836.64.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.i1.b1', 'normal_contained_in': ['32.k1.b1', '32.g1.b1', '32.d1.a1'], 'normal_contains': ['128.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.i1.b1', 'projective_image': '128.2201', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.22', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878659
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.i1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '32.g1.a1', '32.k1.b1', '32.gt1.c1', '32.gt1.g1', '32.gw1.c1', '32.gx1.e1', '32.gx1.f1', '32.gy1.c1'], 'contains': ['128.f1.a1', '128.i1.c1'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8946, 6962, 4763, 7340, 8951, 6959, 4763, 7356], 'generators': [33, 136], 'label': '256.30836.64.i1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.i1.c1', 'normal_contained_in': ['32.k1.b1', '32.g1.a1', '32.d1.b1'], 'normal_contains': ['128.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.i1.c1', 'projective_image': '128.2201', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.22', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.i1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879164
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bp1.a1'], 'contains': ['16.bf1.d1', '16.dz1.b1', '16.eb1.b1', '16.ef1.b1', '16.ei1.b1', '16.ej1.a1', '16.em1.a1'], 'core': '16.bf1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9090, -1, 4431, -1, 9094, -1, 4427, -1], 'generators': [33, 114, 84], 'label': '256.30836.8.gm1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '8.gm1.d1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gm1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878661
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.m1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.d1', '128.i1.b1', '128.i1.c1', '128.m1.a1', '128.m1.b1', '128.j1.a1', '128.j1.b1', '128.k1.a1', '128.k1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.n1.a1', '4.p1.a1', '4.q1.a1', '4.u1.a1', '4.w1.a1', '4.ba1.a1', '4.be1.a1', '4.ee1.a1', '4.eg1.a1', '4.el1.a1', '4.es1.a1', '4.fk1.a1', '4.fm1.a1', '4.fr1.a1', '4.fy1.a1'], 'core': '2.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3083, 7820, 8242, 2873, 3085, 7844, 8250, 2880], 'generators': [65, 2, 68, 16], 'label': '256.30836.2.m1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.m1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.n1.a1', '4.q1.a1', '4.p1.a1', '4.u1.a1', '4.w1.a1', '4.be1.a1', '4.ba1.a1', '4.ee1.a1', '4.eg1.a1', '4.es1.a1', '4.el1.a1', '4.fk1.a1', '4.fm1.a1', '4.fy1.a1', '4.fr1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.m1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.m1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878662
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ed1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.i1', '64.dj1.n1', '64.dj1.f1', '64.dj1.e1', '64.dj1.m1', '64.dj1.j1', '64.dj1.b1', '64.dj1.k1', '64.dj1.c1', '64.dj1.h1', '64.dj1.p1', '64.dj1.o1', '64.dj1.g1', '64.dj1.d1', '64.dj1.l1', '64.dm1.a1', '64.dm1.c2', '64.dm1.g1', '64.dm1.e2', '64.dm1.c1', '64.dm1.a2', '64.dm1.e1', '64.dm1.g2', '64.dm1.b2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dn1.a1', '64.dn1.c2', '64.dn1.b1', '64.dn1.d2', '64.dn1.c1', '64.dn1.a2', '64.dn1.d1', '64.dn1.b2', '64.dn1.e1', '64.dn1.g2', '64.dn1.f1', '64.dn1.h2', '64.dn1.g1', '64.dn1.e2', '64.dn1.h1', '64.dn1.f2', '64.di1.a1', '64.di1.b1', '64.di1.d1', '64.di1.c1', '64.di1.f1', '64.di1.k1', '64.di1.m1', '64.di1.l1', '64.di1.g1', '64.di1.n1', '64.di1.p1', '64.di1.o1', '64.di1.e1', '64.di1.h1', '64.di1.j1', '64.di1.i1'], 'conjugacy_class_count': 1, 'contained_in': ['2.l1.a1', '2.p1.a1', '2.bb1.a1'], 'contains': ['8.cd1.a1', '8.ce1.a1', '8.cj1.a1', '8.dn1.a1', '8.dr1.a1', '8.dx1.a1', '8.fy1.a1'], 'core': '4.ed1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2736, 4749, 7079, 1279, 2738, 4747, 7072, 1283], 'generators': [5, 22, 64], 'label': '256.30836.4.ed1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ed1.a1', 'normal_contained_in': ['2.p1.a1', '2.l1.a1', '2.bb1.a1'], 'normal_contains': ['8.cd1.a1', '8.ce1.a1', '8.cj1.a1', '8.dn1.a1', '8.dr1.a1', '8.dx1.a1', '8.fy1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ed1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ed1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878663
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.m1.a1', '32.bw1.a1', '32.ci1.a1', '32.ci1.b1', '32.cj1.a1', '32.cj1.b1', '32.cj1.c1', '32.cj1.d1', '32.ck1.a1', '32.ck1.b1'], 'contains': ['128.a1.a1', '128.h1.a1', '128.h1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8361, -1, 4367, -1, 8365, -1, 4362, -1], 'generators': [2, 128], 'label': '256.30836.64.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.j1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878664
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '32.m1.a1', '32.bw1.a1', '32.ci1.c1', '32.ci1.d1', '32.cj1.e1', '32.cj1.f1', '32.cj1.g1', '32.cj1.h1', '32.ck1.c1', '32.ck1.d1'], 'contains': ['128.a1.a1', '128.h1.c1', '128.h1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8361, -1, 4230, -1, 8365, -1, 4227, -1], 'generators': [138, 128], 'label': '256.30836.64.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.j1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878665
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.n1.a1', '32.be1.a1', '32.ci1.a1', '32.ci1.c1', '32.cl1.a1', '32.cl1.b1', '32.cm1.a1', '32.cm1.b1', '32.cn1.a1'], 'contains': ['128.a1.a1', '128.i1.a1', '128.i1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8282, -1, 3981, -1, 8286, -1, 3977, -1], 'generators': [1, 128], 'label': '256.30836.64.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.k1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878666
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '32.n1.a1', '32.be1.a1', '32.ci1.b1', '32.ci1.d1', '32.cl1.c1', '32.cl1.d1', '32.cm1.c1', '32.cm1.d1', '32.cn1.b1'], 'contains': ['128.a1.a1', '128.i1.c1', '128.i1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8282, -1, 3952, -1, 8286, -1, 3949, -1], 'generators': [33, 128], 'label': '256.30836.64.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.k1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878667
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.bf1.a1', '32.bx1.a1', '32.cj1.a1', '32.cj1.b1', '32.cj1.e1', '32.cj1.f1', '32.cl1.a1', '32.cl1.c1', '32.co1.a1', '32.co1.b1'], 'contains': ['128.a1.a1', '128.j1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8468, -1, 3577, -1, 8472, -1, 3574, -1], 'generators': [4, 128], 'label': '256.30836.64.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.l1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878668
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '32.bf1.a1', '32.bx1.a1', '32.cj1.c1', '32.cj1.d1', '32.cj1.g1', '32.cj1.h1', '32.cl1.b1', '32.cl1.d1', '32.co1.c1', '32.co1.d1'], 'contains': ['128.a1.a1', '128.j1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8468, -1, 4282, -1, 8472, -1, 4279, -1], 'generators': [140, 128], 'label': '256.30836.64.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.l1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878669
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '32.o1.a1', '32.bg1.a1', '32.cj1.a1', '32.cj1.c1', '32.cj1.e1', '32.cj1.g1', '32.cm1.a1', '32.cm1.c1', '32.cp1.a1', '32.cp1.a2'], 'contains': ['128.a1.a1', '128.k1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8335, -1, 4311, -1, 8339, -1, 4307, -1], 'generators': [6, 128], 'label': '256.30836.64.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.m1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878670
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '32.o1.a1', '32.bg1.a1', '32.cj1.b1', '32.cj1.d1', '32.cj1.f1', '32.cj1.h1', '32.cm1.b1', '32.cm1.d1', '32.cp1.b1', '32.cp1.b2'], 'contains': ['128.a1.a1', '128.k1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8335, -1, 3938, -1, 8339, -1, 3935, -1], 'generators': [38, 128], 'label': '256.30836.64.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.m1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878671
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.p1.a1', '32.bh1.a1', '32.by1.a1', '32.ck1.a1', '32.ck1.b1', '32.ck1.c1', '32.ck1.d1', '32.cl1.a1', '32.cl1.b1', '32.cl1.c1', '32.cl1.d1', '32.cp1.a1', '32.cp1.a2', '32.cp1.b1', '32.cp1.b2'], 'contains': ['128.a1.a1', '128.l1.a1', '128.l1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8442, -1, 3243, -1, 8445, -1, 3241, -1], 'generators': [5, 128], 'label': '256.30836.64.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.n1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878672
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.q1.a1', '32.bi1.a1', '32.bz1.a1', '32.ci1.a1', '32.ci1.b1', '32.ci1.c1', '32.ci1.d1', '32.co1.a1', '32.co1.b1', '32.co1.c1', '32.co1.d1', '32.cp1.a1', '32.cp1.a2', '32.cp1.b1', '32.cp1.b2'], 'contains': ['128.a1.a1', '128.m1.a1', '128.m1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8388, -1, 3257, -1, 8392, -1, 3255, -1], 'generators': [3, 128], 'label': '256.30836.64.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.o1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878673
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ee1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.i1', '64.dj1.n1', '64.dj1.f1', '64.dj1.e1', '64.dj1.m1', '64.dj1.j1', '64.dj1.b1', '64.dj1.k1', '64.dj1.c1', '64.dj1.h1', '64.dj1.p1', '64.dj1.o1', '64.dj1.g1', '64.dj1.d1', '64.dj1.l1', '64.dm1.a1', '64.dm1.c2', '64.dm1.g1', '64.dm1.e2', '64.dm1.c1', '64.dm1.a2', '64.dm1.e1', '64.dm1.g2', '64.dm1.b2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dn1.a1', '64.dn1.c2', '64.dn1.b1', '64.dn1.d2', '64.dn1.c1', '64.dn1.a2', '64.dn1.d1', '64.dn1.b2', '64.dn1.e1', '64.dn1.g2', '64.dn1.f1', '64.dn1.h2', '64.dn1.g1', '64.dn1.e2', '64.dn1.h1', '64.dn1.f2', '64.di1.a1', '64.di1.b1', '64.di1.d1', '64.di1.c1', '64.di1.f1', '64.di1.k1', '64.di1.m1', '64.di1.l1', '64.di1.g1', '64.di1.n1', '64.di1.p1', '64.di1.o1', '64.di1.e1', '64.di1.h1', '64.di1.j1', '64.di1.i1'], 'conjugacy_class_count': 1, 'contained_in': ['2.m1.a1', '2.q1.a1', '2.bb1.a1'], 'contains': ['8.cd1.a1', '8.cf1.a1', '8.ck1.a1', '8.do1.a1', '8.du1.a1', '8.ef1.a1', '8.fh1.a1'], 'core': '4.ee1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1986, 5697, 8650, 1201, 1987, 5696, 8643, 1203], 'generators': [5, 70, 16], 'label': '256.30836.4.ee1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ee1.a1', 'normal_contained_in': ['2.q1.a1', '2.m1.a1', '2.bb1.a1'], 'normal_contains': ['8.cd1.a1', '8.ck1.a1', '8.cf1.a1', '8.do1.a1', '8.du1.a1', '8.fh1.a1', '8.ef1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ee1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ee1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878674
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.r1.a1', '32.bj1.a1', '32.ck1.a1', '32.ck1.c1', '32.cm1.a1', '32.cm1.d1', '32.co1.a1', '32.co1.c1', '32.cq1.a1'], 'contains': ['128.a1.a1', '128.n1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8308, -1, 3967, -1, 8312, -1, 3963, -1], 'generators': [7, 128], 'label': '256.30836.64.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.p1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878675
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.b1', '32.r1.a1', '32.bj1.a1', '32.ck1.b1', '32.ck1.d1', '32.cm1.b1', '32.cm1.c1', '32.co1.b1', '32.co1.d1', '32.cq1.b1'], 'contains': ['128.a1.a1', '128.n1.b1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8308, -1, 3286, -1, 8312, -1, 3283, -1], 'generators': [39, 128], 'label': '256.30836.64.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.p1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.p1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878676
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.s1.a1', '32.bk1.a1', '32.ca1.a1', '32.cq1.a1', '32.cq1.b1'], 'contains': ['128.a1.a1', '128.o1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4482, -1, 6139, -1, 4485, -1, 6133, -1], 'generators': [83, 128], 'label': '256.30836.64.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.fl1.a1', 'old_label': '64.q1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878677
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.t1.a1', '32.bl1.a1', '32.cb1.a1', '32.cn1.a1', '32.cn1.b1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6838, -1, 8048, -1, 6842, -1, 8041, -1], 'generators': [64], 'label': '256.30836.64.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bz1.a1', 'old_label': '64.r1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.r1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878678
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.s1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.v1.a1', '32.bn1.a1', '32.cc1.a1', '32.cn1.a1', '32.cn1.b1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6628, -1, 8065, -1, 6631, -1, 8056, -1], 'generators': [65], 'label': '256.30836.64.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ca1.a1', 'old_label': '64.s1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.s1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878679
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.fd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bb1.a1', '32.br1.a1', '32.cd1.a1', '32.cq1.a1', '32.cq1.b1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5682, -1, 6087, -1, 5675, -1, 6081, -1], 'generators': [84], 'label': '256.30836.64.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.fk1.a1', 'old_label': '64.t1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878680
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.m1.a1', '32.cr1.a1', '32.eb1.a1', '32.eb1.b1', '32.ec1.a1', '32.ec1.b1', '32.ed1.a1', '32.ed1.a2', '32.ee1.a1'], 'contains': ['128.b1.a1', '128.h1.a1', '128.h1.c1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7856, -1, 3473, -1, 7860, -1, 3470, -1], 'generators': [2, 32], 'label': '256.30836.64.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.u1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.u1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878681
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.b1', '32.m1.a1', '32.cr1.a1', '32.eb1.c1', '32.eb1.d1', '32.ec1.c1', '32.ec1.d1', '32.ed1.b1', '32.ed1.b2', '32.ee1.b1'], 'contains': ['128.b1.a1', '128.h1.b1', '128.h1.d1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7856, -1, 3515, -1, 7860, -1, 3512, -1], 'generators': [138, 32], 'label': '256.30836.64.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.u1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.u1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878682
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.n1.a1', '32.dj1.a1', '32.eb1.a1', '32.eb1.c1', '32.ef1.a1', '32.ef1.b1', '32.eg1.a1', '32.eg1.a2', '32.eh1.a1'], 'contains': ['128.b1.a1', '128.i1.a1', '128.i1.c1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7830, -1, 1845, -1, 7833, -1, 1845, -1], 'generators': [1, 32], 'label': '256.30836.64.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.v1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878683
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.b1', '32.n1.a1', '32.dj1.a1', '32.eb1.b1', '32.eb1.d1', '32.ef1.c1', '32.ef1.d1', '32.eg1.b1', '32.eg1.b2', '32.eh1.b1'], 'contains': ['128.b1.a1', '128.i1.b1', '128.i1.d1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7830, -1, 3605, -1, 7833, -1, 3602, -1], 'generators': [129, 32], 'label': '256.30836.64.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.v1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.v1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878684
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ef1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.e1', '64.di1.i1', '64.di1.j1', '64.di1.h1', '64.di1.g1', '64.di1.o1', '64.di1.p1', '64.di1.n1', '64.di1.f1', '64.di1.l1', '64.di1.m1', '64.di1.k1', '64.dj1.a1', '64.dj1.f1', '64.dj1.n1', '64.dj1.i1', '64.dj1.e1', '64.dj1.b1', '64.dj1.j1', '64.dj1.m1', '64.dj1.d1', '64.dj1.g1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.c1', '64.dj1.k1', '64.dj1.p1', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.b2', '64.dn1.a1', '64.dn1.d2', '64.dn1.b1', '64.dn1.c2', '64.dn1.c1', '64.dn1.b2', '64.dn1.d1', '64.dn1.a2', '64.dn1.g1', '64.dn1.f2', '64.dn1.h1', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.f1', '64.dn1.g2'], 'conjugacy_class_count': 1, 'contained_in': ['2.l1.a1', '2.q1.a1', '2.bc1.a1'], 'contains': ['8.cd1.a1', '8.cg1.a1', '8.ci1.a1', '8.dp1.a1', '8.dt1.a1', '8.el1.a1', '8.ey1.a1', '8.he1.a1', '8.he1.b1'], 'core': '4.ef1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2875, 4249, 8980, 348, 2876, 4248, 8972, 348], 'generators': [17, 66, 20, 128], 'label': '256.30836.4.ef1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ef1.a1', 'normal_contained_in': ['2.q1.a1', '2.l1.a1', '2.bc1.a1'], 'normal_contains': ['8.cd1.a1', '8.ci1.a1', '8.cg1.a1', '8.dp1.a1', '8.dt1.a1', '8.ey1.a1', '8.el1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ef1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ef1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878695
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.eg1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.e1', '64.di1.i1', '64.di1.j1', '64.di1.h1', '64.di1.g1', '64.di1.o1', '64.di1.p1', '64.di1.n1', '64.di1.f1', '64.di1.l1', '64.di1.m1', '64.di1.k1', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.f2', '64.dm1.b1', '64.dm1.d2', '64.dm1.h1', '64.dm1.h2', '64.dm1.d1', '64.dm1.b2', '64.dm1.f1', '64.dj1.a1', '64.dj1.f1', '64.dj1.n1', '64.dj1.i1', '64.dj1.e1', '64.dj1.b1', '64.dj1.j1', '64.dj1.m1', '64.dj1.d1', '64.dj1.g1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.c1', '64.dj1.k1', '64.dj1.p1', '64.dn1.a1', '64.dn1.d2', '64.dn1.b1', '64.dn1.c2', '64.dn1.c1', '64.dn1.b2', '64.dn1.d1', '64.dn1.a2', '64.dn1.g1', '64.dn1.f2', '64.dn1.h1', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.f1', '64.dn1.g2'], 'conjugacy_class_count': 1, 'contained_in': ['2.m1.a1', '2.p1.a1', '2.bc1.a1'], 'contains': ['8.cd1.a1', '8.ch1.a1', '8.cl1.a1', '8.dq1.a1', '8.ds1.a1', '8.eq1.a1', '8.fn1.a1'], 'core': '4.eg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1370, 8499, 8016, 197, 1370, 8496, 8009, 197], 'generators': [65, 18, 68], 'label': '256.30836.4.eg1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.eg1.a1', 'normal_contained_in': ['2.p1.a1', '2.m1.a1', '2.bc1.a1'], 'normal_contains': ['8.cd1.a1', '8.cl1.a1', '8.ch1.a1', '8.ds1.a1', '8.dq1.a1', '8.eq1.a1', '8.fn1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.eg1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.eg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878696
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bc1.a1', '32.df1.a1', '32.dw1.a1', '32.eh1.a1', '32.eh1.b1', '32.el1.a1', '32.el1.a2'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3330, -1, 6330, -1, 3332, -1, 6321, -1], 'generators': [69], 'label': '256.30836.64.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cj1.a1', 'old_label': '64.bf1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878697
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.ep1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bd1.a1', '32.di1.a1', '32.ea1.a1', '32.ej1.a1', '32.ej1.b1', '32.el1.a1', '32.el1.a2'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3083, -1, 6253, -1, 2920, -1, 6253, -1], 'generators': [87], 'label': '256.30836.64.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cu1.a1', 'old_label': '64.bg1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878698
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.cr1.a1', '32.em1.a1', '32.fe1.a1', '32.fe1.b1', '32.ff1.a1', '32.ff1.a2', '32.fg1.a1', '32.fg1.b1', '32.fh1.a1'], 'contains': ['128.c1.a1', '128.h1.a1', '128.h1.b1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8042, -1, 3675, -1, 8046, -1, 3671, -1], 'generators': [2, 168], 'label': '256.30836.64.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.bh1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878699
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '32.cr1.a1', '32.em1.a1', '32.fe1.c1', '32.fe1.d1', '32.ff1.b1', '32.ff1.b2', '32.fg1.c1', '32.fg1.d1', '32.fh1.b1'], 'contains': ['128.c1.a1', '128.h1.c1', '128.h1.d1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8042, -1, 3647, -1, 8046, -1, 3644, -1], 'generators': [34, 168], 'label': '256.30836.64.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.bh1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878700
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1', '32.be1.a1', '32.en1.a1', '32.fe1.a1', '32.fe1.c1', '32.fi1.a1', '32.fi1.b1', '32.fj1.a1', '32.fj1.a2', '32.fk1.a1'], 'contains': ['128.c1.a1', '128.i1.a1', '128.i1.c1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8149, -1, 2263, -1, 8153, -1, 2262, -1], 'generators': [1, 168], 'label': '256.30836.64.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.bi1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878701
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.b1', '32.be1.a1', '32.en1.a1', '32.fe1.b1', '32.fe1.d1', '32.fi1.c1', '32.fi1.d1', '32.fj1.b1', '32.fj1.b2', '32.fk1.b1'], 'contains': ['128.c1.a1', '128.i1.b1', '128.i1.d1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8149, -1, 3883, -1, 8153, -1, 3880, -1], 'generators': [129, 168], 'label': '256.30836.64.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.bi1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878702
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bf1.a1', '32.cs1.a1', '32.eo1.a1', '32.ff1.a1', '32.ff1.a2', '32.ff1.b1', '32.ff1.b2', '32.fi1.a1', '32.fi1.b1', '32.fi1.c1', '32.fi1.d1', '32.fl1.a1', '32.fl1.a2', '32.fl1.a3', '32.fl1.a4'], 'contains': ['128.c1.a1', '128.j1.a1', '128.j1.b1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8228, -1, 2674, -1, 8232, -1, 2672, -1], 'generators': [4, 168], 'label': '256.30836.64.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.bj1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878703
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bg1.a1', '32.ct1.a1', '32.ep1.a1', '32.ff1.a1', '32.ff1.a2', '32.ff1.b1', '32.ff1.b2', '32.fj1.a1', '32.fj1.a2', '32.fj1.b1', '32.fj1.b2', '32.fm1.a1', '32.fm1.a2', '32.fm1.b1', '32.fm1.b2'], 'contains': ['128.c1.a1', '128.k1.a1', '128.k1.b1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8202, -1, 2744, -1, 8206, -1, 2741, -1], 'generators': [6, 168], 'label': '256.30836.64.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.bk1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878704
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.bh1.a1', '32.cu1.a1', '32.fg1.a1', '32.fg1.c1', '32.fi1.a1', '32.fi1.c1', '32.fm1.a1', '32.fm1.a2', '32.fn1.a1'], 'contains': ['128.c1.a1', '128.l1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8096, -1, 3619, -1, 8099, -1, 3616, -1], 'generators': [5, 168], 'label': '256.30836.64.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.bl1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878705
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '32.bh1.a1', '32.cu1.a1', '32.fg1.b1', '32.fg1.d1', '32.fi1.b1', '32.fi1.d1', '32.fm1.b1', '32.fm1.b2', '32.fn1.b1'], 'contains': ['128.c1.a1', '128.l1.b1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8096, -1, 2249, -1, 8099, -1, 2248, -1], 'generators': [37, 168], 'label': '256.30836.64.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.bl1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878722
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.o1.a1', '32.ep1.a1', '32.fq1.a1', '32.gc1.a1', '32.gc1.b1', '32.gc1.c1', '32.gc1.d1', '32.gg1.a1', '32.gg1.a2', '32.gg1.b1', '32.gg1.b2', '32.gi1.a1', '32.gi1.b1', '32.gi1.c1', '32.gi1.d1'], 'contains': ['128.d1.a1', '128.k1.a1', '128.k1.b1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8920, -1, 3432, -1, 8925, -1, 3428, -1], 'generators': [6, 160], 'label': '256.30836.64.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.bx1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 30878723
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.by1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.p1.a1', '32.fr1.a1', '32.gd1.a1', '32.gd1.c1', '32.gf1.a1', '32.gf1.c1', '32.gf1.e1', '32.gf1.g1', '32.gi1.a1', '32.gi1.b1'], 'contains': ['128.d1.a1', '128.l1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8867, -1, 4380, -1, 8871, -1, 4376, -1], 'generators': [5, 160], 'label': '256.30836.64.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.by1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.by1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30878706
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.eh1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.i1', '64.dj1.j1', '64.dj1.b1', '64.dj1.e1', '64.dj1.m1', '64.dj1.n1', '64.dj1.f1', '64.dj1.c1', '64.dj1.k1', '64.dj1.l1', '64.dj1.d1', '64.dj1.g1', '64.dj1.o1', '64.dj1.p1', '64.dj1.h1', '64.dn1.a1', '64.dn1.c2', '64.dn1.d1', '64.dn1.b2', '64.dn1.c1', '64.dn1.a2', '64.dn1.b1', '64.dn1.d2', '64.dn1.g2', '64.dn1.e1', '64.dn1.f2', '64.dn1.h1', '64.dn1.e2', '64.dn1.g1', '64.dn1.h2', '64.dn1.f1', '64.di1.a1', '64.di1.b1', '64.di1.c1', '64.di1.d1', '64.di1.f1', '64.di1.k1', '64.di1.l1', '64.di1.m1', '64.di1.e1', '64.di1.h1', '64.di1.i1', '64.di1.j1', '64.di1.g1', '64.di1.n1', '64.di1.o1', '64.di1.p1', '64.dm1.a1', '64.dm1.c2', '64.dm1.e1', '64.dm1.g2', '64.dm1.c1', '64.dm1.a2', '64.dm1.g1', '64.dm1.e2', '64.dm1.f1', '64.dm1.h2', '64.dm1.b1', '64.dm1.d2', '64.dm1.h1', '64.dm1.f2', '64.dm1.d1', '64.dm1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['2.n1.a1', '2.r1.a1', '2.bb1.a1'], 'contains': ['8.ce1.a1', '8.cf1.a1', '8.cm1.a1', '8.dv1.a1', '8.eb1.a1', '8.eg1.a1', '8.fm1.a1'], 'core': '4.eh1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6168, 2474, 5989, 4400, 6171, 2473, 5985, 4410], 'generators': [5, 16, 64], 'label': '256.30836.4.eh1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.eh1.a1', 'normal_contained_in': ['2.r1.a1', '2.n1.a1', '2.bb1.a1'], 'normal_contains': ['8.cf1.a1', '8.ce1.a1', '8.cm1.a1', '8.dv1.a1', '8.eg1.a1', '8.eb1.a1', '8.fm1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.eh1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.eh1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878707
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bi1.a1', '32.cv1.a1', '32.eq1.a1', '32.fe1.a1', '32.fe1.b1', '32.fe1.c1', '32.fe1.d1', '32.fl1.a1', '32.fl1.a2', '32.fl1.a3', '32.fl1.a4', '32.fm1.a1', '32.fm1.a2', '32.fm1.b1', '32.fm1.b2'], 'contains': ['128.c1.a1', '128.m1.a1', '128.m1.b1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8175, -1, 2374, -1, 8179, -1, 2373, -1], 'generators': [3, 168], 'label': '256.30836.64.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.bm1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878708
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bj1.a1', '32.cw1.a1', '32.er1.a1', '32.fg1.a1', '32.fg1.b1', '32.fg1.c1', '32.fg1.d1', '32.fj1.a1', '32.fj1.a2', '32.fj1.b1', '32.fj1.b2', '32.fl1.a1', '32.fl1.a2', '32.fl1.a3', '32.fl1.a4'], 'contains': ['128.c1.a1', '128.n1.a1', '128.n1.b1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8255, -1, 2360, -1, 8259, -1, 2359, -1], 'generators': [7, 168], 'label': '256.30836.64.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.bn1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878709
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bo1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bk1.a1', '32.cx1.a1', '32.es1.a1', '32.fn1.a1', '32.fn1.b1', '32.fo1.a1', '32.fo1.a2'], 'contains': ['128.c1.a1', '128.o1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3167, -1, 7769, -1, 3169, -1, 7762, -1], 'generators': [83, 168], 'label': '256.30836.64.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ef1.a1', 'old_label': '64.bo1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878710
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.bw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bm1.a1', '32.cz1.a1', '32.et1.a1', '32.fk1.a1', '32.fk1.b1', '32.fo1.a1', '32.fo1.a2'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4200, -1, 8281, -1, 4202, -1, 8274, -1], 'generators': [66], 'label': '256.30836.64.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '64.bp1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 30878711
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bo1.a1', '32.da1.a1', '32.eu1.a1', '32.fh1.a1', '32.fh1.b1', '32.fo1.a1', '32.fo1.a2'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3112, -1, 7653, -1, 3114, -1, 7647, -1], 'generators': [17], 'label': '256.30836.64.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '64.bq1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878712
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.br1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.ce1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bp1.a1', '32.db1.a1', '32.ew1.a1', '32.fk1.a1', '32.fk1.b1'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4534, -1, 8218, -1, 4537, -1, 8211, -1], 'generators': [67], 'label': '256.30836.64.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ce1.a1', 'old_label': '64.br1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.br1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878713
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bu1.a1', '32.dg1.a1', '32.fa1.a1', '32.fh1.a1', '32.fh1.b1'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3380, -1, 7290, -1, 3382, -1, 7296, -1], 'generators': [19], 'label': '256.30836.64.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.ba1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bf1.a1', 'old_label': '64.bs1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878714
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bt1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.eq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bv1.a1', '32.dh1.a1', '32.fb1.a1', '32.fn1.a1', '32.fn1.b1'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3404, -1, 7731, -1, 3405, -1, 7724, -1], 'generators': [86], 'label': '256.30836.64.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.eg1.a1', 'old_label': '64.bt1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878715
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.m1.a1', '32.em1.a1', '32.gb1.a1', '32.gb1.b1', '32.gc1.a1', '32.gc1.b1', '32.gd1.a1', '32.gd1.b1', '32.ge1.a1'], 'contains': ['128.d1.a1', '128.h1.a1', '128.h1.d1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8787, -1, 4244, -1, 8792, -1, 4241, -1], 'generators': [2, 160], 'label': '256.30836.64.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.bu1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878716
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.bu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.b1', '32.m1.a1', '32.em1.a1', '32.gb1.c1', '32.gb1.d1', '32.gc1.c1', '32.gc1.d1', '32.gd1.c1', '32.gd1.d1', '32.ge1.b1'], 'contains': ['128.d1.a1', '128.h1.b1', '128.h1.c1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8787, -1, 4258, -1, 8792, -1, 4255, -1], 'generators': [130, 160], 'label': '256.30836.64.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.bu1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.bu1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878717
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ei1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.e1', '64.di1.i1', '64.di1.j1', '64.di1.h1', '64.di1.g1', '64.di1.o1', '64.di1.p1', '64.di1.n1', '64.di1.f1', '64.di1.l1', '64.di1.m1', '64.di1.k1', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.f2', '64.dm1.b1', '64.dm1.d2', '64.dm1.h1', '64.dm1.h2', '64.dm1.d1', '64.dm1.b2', '64.dm1.f1', '64.dj1.a1', '64.dj1.f1', '64.dj1.n1', '64.dj1.i1', '64.dj1.e1', '64.dj1.b1', '64.dj1.j1', '64.dj1.m1', '64.dj1.d1', '64.dj1.g1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.c1', '64.dj1.k1', '64.dj1.p1', '64.dn1.a1', '64.dn1.d2', '64.dn1.b1', '64.dn1.c2', '64.dn1.c1', '64.dn1.b2', '64.dn1.d1', '64.dn1.a2', '64.dn1.g1', '64.dn1.f2', '64.dn1.h1', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.f1', '64.dn1.g2'], 'conjugacy_class_count': 1, 'contained_in': ['2.l1.a1', '2.r1.a1', '2.bd1.a1'], 'contains': ['8.ce1.a1', '8.ci1.a1', '8.cn1.a1', '8.dw1.a1', '8.dz1.a1', '8.ew1.a1', '8.fr1.a1'], 'core': '4.ei1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4739, 4456, 7425, 4944, 4741, 4455, 7418, 4955], 'generators': [17, 20, 64], 'label': '256.30836.4.ei1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ei1.a1', 'normal_contained_in': ['2.r1.a1', '2.l1.a1', '2.bd1.a1'], 'normal_contains': ['8.ci1.a1', '8.ce1.a1', '8.cn1.a1', '8.dw1.a1', '8.ew1.a1', '8.dz1.a1', '8.fr1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ei1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ei1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878728
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ej1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.i1', '64.dj1.j1', '64.dj1.b1', '64.dj1.e1', '64.dj1.m1', '64.dj1.n1', '64.dj1.f1', '64.dj1.c1', '64.dj1.k1', '64.dj1.l1', '64.dj1.d1', '64.dj1.g1', '64.dj1.o1', '64.dj1.p1', '64.dj1.h1', '64.di1.a1', '64.di1.b1', '64.di1.c1', '64.di1.d1', '64.di1.f1', '64.di1.k1', '64.di1.l1', '64.di1.m1', '64.di1.e1', '64.di1.h1', '64.di1.i1', '64.di1.j1', '64.di1.g1', '64.di1.n1', '64.di1.o1', '64.di1.p1', '64.dn1.a1', '64.dn1.c2', '64.dn1.d1', '64.dn1.b2', '64.dn1.c1', '64.dn1.a2', '64.dn1.b1', '64.dn1.d2', '64.dn1.g2', '64.dn1.e1', '64.dn1.f2', '64.dn1.h1', '64.dn1.e2', '64.dn1.g1', '64.dn1.h2', '64.dn1.f1', '64.dm1.a1', '64.dm1.c2', '64.dm1.e1', '64.dm1.g2', '64.dm1.c1', '64.dm1.a2', '64.dm1.g1', '64.dm1.e2', '64.dm1.b1', '64.dm1.d2', '64.dm1.f1', '64.dm1.h2', '64.dm1.d1', '64.dm1.b2', '64.dm1.h1', '64.dm1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.n1.a1', '2.p1.a1', '2.bd1.a1'], 'contains': ['8.ce1.a1', '8.cl1.a1', '8.co1.a1', '8.dy1.a1', '8.ea1.a1', '8.fj1.a1', '8.ft1.a1'], 'core': '4.ej1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3760, 8444, 6037, 2608, 3761, 8441, 6032, 2614], 'generators': [5, 18, 64], 'label': '256.30836.4.ej1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ej1.a1', 'normal_contained_in': ['2.p1.a1', '2.n1.a1', '2.bd1.a1'], 'normal_contains': ['8.cl1.a1', '8.ce1.a1', '8.co1.a1', '8.dy1.a1', '8.fj1.a1', '8.ea1.a1', '8.ft1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ej1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ej1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878729
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.s1.a1', '32.es1.a1', '32.ft1.a1', '32.gj1.a1', '32.gj1.b1'], 'contains': ['128.d1.a1', '128.o1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4825, -1, 6030, -1, 4834, -1, 6026, -1], 'generators': [83, 160], 'label': '256.30836.64.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.eu1.a1', 'old_label': '64.cb1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878730
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.w1.a1', '32.ev1.a1', '32.fu1.a1', '32.ge1.a1', '32.ge1.b1'], 'contains': ['128.d1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7643, -1, 5594, -1, 7647, -1, 5590, -1], 'generators': [22], 'label': '256.30836.64.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bd1.a1', 'old_label': '64.cc1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878731
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.dv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.x1.a1', '32.ex1.a1', '32.fw1.a1', '32.gj1.a1', '32.gj1.b1'], 'contains': ['128.d1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6701, -1, 6009, -1, 6704, -1, 6004, -1], 'generators': [80], 'label': '256.30836.64.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.et1.a1', 'old_label': '64.cd1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878732
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.ce1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.z1.a1', '32.ey1.a1', '32.fx1.a1', '32.ge1.a1', '32.ge1.b1'], 'contains': ['128.d1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7599, -1, 5612, -1, 7603, -1, 5607, -1], 'generators': [20], 'label': '256.30836.64.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.y1.a1', 'old_label': '64.ce1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878733
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.a1', '32.be1.a1', '32.dj1.a1', '32.gk1.a1', '32.gk1.c1', '32.gk1.d1', '32.gk1.e1', '32.gp1.a1', '32.gp1.a2', '32.gq1.a1', '32.gq1.a2'], 'contains': ['128.e1.a1', '128.i1.a1', '128.i1.d1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8495, -1, 4693, -1, 8499, -1, 4694, -1], 'generators': [1, 40], 'label': '256.30836.64.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.cf1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878734
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.k1.b1', '32.be1.a1', '32.dj1.a1', '32.gk1.b1', '32.gk1.f1', '32.gk1.g1', '32.gk1.h1', '32.gp1.b1', '32.gp1.b2', '32.gq1.b1', '32.gq1.b2'], 'contains': ['128.e1.a1', '128.i1.b1', '128.i1.c1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8495, -1, 4707, -1, 8499, -1, 4708, -1], 'generators': [129, 40], 'label': '256.30836.64.cf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.k1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.cf1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cf1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878735
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bf1.a1', '32.dk1.a1', '32.fp1.a1', '32.gl1.a1', '32.gl1.b1', '32.gl1.c1', '32.gl1.d1', '32.gp1.a1', '32.gp1.a2', '32.gp1.b1', '32.gp1.b2', '32.gr1.a1', '32.gr1.a2', '32.gr1.b1', '32.gr1.b2'], 'contains': ['128.e1.a1', '128.j1.a1', '128.j1.b1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8681, -1, 2123, -1, 8685, -1, 2123, -1], 'generators': [4, 40], 'label': '256.30836.64.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.cg1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878736
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.ch1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bg1.a1', '32.dl1.a1', '32.fq1.a1', '32.gl1.a1', '32.gl1.b1', '32.gl1.c1', '32.gl1.d1', '32.gq1.a1', '32.gq1.a2', '32.gq1.b1', '32.gq1.b2', '32.gs1.a1', '32.gs1.a2', '32.gs1.b1', '32.gs1.b2'], 'contains': ['128.e1.a1', '128.k1.a1', '128.k1.b1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8521, -1, 2137, -1, 8525, -1, 2137, -1], 'generators': [6, 40], 'label': '256.30836.64.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.ch1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878737
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.ci1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bh1.a1', '32.dm1.a1', '32.fr1.a1', '32.gm1.a1', '32.gm1.b1', '32.gm1.c1', '32.gm1.d1', '32.gp1.a1', '32.gp1.a2', '32.gp1.b1', '32.gp1.b2', '32.gs1.a1', '32.gs1.a2', '32.gs1.b1', '32.gs1.b2'], 'contains': ['128.e1.a1', '128.l1.a1', '128.l1.b1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8574, -1, 2082, -1, 8579, -1, 2081, -1], 'generators': [5, 40], 'label': '256.30836.64.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.ci1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878738
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.bi1.a1', '32.dn1.a1', '32.gk1.a1', '32.gk1.e1', '32.gk1.f1', '32.gk1.g1', '32.gr1.a1', '32.gr1.a2', '32.gs1.a1', '32.gs1.a2'], 'contains': ['128.e1.a1', '128.m1.a1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8415, -1, 4721, -1, 8419, -1, 4722, -1], 'generators': [3, 40], 'label': '256.30836.64.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.cj1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878883
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.o1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.d1', '128.i1.b1', '128.i1.c1', '128.m1.a1', '128.m1.b1', '128.j1.a1', '128.j1.b1', '128.k1.a1', '128.k1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.q1.a1', '4.r1.a1', '4.s1.a1', '4.bc1.a1', '4.bd1.a1', '4.bf1.a1', '4.bh1.a1', '4.eo1.a1', '4.ep1.a1', '4.eq1.a1', '4.er1.a1', '4.fu1.a1', '4.fv1.a1', '4.fw1.a1', '4.fx1.a1'], 'core': '2.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6707, 2881, 6333, 7491, 6768, 2884, 6332, 7507], 'generators': [65, 2, 68, 80], 'label': '256.30836.2.o1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.o1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.q1.a1', '4.r1.a1', '4.s1.a1', '4.bc1.a1', '4.bd1.a1', '4.bf1.a1', '4.bh1.a1', '4.eq1.a1', '4.er1.a1', '4.eo1.a1', '4.ep1.a1', '4.fw1.a1', '4.fx1.a1', '4.fu1.a1', '4.fv1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.o1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879165
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bq1.a1'], 'contains': ['16.bf1.a1', '16.ea1.a1', '16.ec1.a1', '16.eg1.a1', '16.eh1.a1', '16.ek1.a1', '16.el1.a1'], 'core': '16.bf1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9496, -1, 9281, -1, 9501, -1, 9273, -1], 'generators': [1, 6, 64], 'label': '256.30836.8.gn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '8.gn1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878739
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ek1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.f1', '64.dj1.n1', '64.dj1.i1', '64.dj1.e1', '64.dj1.b1', '64.dj1.j1', '64.dj1.m1', '64.dj1.d1', '64.dj1.g1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.c1', '64.dj1.k1', '64.dj1.p1', '64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.e1', '64.di1.i1', '64.di1.j1', '64.di1.h1', '64.di1.g1', '64.di1.o1', '64.di1.p1', '64.di1.n1', '64.di1.f1', '64.di1.l1', '64.di1.m1', '64.di1.k1', '64.dn1.a1', '64.dn1.d2', '64.dn1.b1', '64.dn1.c2', '64.dn1.c1', '64.dn1.b2', '64.dn1.d1', '64.dn1.a2', '64.dn1.g1', '64.dn1.f2', '64.dn1.h1', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.f1', '64.dn1.g2', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['2.n1.a1', '2.q1.a1', '2.be1.a1'], 'contains': ['8.cf1.a1', '8.cg1.a1', '8.co1.a1', '8.ec1.a1', '8.eh1.a1', '8.en1.a1', '8.fw1.a1'], 'core': '4.ek1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4205, 3469, 6803, 3535, 4207, 3468, 6797, 3543], 'generators': [5, 66, 16], 'label': '256.30836.4.ek1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ek1.a1', 'normal_contained_in': ['2.q1.a1', '2.n1.a1', '2.be1.a1'], 'normal_contains': ['8.cf1.a1', '8.cg1.a1', '8.co1.a1', '8.ec1.a1', '8.eh1.a1', '8.en1.a1', '8.fw1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ek1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ek1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878740
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.b1', '32.bi1.a1', '32.dn1.a1', '32.gk1.b1', '32.gk1.c1', '32.gk1.d1', '32.gk1.h1', '32.gr1.b1', '32.gr1.b2', '32.gs1.b1', '32.gs1.b2'], 'contains': ['128.e1.a1', '128.m1.b1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8415, -1, 4679, -1, 8419, -1, 4680, -1], 'generators': [131, 40], 'label': '256.30836.64.cj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.cj1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cj1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878741
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.ck1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bj1.a1', '32.do1.a1', '32.fs1.a1', '32.gm1.a1', '32.gm1.b1', '32.gm1.c1', '32.gm1.d1', '32.gq1.a1', '32.gq1.a2', '32.gq1.b1', '32.gq1.b2', '32.gr1.a1', '32.gr1.a2', '32.gr1.b1', '32.gr1.b2'], 'contains': ['128.e1.a1', '128.n1.a1', '128.n1.b1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8708, -1, 2109, -1, 8712, -1, 2109, -1], 'generators': [7, 40], 'label': '256.30836.64.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.ck1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878742
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bk1.a1', '32.dp1.a1', '32.ft1.a1', '32.gn1.a1', '32.gn1.b1', '32.gn1.c1', '32.gn1.d1'], 'contains': ['128.e1.a1', '128.o1.a1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4509, -1, 8559, -1, 4512, -1, 8551, -1], 'generators': [83, 40], 'label': '256.30836.64.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '64.cl1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878743
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bq1.a1', '32.dr1.a1', '32.fv1.a1', '32.go1.a1', '32.go1.b1', '32.go1.c1', '32.go1.d1'], 'contains': ['128.e1.a1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4912, -1, 8442, -1, 4909, -1, 8435, -1], 'generators': [23], 'label': '256.30836.64.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '64.cm1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878744
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.dw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bs1.a1', '32.dv1.a1', '32.fz1.a1', '32.gn1.a1', '32.gn1.b1', '32.gn1.c1', '32.gn1.d1'], 'contains': ['128.e1.a1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4850, -1, 8572, -1, 4859, -1, 8564, -1], 'generators': [81], 'label': '256.30836.64.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '64.cn1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878745
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.co1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bt1.a1', '32.dx1.a1', '32.ga1.a1', '32.go1.a1', '32.go1.b1', '32.go1.c1', '32.go1.d1'], 'contains': ['128.e1.a1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4935, -1, 8424, -1, 4932, -1, 8420, -1], 'generators': [21], 'label': '256.30836.64.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '64.co1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.co1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878746
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.a1', '32.bw1.a1', '32.cr1.a1', '32.gt1.a1', '32.gt1.b1', '32.gt1.c1', '32.gt1.d1', '32.gu1.a1', '32.gu1.b1', '32.gv1.a1', '32.gv1.b1'], 'contains': ['128.f1.a1', '128.h1.a1', '128.h1.d1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9027, -1, 4626, -1, 9031, -1, 4612, -1], 'generators': [2, 136], 'label': '256.30836.64.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.cp1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878747
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.j1.b1', '32.bw1.a1', '32.cr1.a1', '32.gt1.e1', '32.gt1.f1', '32.gt1.g1', '32.gt1.h1', '32.gu1.c1', '32.gu1.d1', '32.gv1.c1', '32.gv1.d1'], 'contains': ['128.f1.a1', '128.h1.b1', '128.h1.c1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9027, -1, 4645, -1, 9031, -1, 4647, -1], 'generators': [34, 136], 'label': '256.30836.64.cp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.cp1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cp1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878748
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bx1.a1', '32.cs1.a1', '32.fp1.a1', '32.gu1.a1', '32.gu1.b1', '32.gu1.c1', '32.gu1.d1', '32.gw1.a1', '32.gw1.b1', '32.gw1.c1', '32.gw1.d1', '32.gz1.a1', '32.gz1.b1', '32.gz1.c1', '32.gz1.d1'], 'contains': ['128.f1.a1', '128.j1.a1', '128.j1.b1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9479, -1, 3487, -1, 9484, -1, 3484, -1], 'generators': [4, 136], 'label': '256.30836.64.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.cq1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878749
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '32.ct1.a1', '32.fq1.a1', '32.gu1.a1', '32.gu1.c1', '32.gx1.a1', '32.gx1.c1', '32.gx1.e1', '32.gx1.g1', '32.ha1.a1', '32.ha1.b1'], 'contains': ['128.f1.a1', '128.k1.a1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9080, -1, 4353, -1, 9084, -1, 4349, -1], 'generators': [6, 136], 'label': '256.30836.64.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.cr1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878905
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '128.d1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.f1.a1', '64.g1.a1', '64.bu1.a1', '64.bu1.b1', '64.bv1.a1', '64.bv1.b1', '64.bw1.a1', '64.bw1.b1', '64.bx1.a1', '64.by1.a1', '64.by1.b1', '64.bz1.a1', '64.bz1.b1', '64.ca1.a1', '64.cb1.a1', '64.cc1.a1', '64.cd1.a1', '64.ce1.a1'], 'contains': ['256.a1.a1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8610, 4675, 4258, 6100, 8615, 4655, 4255, 6113], 'generators': [160], 'label': '256.30836.128.d1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.d1.a1', 'normal_contained_in': ['64.g1.a1', '64.a1.a1', '64.f1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.d1.a1', 'projective_image': '128.2222', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2222', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879166
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bq1.a1'], 'contains': ['16.bf1.b1', '16.ea1.a1', '16.ec1.a1', '16.eg1.b1', '16.eh1.b1', '16.ek1.b1', '16.el1.b1'], 'core': '16.bf1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9496, -1, 9217, -1, 9501, -1, 9209, -1], 'generators': [1, 38, 64], 'label': '256.30836.8.gn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '8.gn1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gn1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878750
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.el1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.di1.i1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.l1', '64.dm1.a1', '64.dm1.a2', '64.dm1.g1', '64.dm1.g2', '64.dm1.c1', '64.dm1.c2', '64.dm1.e1', '64.dm1.e2', '64.dm1.h2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.f2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dj1.a1', '64.dj1.m1', '64.dj1.n1', '64.dj1.b1', '64.dj1.e1', '64.dj1.i1', '64.dj1.j1', '64.dj1.f1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.dj1.h1', '64.dn1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.b2', '64.dn1.c1', '64.dn1.c2', '64.dn1.d1', '64.dn1.d2', '64.dn1.e1', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.m1.a1', '2.r1.a1', '2.be1.a1'], 'contains': ['8.cf1.a1', '8.ch1.a1', '8.cn1.a1', '8.ed1.a1', '8.ee1.a1', '8.es1.a1', '8.fo1.a1'], 'core': '4.el1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4876, 3740, 7010, 4343, 4878, 3738, 7004, 4353], 'generators': [65, 68, 16], 'label': '256.30836.4.el1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.el1.a1', 'normal_contained_in': ['2.r1.a1', '2.m1.a1', '2.be1.a1'], 'normal_contains': ['8.cf1.a1', '8.ch1.a1', '8.cn1.a1', '8.ed1.a1', '8.ee1.a1', '8.es1.a1', '8.fo1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.el1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.el1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878751
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '32.ct1.a1', '32.fq1.a1', '32.gu1.b1', '32.gu1.d1', '32.gx1.b1', '32.gx1.d1', '32.gx1.f1', '32.gx1.h1', '32.ha1.c1', '32.ha1.d1'], 'contains': ['128.f1.a1', '128.k1.b1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9080, -1, 4339, -1, 9084, -1, 4335, -1], 'generators': [38, 136], 'label': '256.30836.64.cr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.cr1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cr1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878752
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.by1.a1', '32.cu1.a1', '32.fr1.a1', '32.gv1.a1', '32.gv1.b1', '32.gv1.c1', '32.gv1.d1', '32.gw1.a1', '32.gw1.b1', '32.gw1.c1', '32.gw1.d1', '32.ha1.a1', '32.ha1.b1', '32.ha1.c1', '32.ha1.d1'], 'contains': ['128.f1.a1', '128.l1.a1', '128.l1.b1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9373, -1, 3418, -1, 9377, -1, 3415, -1], 'generators': [5, 136], 'label': '256.30836.64.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.cs1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878753
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.ct1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.a1', '32.bz1.a1', '32.cv1.a1', '32.gt1.a1', '32.gt1.d1', '32.gt1.f1', '32.gt1.g1', '32.gz1.a1', '32.gz1.b1', '32.ha1.a1', '32.ha1.c1'], 'contains': ['128.f1.a1', '128.m1.a1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9054, -1, 4665, -1, 9058, -1, 4666, -1], 'generators': [3, 136], 'label': '256.30836.64.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.ct1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878754
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.ct1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.l1.b1', '32.bz1.a1', '32.cv1.a1', '32.gt1.b1', '32.gt1.c1', '32.gt1.e1', '32.gt1.h1', '32.gz1.c1', '32.gz1.d1', '32.ha1.b1', '32.ha1.d1'], 'contains': ['128.f1.a1', '128.m1.b1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9054, -1, 4296, -1, 9058, -1, 4293, -1], 'generators': [35, 136], 'label': '256.30836.64.ct1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.ct1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.ct1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878755
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.cw1.a1', '32.fs1.a1', '32.gv1.a1', '32.gv1.c1', '32.gx1.a1', '32.gx1.c1', '32.gx1.f1', '32.gx1.h1', '32.gz1.a1', '32.gz1.c1'], 'contains': ['128.f1.a1', '128.n1.a1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9586, -1, 4592, -1, 9590, -1, 4588, -1], 'generators': [7, 136], 'label': '256.30836.64.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.cu1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878756
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.b1', '32.cw1.a1', '32.fs1.a1', '32.gv1.b1', '32.gv1.d1', '32.gx1.b1', '32.gx1.d1', '32.gx1.e1', '32.gx1.g1', '32.gz1.b1', '32.gz1.d1'], 'contains': ['128.f1.a1', '128.n1.b1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9586, -1, 3591, -1, 9590, -1, 3588, -1], 'generators': [39, 136], 'label': '256.30836.64.cu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.cu1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cu1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878757
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ca1.a1', '32.cx1.a1', '32.ft1.a1', '32.gy1.a1', '32.gy1.b1', '32.gy1.c1', '32.gy1.d1'], 'contains': ['128.f1.a1', '128.o1.a1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5393, -1, 5857, -1, 5386, -1, 5852, -1], 'generators': [83, 136], 'label': '256.30836.64.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '64.cv1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878758
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.ec1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ce1.a1', '32.de1.a1', '32.fy1.a1', '32.gy1.a1', '32.gy1.b1', '32.gy1.c1', '32.gy1.d1'], 'contains': ['128.f1.a1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5795, -1, 5844, -1, 5788, -1, 5839, -1], 'generators': [82], 'label': '256.30836.64.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '64.cw1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878759
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.a1', '32.bw1.a1', '32.em1.a1', '32.hb1.a1', '32.hb1.b1', '32.hc1.a1', '32.hc1.b1', '32.hd1.a1', '32.hd1.b1', '32.hd1.c1', '32.hd1.d1'], 'contains': ['128.g1.a1', '128.h1.a1', '128.h1.c1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8734, -1, 3744, -1, 8738, -1, 3741, -1], 'generators': [2, 8], 'label': '256.30836.64.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.cx1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878760
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.h1.b1', '32.bw1.a1', '32.em1.a1', '32.hb1.c1', '32.hb1.d1', '32.hc1.c1', '32.hc1.d1', '32.hd1.e1', '32.hd1.f1', '32.hd1.g1', '32.hd1.h1'], 'contains': ['128.g1.a1', '128.h1.b1', '128.h1.d1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8734, -1, 3758, -1, 8738, -1, 3755, -1], 'generators': [130, 8], 'label': '256.30836.64.cx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.cx1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cx1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878916
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.c1', '64.k1.b1', '64.v1.a1', '64.bi1.a1', '64.bv1.b1', '64.cf1.b1', '64.cy1.b1', '64.di1.c1', '64.di1.i1', '64.di1.l1', '64.di1.o1', '64.dl1.i1', '64.dl1.j1', '64.dl1.k1', '64.dl1.l1', '64.dm1.e1', '64.dm1.e2', '64.dm1.f1', '64.dm1.f2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8657, -1, 1964, -1, 8662, -1, 1963, -1], 'generators': [33], 'label': '256.30836.128.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.i1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '128.i1.c1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.i1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879167
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bq1.a1'], 'contains': ['16.bf1.c1', '16.ea1.b1', '16.ec1.b1', '16.eg1.a1', '16.eh1.a1', '16.ek1.b1', '16.el1.b1'], 'core': '16.bf1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9496, -1, 9313, -1, 9501, -1, 9305, -1], 'generators': [33, 6, 64], 'label': '256.30836.8.gn1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '8.gn1.c1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gn1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878761
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.em1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.p1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.f1', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.c1', '64.dj1.d1', '64.dj1.p1', '64.dj1.o1', '64.dj1.g1', '64.dj1.h1', '64.dj1.l1', '64.dj1.k1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.f1', '64.dn1.e2', '64.dn1.e1', '64.dn1.f2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.h2', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.l1.a1', '2.s1.a1', '2.be1.a1'], 'contains': ['8.cg1.a1', '8.cj1.a1', '8.cn1.a1', '8.ei1.a1', '8.em1.a1', '8.fc1.a1', '8.fv1.a1'], 'core': '4.em1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5357, 3575, 8467, 2905, 5360, 3573, 8459, 2911], 'generators': [81, 66, 84], 'label': '256.30836.4.em1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.em1.a1', 'normal_contained_in': ['2.s1.a1', '2.l1.a1', '2.be1.a1'], 'normal_contains': ['8.cg1.a1', '8.cj1.a1', '8.cn1.a1', '8.ei1.a1', '8.em1.a1', '8.fc1.a1', '8.fv1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.em1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.em1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878762
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '32.dj1.a1', '32.en1.a1', '32.hb1.a1', '32.hb1.c1', '32.he1.a1', '32.he1.b1', '32.hf1.a1', '32.hf1.b1', '32.hg1.a1'], 'contains': ['128.g1.a1', '128.i1.a1', '128.i1.b1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8601, -1, 3731, -1, 8605, -1, 3727, -1], 'generators': [1, 8], 'label': '256.30836.64.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.cy1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878763
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '32.dj1.a1', '32.en1.a1', '32.hb1.b1', '32.hb1.d1', '32.he1.c1', '32.he1.d1', '32.hf1.c1', '32.hf1.d1', '32.hg1.b1'], 'contains': ['128.g1.a1', '128.i1.c1', '128.i1.d1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8601, -1, 3717, -1, 8605, -1, 3713, -1], 'generators': [33, 8], 'label': '256.30836.64.cy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '64.cy1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cy1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878764
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.cz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bx1.a1', '32.dk1.a1', '32.eo1.a1', '32.hc1.a1', '32.hc1.b1', '32.hc1.c1', '32.hc1.d1', '32.he1.a1', '32.he1.b1', '32.he1.c1', '32.he1.d1', '32.hh1.a1', '32.hh1.a2', '32.hh1.b1', '32.hh1.b2'], 'contains': ['128.g1.a1', '128.j1.a1', '128.j1.b1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8814, -1, 3216, -1, 8818, -1, 3213, -1], 'generators': [4, 8], 'label': '256.30836.64.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.cz1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878765
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.da1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '32.dl1.a1', '32.ep1.a1', '32.hc1.a1', '32.hc1.c1', '32.hf1.a1', '32.hf1.c1', '32.hi1.a1', '32.hi1.b1', '32.hj1.a1'], 'contains': ['128.g1.a1', '128.k1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8548, -1, 3703, -1, 8552, -1, 3699, -1], 'generators': [6, 8], 'label': '256.30836.64.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.da1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.da1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878766
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.da1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '32.dl1.a1', '32.ep1.a1', '32.hc1.b1', '32.hc1.d1', '32.hf1.b1', '32.hf1.d1', '32.hi1.c1', '32.hi1.d1', '32.hj1.b1'], 'contains': ['128.g1.a1', '128.k1.b1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8548, -1, 3633, -1, 8552, -1, 3630, -1], 'generators': [38, 8], 'label': '256.30836.64.da1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '64.da1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.da1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878767
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.db1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.a1', '32.by1.a1', '32.dm1.a1', '32.hd1.a1', '32.hd1.b1', '32.hd1.e1', '32.hd1.f1', '32.he1.a1', '32.he1.c1', '32.hi1.a1', '32.hi1.c1'], 'contains': ['128.g1.a1', '128.l1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8627, -1, 3924, -1, 8632, -1, 3921, -1], 'generators': [5, 8], 'label': '256.30836.64.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.db1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.db1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878768
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.db1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.i1.b1', '32.by1.a1', '32.dm1.a1', '32.hd1.c1', '32.hd1.d1', '32.hd1.g1', '32.hd1.h1', '32.he1.b1', '32.he1.d1', '32.hi1.b1', '32.hi1.d1'], 'contains': ['128.g1.a1', '128.l1.b1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8627, -1, 2939, -1, 8632, -1, 2936, -1], 'generators': [37, 8], 'label': '256.30836.64.db1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.db1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.db1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878769
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.dc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.bz1.a1', '32.dn1.a1', '32.eq1.a1', '32.hb1.a1', '32.hb1.b1', '32.hb1.c1', '32.hb1.d1', '32.hh1.a1', '32.hh1.a2', '32.hh1.b1', '32.hh1.b2', '32.hi1.a1', '32.hi1.b1', '32.hi1.c1', '32.hi1.d1'], 'contains': ['128.g1.a1', '128.m1.a1', '128.m1.b1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8761, -1, 3230, -1, 8765, -1, 3227, -1], 'generators': [3, 8], 'label': '256.30836.64.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dc1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878770
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.dd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.do1.a1', '32.er1.a1', '32.hd1.a1', '32.hd1.c1', '32.hd1.e1', '32.hd1.g1', '32.hf1.a1', '32.hf1.d1', '32.hh1.a1', '32.hh1.a2'], 'contains': ['128.g1.a1', '128.n1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8840, -1, 3689, -1, 8845, -1, 3685, -1], 'generators': [7, 8], 'label': '256.30836.64.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.dd1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878771
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.dd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.b1', '32.do1.a1', '32.er1.a1', '32.hd1.b1', '32.hd1.d1', '32.hd1.f1', '32.hd1.h1', '32.hf1.b1', '32.hf1.c1', '32.hh1.b1', '32.hh1.b2'], 'contains': ['128.g1.a1', '128.n1.b1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8840, -1, 3271, -1, 8845, -1, 3269, -1], 'generators': [39, 8], 'label': '256.30836.64.dd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.dd1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dd1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878772
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.n1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.j1.a1', '128.j1.b1', '128.i1.a1', '128.i1.b1', '128.i1.c1', '128.i1.d1', '128.k1.a1', '128.k1.b1', '128.m1.a1', '128.m1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.o1.a1', '4.p1.a1', '4.s1.a1', '4.x1.a1', '4.z1.a1', '4.bb1.a1', '4.bi1.a1', '4.eh1.a1', '4.ej1.a1', '4.ek1.a1', '4.en1.a1', '4.fn1.a1', '4.fp1.a1', '4.fq1.a1', '4.fs1.a1'], 'core': '2.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4410, 3271, 6466, 3969, 4412, 3242, 6456, 3976], 'generators': [5, 2, 16, 64], 'label': '256.30836.2.n1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.n1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.p1.a1', '4.o1.a1', '4.s1.a1', '4.x1.a1', '4.bb1.a1', '4.z1.a1', '4.bi1.a1', '4.ek1.a1', '4.eh1.a1', '4.en1.a1', '4.ej1.a1', '4.fq1.a1', '4.fn1.a1', '4.fs1.a1', '4.fp1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.n1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.n1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878773
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.en1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.f1', '64.dj1.n1', '64.dj1.i1', '64.dj1.e1', '64.dj1.b1', '64.dj1.j1', '64.dj1.m1', '64.dj1.d1', '64.dj1.g1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.c1', '64.dj1.k1', '64.dj1.p1', '64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.e1', '64.di1.i1', '64.di1.j1', '64.di1.h1', '64.di1.g1', '64.di1.o1', '64.di1.p1', '64.di1.n1', '64.di1.f1', '64.di1.l1', '64.di1.m1', '64.di1.k1', '64.dn1.a1', '64.dn1.d2', '64.dn1.b1', '64.dn1.c2', '64.dn1.c1', '64.dn1.b2', '64.dn1.d1', '64.dn1.a2', '64.dn1.g1', '64.dn1.f2', '64.dn1.h1', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.f1', '64.dn1.g2', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['2.n1.a1', '2.s1.a1', '2.bc1.a1'], 'contains': ['8.cg1.a1', '8.cl1.a1', '8.cm1.a1', '8.ej1.a1', '8.ek1.a1', '8.fi1.a1', '8.fu1.a1'], 'core': '4.en1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4650, 1567, 7566, 483, 4653, 1566, 7559, 485], 'generators': [5, 66, 80], 'label': '256.30836.4.en1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.en1.a1', 'normal_contained_in': ['2.s1.a1', '2.n1.a1', '2.bc1.a1'], 'normal_contains': ['8.cl1.a1', '8.cg1.a1', '8.cm1.a1', '8.ej1.a1', '8.fi1.a1', '8.ek1.a1', '8.fu1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.en1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.en1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878774
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.de1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ca1.a1', '32.dp1.a1', '32.es1.a1', '32.hj1.a1', '32.hj1.b1'], 'contains': ['128.g1.a1', '128.o1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4798, -1, 6686, -1, 4807, -1, 6680, -1], 'generators': [83, 8], 'label': '256.30836.64.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.dp1.a1', 'old_label': '64.de1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.de1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878775
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.df1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cf1.a1', '32.du1.a1', '32.ez1.a1', '32.hg1.a1', '32.hg1.b1'], 'contains': ['128.g1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7466, -1, 7743, -1, 7470, -1, 7736, -1], 'generators': [70], 'label': '256.30836.64.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ch1.a1', 'old_label': '64.df1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.df1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878776
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.dg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.ez1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cg1.a1', '32.dy1.a1', '32.fc1.a1', '32.hj1.a1', '32.hj1.b1'], 'contains': ['128.g1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6603, -1, 6600, -1, 6608, -1, 6594, -1], 'generators': [85], 'label': '256.30836.64.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.do1.a1', 'old_label': '64.dg1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878777
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '64.dh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16384, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ch1.a1', '32.dz1.a1', '32.fd1.a1', '32.hg1.a1', '32.hg1.b1'], 'contains': ['128.g1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6651, -1, 7755, -1, 6654, -1, 7749, -1], 'generators': [71], 'label': '256.30836.64.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cd1.a1', 'old_label': '64.dh1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878778
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.a1', '32.eb1.a1', '32.fe1.a1', '32.gb1.a1', '32.gk1.a1', '32.gt1.a1', '32.hb1.a1', '32.hk1.a1', '32.hk1.b1', '32.hk1.c1', '32.hk1.d1', '32.hk1.e1', '32.hk1.f1', '32.hk1.g1', '32.hk1.h1'], 'contains': ['128.h1.a1', '128.i1.a1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2206, -1, 8978, -1, 2206, -1], 'generators': [1, 2], 'label': '256.30836.64.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878779
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.a1', '32.eb1.b1', '32.fe1.b1', '32.gb1.b1', '32.gk1.b1', '32.gt1.b1', '32.hb1.a1', '32.hk1.i1', '32.hk1.j1', '32.hk1.k1', '32.hk1.l1', '32.hk1.m1', '32.hk1.n1', '32.hk1.o1', '32.hk1.p1'], 'contains': ['128.h1.a1', '128.i1.b1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2841, -1, 8978, -1, 2838, -1], 'generators': [129, 2], 'label': '256.30836.64.di1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878780
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.b1', '32.eb1.a1', '32.fe1.a1', '32.gb1.b1', '32.gk1.b1', '32.gt1.c1', '32.hb1.b1', '32.hk1.q1', '32.hk1.r1', '32.hk1.s1', '32.hk1.t1', '32.hk1.u1', '32.hk1.v1', '32.hk1.w1', '32.hk1.x1'], 'contains': ['128.h1.a1', '128.i1.c1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 1539, -1, 8978, -1, 1540, -1], 'generators': [33, 2], 'label': '256.30836.64.di1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.c1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878781
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.b1', '32.eb1.b1', '32.fe1.b1', '32.gb1.a1', '32.gk1.a1', '32.gt1.d1', '32.hb1.b1', '32.hk1.y1', '32.hk1.z1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.bc1', '32.hk1.bd1', '32.hk1.be1', '32.hk1.bf1'], 'contains': ['128.h1.a1', '128.i1.d1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 3008, -1, 8978, -1, 3005, -1], 'generators': [161, 2], 'label': '256.30836.64.di1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.d1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878782
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.a1', '32.eb1.c1', '32.fe1.a1', '32.gb1.c1', '32.gk1.c1', '32.gt1.e1', '32.hb1.c1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.bm1', '32.hk1.bn1'], 'contains': ['128.h1.b1', '128.i1.a1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 1554, -1, 8978, -1, 1554, -1], 'generators': [1, 170], 'label': '256.30836.64.di1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.e1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878783
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.c1', '32.eb1.a1', '32.fe1.c1', '32.gb1.c1', '32.gk1.d1', '32.gt1.e1', '32.hb1.a1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.bs1', '32.hk1.bt1', '32.hk1.bu1', '32.hk1.bv1'], 'contains': ['128.h1.c1', '128.i1.a1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 1208, -1, 8978, -1, 1207, -1], 'generators': [1, 34], 'label': '256.30836.64.di1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.f1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878926
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.o1.a1', '64.z1.a1', '64.bm1.a1', '64.bz1.b1', '64.cj1.b1', '64.ct1.b1', '64.dc1.a1', '64.di1.b1', '64.di1.c1', '64.di1.e1', '64.di1.f1', '64.di1.j1', '64.di1.m1', '64.di1.n1', '64.di1.o1', '64.dn1.c1', '64.dn1.c2', '64.dn1.d1', '64.dn1.d2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2', '64.do1.b1', '64.do1.b2', '64.do1.d1', '64.do1.d2', '64.do1.f1', '64.do1.f2', '64.do1.h1', '64.do1.h2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8705, -1, 1799, -1, 8708, -1, 1803, -1], 'generators': [35], 'label': '256.30836.128.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '128.m1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879599
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.io1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.hi1.a1', '8.hi1.b1'], 'contains': ['32.j1.a1', '32.fu1.a1', '32.fx1.a1', '32.ge1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8482, -1, 4680, -1, 8486, -1, 4675, -1], 'generators': [2, 20, 136], 'label': '256.30836.16.io1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.io1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.io1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878784
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.eo1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.di1.i1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.l1', '64.dm1.a1', '64.dm1.a2', '64.dm1.g1', '64.dm1.g2', '64.dm1.c1', '64.dm1.c2', '64.dm1.e1', '64.dm1.e2', '64.dm1.h2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.f2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dj1.a1', '64.dj1.m1', '64.dj1.n1', '64.dj1.b1', '64.dj1.e1', '64.dj1.i1', '64.dj1.j1', '64.dj1.f1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.dj1.h1', '64.dn1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.b2', '64.dn1.c1', '64.dn1.c2', '64.dn1.d1', '64.dn1.d2', '64.dn1.e1', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.o1.a1', '2.r1.a1', '2.bc1.a1'], 'contains': ['8.ch1.a1', '8.ci1.a1', '8.cm1.a1', '8.eo1.a1', '8.er1.a1', '8.ev1.a1', '8.fl1.a1'], 'core': '4.eo1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6489, 1348, 6167, 4999, 6493, 1348, 6162, 5010], 'generators': [65, 68, 80], 'label': '256.30836.4.eo1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.eo1.a1', 'normal_contained_in': ['2.r1.a1', '2.o1.a1', '2.bc1.a1'], 'normal_contains': ['8.ch1.a1', '8.ci1.a1', '8.cm1.a1', '8.eo1.a1', '8.er1.a1', '8.ev1.a1', '8.fl1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.eo1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.eo1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878785
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.c1', '32.eb1.c1', '32.fe1.c1', '32.gb1.a1', '32.gk1.e1', '32.gt1.a1', '32.hb1.c1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.ca1', '32.hk1.cb1', '32.hk1.cc1', '32.hk1.cd1'], 'contains': ['128.h1.d1', '128.i1.a1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2054, -1, 8978, -1, 2054, -1], 'generators': [1, 138], 'label': '256.30836.64.di1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.g1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878786
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.a1', '32.eb1.d1', '32.fe1.b1', '32.gb1.d1', '32.gk1.f1', '32.gt1.f1', '32.hb1.c1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.ck1', '32.hk1.cl1'], 'contains': ['128.h1.b1', '128.i1.b1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 3022, -1, 8978, -1, 3019, -1], 'generators': [129, 170], 'label': '256.30836.64.di1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.h1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878787
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.b1', '32.eb1.c1', '32.fe1.a1', '32.gb1.d1', '32.gk1.f1', '32.gt1.g1', '32.hb1.d1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.cs1', '32.hk1.ct1'], 'contains': ['128.h1.b1', '128.i1.c1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2234, -1, 8978, -1, 2234, -1], 'generators': [33, 170], 'label': '256.30836.64.di1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.i1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878788
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.b1', '32.eb1.d1', '32.fe1.b1', '32.gb1.c1', '32.gk1.c1', '32.gt1.h1', '32.hb1.d1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.cy1', '32.hk1.cz1', '32.hk1.da1', '32.hk1.db1'], 'contains': ['128.h1.b1', '128.i1.d1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2854, -1, 8978, -1, 2852, -1], 'generators': [161, 170], 'label': '256.30836.64.di1.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.j1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878789
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.c1', '32.eb1.b1', '32.fe1.d1', '32.gb1.d1', '32.gk1.g1', '32.gt1.f1', '32.hb1.a1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.di1', '32.hk1.dj1'], 'contains': ['128.h1.c1', '128.i1.b1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2994, -1, 8978, -1, 2991, -1], 'generators': [129, 34], 'label': '256.30836.64.di1.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.k1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878790
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.d1', '32.eb1.a1', '32.fe1.c1', '32.gb1.d1', '32.gk1.g1', '32.gt1.g1', '32.hb1.b1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dq1', '32.hk1.dr1'], 'contains': ['128.h1.c1', '128.i1.c1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2068, -1, 8978, -1, 2068, -1], 'generators': [33, 34], 'label': '256.30836.64.di1.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.l1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878791
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.d1', '32.eb1.b1', '32.fe1.d1', '32.gb1.c1', '32.gk1.d1', '32.gt1.h1', '32.hb1.b1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.dw1', '32.hk1.dx1', '32.hk1.dy1', '32.hk1.dz1'], 'contains': ['128.h1.c1', '128.i1.d1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2730, -1, 8978, -1, 2727, -1], 'generators': [161, 34], 'label': '256.30836.64.di1.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.m1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878792
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.c1', '32.eb1.d1', '32.fe1.d1', '32.gb1.b1', '32.gk1.h1', '32.gt1.b1', '32.hb1.c1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.eg1', '32.hk1.eh1'], 'contains': ['128.h1.d1', '128.i1.b1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2660, -1, 8978, -1, 2658, -1], 'generators': [129, 138], 'label': '256.30836.64.di1.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.n1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878793
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.d1', '32.eb1.c1', '32.fe1.c1', '32.gb1.b1', '32.gk1.h1', '32.gt1.c1', '32.hb1.d1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.em1', '32.hk1.en1', '32.hk1.eo1', '32.hk1.ep1'], 'contains': ['128.h1.d1', '128.i1.c1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 1354, -1, 8978, -1, 1352, -1], 'generators': [33, 138], 'label': '256.30836.64.di1.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.o1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878794
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.di1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ci1.d1', '32.eb1.d1', '32.fe1.d1', '32.gb1.a1', '32.gk1.e1', '32.gt1.d1', '32.hb1.d1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.es1', '32.hk1.et1', '32.hk1.eu1', '32.hk1.ev1', '32.hk1.ew1', '32.hk1.ex1'], 'contains': ['128.h1.d1', '128.i1.d1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2924, -1, 8978, -1, 2922, -1], 'generators': [161, 138], 'label': '256.30836.64.di1.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.di1.p1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.di1.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879168
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gn1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bq1.a1'], 'contains': ['16.bf1.d1', '16.ea1.b1', '16.ec1.b1', '16.eg1.b1', '16.eh1.b1', '16.ek1.a1', '16.el1.a1'], 'core': '16.bf1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9496, -1, 9249, -1, 9501, -1, 9241, -1], 'generators': [33, 38, 64], 'label': '256.30836.8.gn1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '8.gn1.d1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gn1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878795
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ep1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.k1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.dm1.a1', '64.dm1.a2', '64.dm1.g1', '64.dm1.g2', '64.dm1.c1', '64.dm1.c2', '64.dm1.e1', '64.dm1.e2', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dn1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.b2', '64.dn1.c1', '64.dn1.c2', '64.dn1.d1', '64.dn1.d2', '64.dn1.e2', '64.dn1.e1', '64.dn1.f2', '64.dn1.f1', '64.dn1.g2', '64.dn1.g1', '64.dn1.h2', '64.dn1.h1', '64.dj1.a1', '64.dj1.m1', '64.dj1.n1', '64.dj1.b1', '64.dj1.e1', '64.dj1.i1', '64.dj1.j1', '64.dj1.f1', '64.dj1.o1', '64.dj1.c1', '64.dj1.d1', '64.dj1.p1', '64.dj1.k1', '64.dj1.g1', '64.dj1.h1', '64.dj1.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.o1.a1', '2.p1.a1', '2.be1.a1'], 'contains': ['8.ch1.a1', '8.cj1.a1', '8.co1.a1', '8.ep1.a1', '8.et1.a1', '8.fb1.a1', '8.fp1.a1'], 'core': '4.ep1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5772, 3628, 5734, 6299, 5775, 3627, 5729, 6313], 'generators': [65, 82, 68], 'label': '256.30836.4.ep1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ep1.a1', 'normal_contained_in': ['2.p1.a1', '2.o1.a1', '2.be1.a1'], 'normal_contains': ['8.ch1.a1', '8.cj1.a1', '8.co1.a1', '8.ep1.a1', '8.et1.a1', '8.fb1.a1', '8.fp1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ep1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ep1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878796
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.a1', '32.ec1.a1', '32.ff1.a1', '32.gc1.a1', '32.gl1.a1', '32.gu1.a1', '32.hc1.a1', '32.hk1.a1', '32.hk1.b1', '32.hk1.i1', '32.hk1.j1', '32.hk1.q1', '32.hk1.r1', '32.hk1.y1', '32.hk1.z1'], 'contains': ['128.h1.a1', '128.j1.a1', '128.k1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 1929, -1, 9138, -1, 1929, -1], 'generators': [2, 4], 'label': '256.30836.64.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878797
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.b1', '32.ec1.a1', '32.ff1.a2', '32.gc1.a1', '32.gl1.a1', '32.gu1.b1', '32.hc1.b1', '32.hk1.c1', '32.hk1.d1', '32.hk1.k1', '32.hk1.l1', '32.hk1.s1', '32.hk1.t1', '32.hk1.ba1', '32.hk1.bb1'], 'contains': ['128.h1.a1', '128.j1.a1', '128.k1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 1789, -1, 9138, -1, 1790, -1], 'generators': [42, 4], 'label': '256.30836.64.dj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878798
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.c1', '32.ec1.b1', '32.ff1.a2', '32.gc1.b1', '32.gl1.a1', '32.gu1.a1', '32.hc1.a1', '32.hk1.e1', '32.hk1.f1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.bc1', '32.hk1.bd1'], 'contains': ['128.h1.a1', '128.j1.b1', '128.k1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2813, -1, 9138, -1, 2811, -1], 'generators': [2, 140], 'label': '256.30836.64.dj1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.c1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878799
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.d1', '32.ec1.b1', '32.ff1.a1', '32.gc1.b1', '32.gl1.a1', '32.gu1.b1', '32.hc1.b1', '32.hk1.g1', '32.hk1.h1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.be1', '32.hk1.bf1'], 'contains': ['128.h1.a1', '128.j1.b1', '128.k1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2633, -1, 9138, -1, 2630, -1], 'generators': [42, 140], 'label': '256.30836.64.dj1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.d1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878800
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.a1', '32.ec1.c1', '32.ff1.a2', '32.gc1.c1', '32.gl1.b1', '32.gu1.c1', '32.hc1.c1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.cu1', '32.hk1.cv1'], 'contains': ['128.h1.b1', '128.j1.a1', '128.k1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 1985, -1, 9138, -1, 1984, -1], 'generators': [130, 4], 'label': '256.30836.64.dj1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.e1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878801
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.b1', '32.ec1.c1', '32.ff1.a1', '32.gc1.c1', '32.gl1.b1', '32.gu1.d1', '32.hc1.d1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.cw1', '32.hk1.cx1'], 'contains': ['128.h1.b1', '128.j1.a1', '128.k1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 1957, -1, 9138, -1, 1957, -1], 'generators': [170, 4], 'label': '256.30836.64.dj1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.f1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878802
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.c1', '32.ec1.d1', '32.ff1.a1', '32.gc1.d1', '32.gl1.b1', '32.gu1.c1', '32.hc1.c1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.cy1', '32.hk1.cz1'], 'contains': ['128.h1.b1', '128.j1.b1', '128.k1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2757, -1, 9138, -1, 2755, -1], 'generators': [130, 140], 'label': '256.30836.64.dj1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.g1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878803
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.d1', '32.ec1.d1', '32.ff1.a2', '32.gc1.d1', '32.gl1.b1', '32.gu1.d1', '32.hc1.d1', '32.hk1.bm1', '32.hk1.bn1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.da1', '32.hk1.db1'], 'contains': ['128.h1.b1', '128.j1.b1', '128.k1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2827, -1, 9138, -1, 2824, -1], 'generators': [170, 140], 'label': '256.30836.64.dj1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.h1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878804
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.e1', '32.ec1.a1', '32.ff1.b2', '32.gc1.c1', '32.gl1.c1', '32.gu1.c1', '32.hc1.a1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.ds1', '32.hk1.dt1'], 'contains': ['128.h1.c1', '128.j1.a1', '128.k1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 1525, -1, 9138, -1, 1526, -1], 'generators': [10, 4], 'label': '256.30836.64.dj1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.i1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878805
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.f1', '32.ec1.a1', '32.ff1.b1', '32.gc1.c1', '32.gl1.c1', '32.gu1.d1', '32.hc1.b1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.du1', '32.hk1.dv1'], 'contains': ['128.h1.c1', '128.j1.a1', '128.k1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 1498, -1, 9138, -1, 1498, -1], 'generators': [34, 4], 'label': '256.30836.64.dj1.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.j1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879429
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ev1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.gq1.a1', '8.gs1.a1'], 'contains': ['32.g1.a1', '32.cx1.a1', '32.de1.a1', '32.gy1.a1', '32.gy1.c1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1908, -1, 5822, -1, 1909, -1, 5817, -1], 'generators': [1, 82, 32], 'label': '256.30836.16.ev1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.q1.a1', 'old_label': '16.ev1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ev1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878806
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.eq1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.f1', '64.dn1.h2', '64.dn1.e1', '64.dn1.e2', '64.dn1.h1', '64.dm1.a1', '64.dm1.e2', '64.dm1.e1', '64.dm1.a2', '64.dm1.c1', '64.dm1.g2', '64.dm1.g1', '64.dm1.c2', '64.dm1.b1', '64.dm1.f2', '64.dm1.f1', '64.dm1.b2', '64.dm1.d1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.g1', '64.dj1.d1', '64.dj1.p1', '64.dj1.k1', '64.dj1.c1', '64.dj1.h1', '64.dj1.l1', '64.dj1.o1'], 'conjugacy_class_count': 1, 'contained_in': ['2.o1.a1', '2.q1.a1', '2.bd1.a1'], 'contains': ['8.ci1.a1', '8.ck1.a1', '8.co1.a1', '8.eu1.a1', '8.ex1.a1', '8.ff1.a1', '8.fq1.a1'], 'core': '4.eq1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4784, 5451, 7304, 8013, 4786, 5449, 7298, 8030], 'generators': [17, 82, 20], 'label': '256.30836.4.eq1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.eq1.a1', 'normal_contained_in': ['2.q1.a1', '2.o1.a1', '2.bd1.a1'], 'normal_contains': ['8.ck1.a1', '8.ci1.a1', '8.co1.a1', '8.eu1.a1', '8.ff1.a1', '8.ex1.a1', '8.fq1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.eq1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.eq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878807
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.g1', '32.ec1.b1', '32.ff1.b1', '32.gc1.d1', '32.gl1.c1', '32.gu1.c1', '32.hc1.a1', '32.hk1.bs1', '32.hk1.bt1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dw1', '32.hk1.dx1'], 'contains': ['128.h1.c1', '128.j1.b1', '128.k1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2716, -1, 9138, -1, 2713, -1], 'generators': [10, 140], 'label': '256.30836.64.dj1.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.k1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878808
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.h1', '32.ec1.b1', '32.ff1.b2', '32.gc1.d1', '32.gl1.c1', '32.gu1.d1', '32.hc1.b1', '32.hk1.bu1', '32.hk1.bv1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.dy1', '32.hk1.dz1'], 'contains': ['128.h1.c1', '128.j1.b1', '128.k1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2702, -1, 9138, -1, 2699, -1], 'generators': [34, 140], 'label': '256.30836.64.dj1.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.l1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878809
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.e1', '32.ec1.c1', '32.ff1.b1', '32.gc1.a1', '32.gl1.d1', '32.gu1.a1', '32.hc1.c1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.eq1', '32.hk1.er1'], 'contains': ['128.h1.d1', '128.j1.a1', '128.k1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 1623, -1, 9138, -1, 1623, -1], 'generators': [138, 4], 'label': '256.30836.64.dj1.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.m1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878810
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.f1', '32.ec1.c1', '32.ff1.b2', '32.gc1.a1', '32.gl1.d1', '32.gu1.b1', '32.hc1.d1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.es1', '32.hk1.et1'], 'contains': ['128.h1.d1', '128.j1.a1', '128.k1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 1511, -1, 9138, -1, 1512, -1], 'generators': [162, 4], 'label': '256.30836.64.dj1.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.n1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878811
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.g1', '32.ec1.d1', '32.ff1.b2', '32.gc1.b1', '32.gl1.d1', '32.gu1.a1', '32.hc1.c1', '32.hk1.ca1', '32.hk1.cb1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.eu1', '32.hk1.ev1'], 'contains': ['128.h1.d1', '128.j1.b1', '128.k1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2646, -1, 9138, -1, 2644, -1], 'generators': [138, 140], 'label': '256.30836.64.dj1.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.o1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878812
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dj1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cj1.h1', '32.ec1.d1', '32.ff1.b1', '32.gc1.b1', '32.gl1.d1', '32.gu1.b1', '32.hc1.d1', '32.hk1.cc1', '32.hk1.cd1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.ew1', '32.hk1.ex1'], 'contains': ['128.h1.d1', '128.j1.b1', '128.k1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2500, -1, 9138, -1, 2505, -1], 'generators': [162, 140], 'label': '256.30836.64.dj1.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dj1.p1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dj1.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878813
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.a1', '32.ed1.a1', '32.fg1.a1', '32.gd1.a1', '32.gm1.a1', '32.gv1.a1', '32.hd1.a1', '32.hk1.a1', '32.hk1.e1', '32.hk1.i1', '32.hk1.m1', '32.hk1.s1', '32.hk1.w1', '32.hk1.ba1', '32.hk1.be1'], 'contains': ['128.h1.a1', '128.l1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 2868, -1, 9244, -1, 2866, -1], 'generators': [5, 2], 'label': '256.30836.64.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878814
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.b1', '32.ed1.a2', '32.fg1.a1', '32.gd1.a1', '32.gm1.a1', '32.gv1.b1', '32.hd1.b1', '32.hk1.c1', '32.hk1.g1', '32.hk1.k1', '32.hk1.o1', '32.hk1.q1', '32.hk1.u1', '32.hk1.y1', '32.hk1.bc1'], 'contains': ['128.h1.a1', '128.l1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 2429, -1, 9244, -1, 2429, -1], 'generators': [173, 2], 'label': '256.30836.64.dk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878815
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.a1', '32.ed1.a2', '32.fg1.b1', '32.gd1.b1', '32.gm1.a1', '32.gv1.a1', '32.hd1.c1', '32.hk1.b1', '32.hk1.f1', '32.hk1.j1', '32.hk1.n1', '32.hk1.t1', '32.hk1.x1', '32.hk1.bb1', '32.hk1.bf1'], 'contains': ['128.h1.a1', '128.l1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 1998, -1, 9244, -1, 1998, -1], 'generators': [141, 2], 'label': '256.30836.64.dk1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.c1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878816
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.b1', '32.ed1.a1', '32.fg1.b1', '32.gd1.b1', '32.gm1.a1', '32.gv1.b1', '32.hd1.d1', '32.hk1.d1', '32.hk1.h1', '32.hk1.l1', '32.hk1.p1', '32.hk1.r1', '32.hk1.v1', '32.hk1.z1', '32.hk1.bd1'], 'contains': ['128.h1.a1', '128.l1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 1693, -1, 9244, -1, 1693, -1], 'generators': [37, 2], 'label': '256.30836.64.dk1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.d1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879430
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ev1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.gq1.b1', '8.gs1.b1'], 'contains': ['32.g1.b1', '32.cx1.a1', '32.de1.a1', '32.gy1.b1', '32.gy1.d1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1908, -1, 5846, -1, 1909, -1, 5840, -1], 'generators': [129, 82, 32], 'label': '256.30836.16.ev1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.q1.a1', 'old_label': '16.ev1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ev1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878817
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.er1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.i1', '64.dj1.n1', '64.dj1.f1', '64.dj1.e1', '64.dj1.m1', '64.dj1.j1', '64.dj1.b1', '64.dj1.k1', '64.dj1.c1', '64.dj1.h1', '64.dj1.p1', '64.dj1.o1', '64.dj1.g1', '64.dj1.d1', '64.dj1.l1', '64.dm1.a1', '64.dm1.c2', '64.dm1.g1', '64.dm1.e2', '64.dm1.c1', '64.dm1.a2', '64.dm1.e1', '64.dm1.g2', '64.dm1.b2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dn1.a1', '64.dn1.c2', '64.dn1.b1', '64.dn1.d2', '64.dn1.c1', '64.dn1.a2', '64.dn1.d1', '64.dn1.b2', '64.dn1.e1', '64.dn1.g2', '64.dn1.f1', '64.dn1.h2', '64.dn1.g1', '64.dn1.e2', '64.dn1.h1', '64.dn1.f2', '64.di1.a1', '64.di1.b1', '64.di1.d1', '64.di1.c1', '64.di1.f1', '64.di1.k1', '64.di1.m1', '64.di1.l1', '64.di1.g1', '64.di1.n1', '64.di1.p1', '64.di1.o1', '64.di1.e1', '64.di1.h1', '64.di1.j1', '64.di1.i1'], 'conjugacy_class_count': 1, 'contained_in': ['2.o1.a1', '2.s1.a1', '2.bb1.a1'], 'contains': ['8.cj1.a1', '8.ck1.a1', '8.cm1.a1', '8.ez1.a1', '8.fa1.a1', '8.fe1.a1', '8.fx1.a1', '8.hf1.a1', '8.hf1.b1'], 'core': '4.er1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8318, 1631, 6717, 5171, 8322, 1630, 6711, 5183], 'generators': [5, 70, 80, 128], 'label': '256.30836.4.er1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.er1.a1', 'normal_contained_in': ['2.s1.a1', '2.o1.a1', '2.bb1.a1'], 'normal_contains': ['8.ck1.a1', '8.cj1.a1', '8.cm1.a1', '8.ez1.a1', '8.fe1.a1', '8.fa1.a1', '8.fx1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.er1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.er1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878818
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.a1', '32.ed1.b2', '32.fg1.a1', '32.gd1.c1', '32.gm1.b1', '32.gv1.c1', '32.hd1.e1', '32.hk1.bg1', '32.hk1.bk1', '32.hk1.ce1', '32.hk1.ci1', '32.hk1.co1', '32.hk1.cs1', '32.hk1.cw1', '32.hk1.da1'], 'contains': ['128.h1.b1', '128.l1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 2896, -1, 9244, -1, 2894, -1], 'generators': [173, 170], 'label': '256.30836.64.dk1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.e1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878819
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.b1', '32.ed1.b1', '32.fg1.a1', '32.gd1.c1', '32.gm1.b1', '32.gv1.d1', '32.hd1.f1', '32.hk1.bi1', '32.hk1.bm1', '32.hk1.cg1', '32.hk1.ck1', '32.hk1.cm1', '32.hk1.cq1', '32.hk1.cu1', '32.hk1.cy1'], 'contains': ['128.h1.b1', '128.l1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 2453, -1, 9244, -1, 2449, -1], 'generators': [5, 170], 'label': '256.30836.64.dk1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.f1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878820
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.a1', '32.ed1.b1', '32.fg1.b1', '32.gd1.d1', '32.gm1.b1', '32.gv1.c1', '32.hd1.g1', '32.hk1.bh1', '32.hk1.bl1', '32.hk1.cf1', '32.hk1.cj1', '32.hk1.cp1', '32.hk1.ct1', '32.hk1.cx1', '32.hk1.db1'], 'contains': ['128.h1.b1', '128.l1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 2026, -1, 9244, -1, 2026, -1], 'generators': [37, 170], 'label': '256.30836.64.dk1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.g1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878821
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.b1', '32.ed1.b2', '32.fg1.b1', '32.gd1.d1', '32.gm1.b1', '32.gv1.d1', '32.hd1.h1', '32.hk1.bj1', '32.hk1.bn1', '32.hk1.ch1', '32.hk1.cl1', '32.hk1.cn1', '32.hk1.cr1', '32.hk1.cv1', '32.hk1.cz1'], 'contains': ['128.h1.b1', '128.l1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 1901, -1, 9244, -1, 1901, -1], 'generators': [141, 170], 'label': '256.30836.64.dk1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.h1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878822
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.c1', '32.ed1.a2', '32.fg1.c1', '32.gd1.c1', '32.gm1.c1', '32.gv1.c1', '32.hd1.a1', '32.hk1.bo1', '32.hk1.bs1', '32.hk1.dc1', '32.hk1.dg1', '32.hk1.dm1', '32.hk1.dq1', '32.hk1.du1', '32.hk1.dy1'], 'contains': ['128.h1.c1', '128.l1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 2799, -1, 9244, -1, 2797, -1], 'generators': [173, 34], 'label': '256.30836.64.dk1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.i1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878823
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.d1', '32.ed1.a1', '32.fg1.c1', '32.gd1.c1', '32.gm1.c1', '32.gv1.d1', '32.hd1.b1', '32.hk1.bq1', '32.hk1.bu1', '32.hk1.de1', '32.hk1.di1', '32.hk1.dk1', '32.hk1.do1', '32.hk1.ds1', '32.hk1.dw1'], 'contains': ['128.h1.c1', '128.l1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 2304, -1, 9244, -1, 2304, -1], 'generators': [5, 34], 'label': '256.30836.64.dk1.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.j1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878824
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.c1', '32.ed1.a1', '32.fg1.d1', '32.gd1.d1', '32.gm1.c1', '32.gv1.c1', '32.hd1.c1', '32.hk1.bp1', '32.hk1.bt1', '32.hk1.dd1', '32.hk1.dh1', '32.hk1.dn1', '32.hk1.dr1', '32.hk1.dv1', '32.hk1.dz1'], 'contains': ['128.h1.c1', '128.l1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 1637, -1, 9244, -1, 1637, -1], 'generators': [37, 34], 'label': '256.30836.64.dk1.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.k1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878825
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.d1', '32.ed1.a2', '32.fg1.d1', '32.gd1.d1', '32.gm1.c1', '32.gv1.d1', '32.hd1.d1', '32.hk1.br1', '32.hk1.bv1', '32.hk1.df1', '32.hk1.dj1', '32.hk1.dl1', '32.hk1.dp1', '32.hk1.dt1', '32.hk1.dx1'], 'contains': ['128.h1.c1', '128.l1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 1340, -1, 9244, -1, 1339, -1], 'generators': [141, 34], 'label': '256.30836.64.dk1.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.l1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878826
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.c1', '32.ed1.b1', '32.fg1.c1', '32.gd1.a1', '32.gm1.d1', '32.gv1.a1', '32.hd1.e1', '32.hk1.bw1', '32.hk1.ca1', '32.hk1.ea1', '32.hk1.ee1', '32.hk1.ek1', '32.hk1.eo1', '32.hk1.es1', '32.hk1.ew1'], 'contains': ['128.h1.d1', '128.l1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 2785, -1, 9244, -1, 2783, -1], 'generators': [5, 138], 'label': '256.30836.64.dk1.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.m1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878827
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.d1', '32.ed1.b2', '32.fg1.c1', '32.gd1.a1', '32.gm1.d1', '32.gv1.b1', '32.hd1.f1', '32.hk1.by1', '32.hk1.cc1', '32.hk1.ec1', '32.hk1.eg1', '32.hk1.ei1', '32.hk1.em1', '32.hk1.eq1', '32.hk1.eu1'], 'contains': ['128.h1.d1', '128.l1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 2290, -1, 9244, -1, 2290, -1], 'generators': [173, 138], 'label': '256.30836.64.dk1.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.n1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879431
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ew1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '8.gp1.a1', '8.gs1.a1'], 'contains': ['32.g1.a1', '32.cy1.a1', '32.da1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1409, -1, 7753, -1, 1410, -1, 7747, -1], 'generators': [1, 16], 'label': '256.30836.16.ew1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.ew1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ew1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 30878828
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.es1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.p1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.f1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2', '64.dn1.e1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2', '64.dn1.g1', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.d1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.m1.a1', '2.s1.a1', '2.bd1.a1'], 'contains': ['8.ck1.a1', '8.cl1.a1', '8.cn1.a1', '8.fd1.a1', '8.fg1.a1', '8.fk1.a1', '8.fs1.a1'], 'core': '4.es1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4695, 9392, 8701, 2408, 4698, 9389, 8694, 2414], 'generators': [81, 18, 84], 'label': '256.30836.4.es1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.es1.a1', 'normal_contained_in': ['2.s1.a1', '2.m1.a1', '2.bd1.a1'], 'normal_contains': ['8.ck1.a1', '8.cl1.a1', '8.cn1.a1', '8.fd1.a1', '8.fg1.a1', '8.fk1.a1', '8.fs1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.es1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.es1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878829
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.c1', '32.ed1.b2', '32.fg1.d1', '32.gd1.b1', '32.gm1.d1', '32.gv1.a1', '32.hd1.g1', '32.hk1.bx1', '32.hk1.cb1', '32.hk1.eb1', '32.hk1.ef1', '32.hk1.el1', '32.hk1.ep1', '32.hk1.et1', '32.hk1.ex1'], 'contains': ['128.h1.d1', '128.l1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 1776, -1, 9244, -1, 1776, -1], 'generators': [141, 138], 'label': '256.30836.64.dk1.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.o1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878830
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dk1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.ck1.d1', '32.ed1.b1', '32.fg1.d1', '32.gd1.b1', '32.gm1.d1', '32.gv1.b1', '32.hd1.h1', '32.hk1.bz1', '32.hk1.cd1', '32.hk1.ed1', '32.hk1.eh1', '32.hk1.ej1', '32.hk1.en1', '32.hk1.er1', '32.hk1.ev1'], 'contains': ['128.h1.d1', '128.l1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 1400, -1, 9244, -1, 1401, -1], 'generators': [37, 138], 'label': '256.30836.64.dk1.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dk1.p1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dk1.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878831
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.a1', '32.ef1.a1', '32.fi1.a1', '32.gf1.a1', '32.gp1.a1', '32.gw1.a1', '32.he1.a1', '32.hk1.a1', '32.hk1.c1', '32.hk1.bg1', '32.hk1.bi1', '32.hk1.bo1', '32.hk1.bq1', '32.hk1.bw1', '32.hk1.by1'], 'contains': ['128.i1.a1', '128.j1.a1', '128.l1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 1414, -1, 9164, -1, 1415, -1], 'generators': [1, 4], 'label': '256.30836.64.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878832
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.a1', '32.ef1.a1', '32.fi1.b1', '32.gf1.b1', '32.gp1.a2', '32.gw1.a1', '32.he1.b1', '32.hk1.b1', '32.hk1.d1', '32.hk1.bh1', '32.hk1.bj1', '32.hk1.bp1', '32.hk1.br1', '32.hk1.bx1', '32.hk1.bz1'], 'contains': ['128.i1.a1', '128.j1.a1', '128.l1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 645, -1, 9164, -1, 644, -1], 'generators': [137, 4], 'label': '256.30836.64.dl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878833
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.b1', '32.ef1.b1', '32.fi1.a1', '32.gf1.c1', '32.gp1.a2', '32.gw1.a1', '32.he1.a1', '32.hk1.e1', '32.hk1.g1', '32.hk1.bk1', '32.hk1.bm1', '32.hk1.bs1', '32.hk1.bu1', '32.hk1.ca1', '32.hk1.cc1'], 'contains': ['128.i1.a1', '128.j1.b1', '128.l1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 2192, -1, 9164, -1, 2193, -1], 'generators': [137, 140], 'label': '256.30836.64.dl1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.c1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878834
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.b1', '32.ef1.b1', '32.fi1.b1', '32.gf1.d1', '32.gp1.a1', '32.gw1.a1', '32.he1.b1', '32.hk1.f1', '32.hk1.h1', '32.hk1.bl1', '32.hk1.bn1', '32.hk1.bt1', '32.hk1.bv1', '32.hk1.cb1', '32.hk1.cd1'], 'contains': ['128.i1.a1', '128.j1.b1', '128.l1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 1236, -1, 9164, -1, 1234, -1], 'generators': [1, 140], 'label': '256.30836.64.dl1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.d1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878835
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.a1', '32.ef1.c1', '32.fi1.c1', '32.gf1.e1', '32.gp1.b2', '32.gw1.b1', '32.he1.a1', '32.hk1.i1', '32.hk1.k1', '32.hk1.ce1', '32.hk1.cg1', '32.hk1.dc1', '32.hk1.de1', '32.hk1.ea1', '32.hk1.ec1'], 'contains': ['128.i1.b1', '128.j1.a1', '128.l1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 2179, -1, 9164, -1, 2179, -1], 'generators': [9, 4], 'label': '256.30836.64.dl1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.e1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878836
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.a1', '32.ef1.c1', '32.fi1.d1', '32.gf1.f1', '32.gp1.b1', '32.gw1.b1', '32.he1.b1', '32.hk1.j1', '32.hk1.l1', '32.hk1.cf1', '32.hk1.ch1', '32.hk1.dd1', '32.hk1.df1', '32.hk1.eb1', '32.hk1.ed1'], 'contains': ['128.i1.b1', '128.j1.a1', '128.l1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 1381, -1, 9164, -1, 1380, -1], 'generators': [129, 4], 'label': '256.30836.64.dl1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.f1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878837
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.b1', '32.ef1.d1', '32.fi1.c1', '32.gf1.g1', '32.gp1.b1', '32.gw1.b1', '32.he1.a1', '32.hk1.m1', '32.hk1.o1', '32.hk1.ci1', '32.hk1.ck1', '32.hk1.dg1', '32.hk1.di1', '32.hk1.ee1', '32.hk1.eg1'], 'contains': ['128.i1.b1', '128.j1.b1', '128.l1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 2980, -1, 9164, -1, 2977, -1], 'generators': [129, 140], 'label': '256.30836.64.dl1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.g1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878838
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.b1', '32.ef1.d1', '32.fi1.d1', '32.gf1.h1', '32.gp1.b2', '32.gw1.b1', '32.he1.b1', '32.hk1.n1', '32.hk1.p1', '32.hk1.cj1', '32.hk1.cl1', '32.hk1.dh1', '32.hk1.dj1', '32.hk1.ef1', '32.hk1.eh1'], 'contains': ['128.i1.b1', '128.j1.b1', '128.l1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 2332, -1, 9164, -1, 2331, -1], 'generators': [9, 140], 'label': '256.30836.64.dl1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.h1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879432
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ew1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.t1.a1', '8.gp1.b1', '8.gs1.b1'], 'contains': ['32.g1.b1', '32.cy1.a1', '32.da1.a1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1409, -1, 7773, -1, 1410, -1, 7766, -1], 'generators': [129, 16], 'label': '256.30836.16.ew1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.ew1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ew1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878839
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.et1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.d1', '64.dl1.a1', '64.dl1.b1', '64.dl1.j1', '64.dl1.i1', '64.dl1.f1', '64.dl1.e1', '64.dl1.m1', '64.dl1.n1', '64.dl1.d1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.o1', '64.dk1.m1', '64.dk1.n1', '64.dk1.p1', '64.dk1.k1', '64.dk1.i1', '64.dk1.j1', '64.dk1.l1', '64.dk1.e1', '64.dk1.g1', '64.dk1.h1', '64.dk1.f1', '64.dm1.a1', '64.dm1.a2', '64.dm1.e1', '64.dm1.e2', '64.dm1.c1', '64.dm1.c2', '64.dm1.g1', '64.dm1.g2', '64.dm1.b1', '64.dm1.b2', '64.dm1.f1', '64.dm1.f2', '64.dm1.d1', '64.dm1.d2', '64.dm1.h1', '64.dm1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.x1.a1', '2.bb1.a1'], 'contains': ['8.cp1.a1', '8.cq1.a1', '8.cr1.a1', '8.dn1.a1', '8.do1.a1', '8.dv1.a1', '8.fe1.a1'], 'core': '4.et1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3536, 3354, 7885, 5372, 3538, 3353, 7878, 5383], 'generators': [3, 16, 64], 'label': '256.30836.4.et1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.et1.a1', 'normal_contained_in': ['2.d1.a1', '2.x1.a1', '2.bb1.a1'], 'normal_contains': ['8.cp1.a1', '8.cq1.a1', '8.cr1.a1', '8.do1.a1', '8.dn1.a1', '8.fe1.a1', '8.dv1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.et1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.et1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878840
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.c1', '32.ef1.a1', '32.fi1.a1', '32.gf1.e1', '32.gp1.b1', '32.gw1.c1', '32.he1.c1', '32.hk1.q1', '32.hk1.s1', '32.hk1.cm1', '32.hk1.co1', '32.hk1.dk1', '32.hk1.dm1', '32.hk1.ei1', '32.hk1.ek1'], 'contains': ['128.i1.c1', '128.j1.a1', '128.l1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 1470, -1, 9164, -1, 1470, -1], 'generators': [169, 4], 'label': '256.30836.64.dl1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.i1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878841
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.c1', '32.ef1.a1', '32.fi1.b1', '32.gf1.f1', '32.gp1.b2', '32.gw1.c1', '32.he1.d1', '32.hk1.r1', '32.hk1.t1', '32.hk1.cn1', '32.hk1.cp1', '32.hk1.dl1', '32.hk1.dn1', '32.hk1.ej1', '32.hk1.el1'], 'contains': ['128.i1.c1', '128.j1.a1', '128.l1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 725, -1, 9164, -1, 700, -1], 'generators': [33, 4], 'label': '256.30836.64.dl1.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.j1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878842
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.d1', '32.ef1.b1', '32.fi1.a1', '32.gf1.g1', '32.gp1.b2', '32.gw1.c1', '32.he1.c1', '32.hk1.u1', '32.hk1.w1', '32.hk1.cq1', '32.hk1.cs1', '32.hk1.do1', '32.hk1.dq1', '32.hk1.em1', '32.hk1.eo1'], 'contains': ['128.i1.c1', '128.j1.b1', '128.l1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 2346, -1, 9164, -1, 2345, -1], 'generators': [33, 140], 'label': '256.30836.64.dl1.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.k1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878843
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.d1', '32.ef1.b1', '32.fi1.b1', '32.gf1.h1', '32.gp1.b1', '32.gw1.c1', '32.he1.d1', '32.hk1.v1', '32.hk1.x1', '32.hk1.cr1', '32.hk1.ct1', '32.hk1.dp1', '32.hk1.dr1', '32.hk1.en1', '32.hk1.ep1'], 'contains': ['128.i1.c1', '128.j1.b1', '128.l1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 1428, -1, 9164, -1, 1429, -1], 'generators': [169, 140], 'label': '256.30836.64.dl1.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.l1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878844
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.c1', '32.ef1.c1', '32.fi1.c1', '32.gf1.a1', '32.gp1.a2', '32.gw1.d1', '32.he1.c1', '32.hk1.y1', '32.hk1.ba1', '32.hk1.cu1', '32.hk1.cw1', '32.hk1.ds1', '32.hk1.du1', '32.hk1.eq1', '32.hk1.es1'], 'contains': ['128.i1.d1', '128.j1.a1', '128.l1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 2318, -1, 9164, -1, 2318, -1], 'generators': [161, 4], 'label': '256.30836.64.dl1.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.m1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878845
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.c1', '32.ef1.c1', '32.fi1.d1', '32.gf1.b1', '32.gp1.a1', '32.gw1.d1', '32.he1.d1', '32.hk1.z1', '32.hk1.bb1', '32.hk1.cv1', '32.hk1.cx1', '32.hk1.dt1', '32.hk1.dv1', '32.hk1.er1', '32.hk1.et1'], 'contains': ['128.i1.d1', '128.j1.a1', '128.l1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 1368, -1, 9164, -1, 1366, -1], 'generators': [41, 4], 'label': '256.30836.64.dl1.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.n1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878846
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.d1', '32.ef1.d1', '32.fi1.c1', '32.gf1.c1', '32.gp1.a1', '32.gw1.d1', '32.he1.c1', '32.hk1.bc1', '32.hk1.be1', '32.hk1.cy1', '32.hk1.da1', '32.hk1.dw1', '32.hk1.dy1', '32.hk1.eu1', '32.hk1.ew1'], 'contains': ['128.i1.d1', '128.j1.b1', '128.l1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 2966, -1, 9164, -1, 2963, -1], 'generators': [41, 140], 'label': '256.30836.64.dl1.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.o1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878847
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dl1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cl1.d1', '32.ef1.d1', '32.fi1.d1', '32.gf1.d1', '32.gp1.a2', '32.gw1.d1', '32.he1.d1', '32.hk1.bd1', '32.hk1.bf1', '32.hk1.cz1', '32.hk1.db1', '32.hk1.dx1', '32.hk1.dz1', '32.hk1.ev1', '32.hk1.ex1'], 'contains': ['128.i1.d1', '128.j1.b1', '128.l1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9160, -1, 2220, -1, 9164, -1, 2220, -1], 'generators': [161, 140], 'label': '256.30836.64.dl1.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dl1.p1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dl1.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878848
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.a1', '32.eg1.a1', '32.fj1.a1', '32.gg1.a1', '32.gq1.a1', '32.gx1.a1', '32.hf1.a1', '32.hk1.a1', '32.hk1.f1', '32.hk1.bh1', '32.hk1.bk1', '32.hk1.bp1', '32.hk1.bs1', '32.hk1.bw1', '32.hk1.cb1'], 'contains': ['128.i1.a1', '128.k1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1803, -1, 9218, -1, 1804, -1], 'generators': [1, 6], 'label': '256.30836.64.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878849
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.a1', '32.eg1.a2', '32.fj1.a2', '32.gg1.a2', '32.gq1.a2', '32.gx1.a1', '32.hf1.a1', '32.hk1.b1', '32.hk1.e1', '32.hk1.bg1', '32.hk1.bl1', '32.hk1.bo1', '32.hk1.bt1', '32.hk1.bx1', '32.hk1.ca1'], 'contains': ['128.i1.a1', '128.k1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1568, -1, 9218, -1, 1568, -1], 'generators': [137, 6], 'label': '256.30836.64.dm1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.a2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879433
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ex1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '8.gr1.a1', '8.gs1.a1'], 'contains': ['32.g1.a1', '32.cz1.a1', '32.db1.a1', '32.fk1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1709, -1, 8322, -1, 1710, -1, 8315, -1], 'generators': [1, 66, 32], 'label': '256.30836.16.ex1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.ex1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ex1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878850
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.eu1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.d1', '64.dl1.o1', '64.dl1.p1', '64.dl1.c1', '64.dl1.g1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.d1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.m1', '64.dk1.p1', '64.dk1.n1', '64.dk1.o1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.e1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.dk1.i1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.y1.a1', '2.bc1.a1'], 'contains': ['8.cp1.a1', '8.cs1.a1', '8.ct1.a1', '8.dp1.a1', '8.dq1.a1', '8.ek1.a1', '8.eo1.a1'], 'core': '4.eu1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1898, 3101, 7751, 4635, 1899, 3100, 7745, 4645], 'generators': [65, 66, 80], 'label': '256.30836.4.eu1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.eu1.a1', 'normal_contained_in': ['2.d1.a1', '2.y1.a1', '2.bc1.a1'], 'normal_contains': ['8.cp1.a1', '8.cs1.a1', '8.ct1.a1', '8.dq1.a1', '8.dp1.a1', '8.eo1.a1', '8.ek1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.eu1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.eu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878851
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.b1', '32.eg1.a1', '32.fj1.a1', '32.gg1.a2', '32.gq1.a2', '32.gx1.b1', '32.hf1.b1', '32.hk1.d1', '32.hk1.g1', '32.hk1.bi1', '32.hk1.bn1', '32.hk1.bq1', '32.hk1.bv1', '32.hk1.bz1', '32.hk1.cc1'], 'contains': ['128.i1.a1', '128.k1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1326, -1, 9218, -1, 1325, -1], 'generators': [1, 38], 'label': '256.30836.64.dm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878852
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.b1', '32.eg1.a2', '32.fj1.a2', '32.gg1.a1', '32.gq1.a1', '32.gx1.b1', '32.hf1.b1', '32.hk1.c1', '32.hk1.h1', '32.hk1.bj1', '32.hk1.bm1', '32.hk1.br1', '32.hk1.bu1', '32.hk1.by1', '32.hk1.cd1'], 'contains': ['128.i1.a1', '128.k1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1456, -1, 9218, -1, 1457, -1], 'generators': [137, 38], 'label': '256.30836.64.dm1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.b2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878853
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.a1', '32.eg1.b1', '32.fj1.b2', '32.gg1.b2', '32.gq1.b1', '32.gx1.c1', '32.hf1.a1', '32.hk1.j1', '32.hk1.m1', '32.hk1.ce1', '32.hk1.cj1', '32.hk1.dc1', '32.hk1.dh1', '32.hk1.eb1', '32.hk1.ee1'], 'contains': ['128.i1.b1', '128.k1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 2771, -1, 9218, -1, 2769, -1], 'generators': [129, 6], 'label': '256.30836.64.dm1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.c1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878854
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.a1', '32.eg1.b2', '32.fj1.b1', '32.gg1.b1', '32.gq1.b2', '32.gx1.c1', '32.hf1.a1', '32.hk1.i1', '32.hk1.n1', '32.hk1.cf1', '32.hk1.ci1', '32.hk1.dd1', '32.hk1.dg1', '32.hk1.ea1', '32.hk1.ef1'], 'contains': ['128.i1.b1', '128.k1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 2514, -1, 9218, -1, 2519, -1], 'generators': [9, 6], 'label': '256.30836.64.dm1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.c2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878855
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.b1', '32.eg1.b1', '32.fj1.b2', '32.gg1.b1', '32.gq1.b2', '32.gx1.d1', '32.hf1.b1', '32.hk1.k1', '32.hk1.p1', '32.hk1.ch1', '32.hk1.ck1', '32.hk1.df1', '32.hk1.di1', '32.hk1.ec1', '32.hk1.eh1'], 'contains': ['128.i1.b1', '128.k1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 2040, -1, 9218, -1, 2040, -1], 'generators': [129, 38], 'label': '256.30836.64.dm1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.d1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878856
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.b1', '32.eg1.b2', '32.fj1.b1', '32.gg1.b2', '32.gq1.b1', '32.gx1.d1', '32.hf1.b1', '32.hk1.l1', '32.hk1.o1', '32.hk1.cg1', '32.hk1.cl1', '32.hk1.de1', '32.hk1.dj1', '32.hk1.ed1', '32.hk1.eg1'], 'contains': ['128.i1.b1', '128.k1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 2277, -1, 9218, -1, 2276, -1], 'generators': [9, 38], 'label': '256.30836.64.dm1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.d2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.d2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878857
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.c1', '32.eg1.a1', '32.fj1.a2', '32.gg1.b2', '32.gq1.b2', '32.gx1.e1', '32.hf1.c1', '32.hk1.r1', '32.hk1.u1', '32.hk1.cm1', '32.hk1.cr1', '32.hk1.dk1', '32.hk1.dp1', '32.hk1.ej1', '32.hk1.em1'], 'contains': ['128.i1.c1', '128.k1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1596, -1, 9218, -1, 1595, -1], 'generators': [33, 6], 'label': '256.30836.64.dm1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.e1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878858
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.c1', '32.eg1.a2', '32.fj1.a1', '32.gg1.b1', '32.gq1.b1', '32.gx1.e1', '32.hf1.c1', '32.hk1.q1', '32.hk1.v1', '32.hk1.cn1', '32.hk1.cq1', '32.hk1.dl1', '32.hk1.do1', '32.hk1.ei1', '32.hk1.en1'], 'contains': ['128.i1.c1', '128.k1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1442, -1, 9218, -1, 1443, -1], 'generators': [169, 6], 'label': '256.30836.64.dm1.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.e2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.e2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878859
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.d1', '32.eg1.a1', '32.fj1.a2', '32.gg1.b1', '32.gq1.b1', '32.gx1.f1', '32.hf1.d1', '32.hk1.s1', '32.hk1.x1', '32.hk1.cp1', '32.hk1.cs1', '32.hk1.dn1', '32.hk1.dq1', '32.hk1.ek1', '32.hk1.ep1'], 'contains': ['128.i1.c1', '128.k1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1651, -1, 9218, -1, 1651, -1], 'generators': [33, 38], 'label': '256.30836.64.dm1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.f1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878860
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.d1', '32.eg1.a2', '32.fj1.a1', '32.gg1.b2', '32.gq1.b2', '32.gx1.f1', '32.hf1.d1', '32.hk1.t1', '32.hk1.w1', '32.hk1.co1', '32.hk1.ct1', '32.hk1.dm1', '32.hk1.dr1', '32.hk1.el1', '32.hk1.eo1'], 'contains': ['128.i1.c1', '128.k1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 1859, -1, 9218, -1, 1859, -1], 'generators': [169, 38], 'label': '256.30836.64.dm1.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.f2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.f2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879434
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ex1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '8.gr1.b1', '8.gs1.b1'], 'contains': ['32.g1.b1', '32.cz1.a1', '32.db1.a1', '32.fk1.b1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1709, -1, 8349, -1, 1710, -1, 8342, -1], 'generators': [129, 66, 32], 'label': '256.30836.16.ex1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.ex1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ex1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878861
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ev1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.o1', '64.dl1.d1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.c1', '64.dl1.p1', '64.dk1.a1', '64.dk1.d1', '64.dk1.c1', '64.dk1.b1', '64.dk1.k1', '64.dk1.j1', '64.dk1.i1', '64.dk1.l1', '64.dk1.g1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.n1', '64.dj1.a1', '64.dj1.b1', '64.dj1.j1', '64.dj1.i1', '64.dj1.e1', '64.dj1.f1', '64.dj1.n1', '64.dj1.m1', '64.dj1.c1', '64.dj1.d1', '64.dj1.l1', '64.dj1.k1', '64.dj1.g1', '64.dj1.h1', '64.dj1.p1', '64.dj1.o1', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.h1', '64.dm1.b2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dm1.d2', '64.dm1.b1', '64.dm1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.y1.a1', '2.bb1.a1'], 'contains': ['8.cp1.a1', '8.cu1.a1', '8.cz1.a1', '8.dr1.a1', '8.du1.a1', '8.fa1.a1', '8.fm1.a1'], 'core': '4.ev1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5948, 2106, 5824, 7883, 5951, 2104, 5818, 7900], 'generators': [69, 70, 80], 'label': '256.30836.4.ev1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ev1.a1', 'normal_contained_in': ['2.e1.a1', '2.y1.a1', '2.bb1.a1'], 'normal_contains': ['8.cp1.a1', '8.cu1.a1', '8.cz1.a1', '8.dr1.a1', '8.du1.a1', '8.fa1.a1', '8.fm1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ev1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ev1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878862
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.c1', '32.eg1.b1', '32.fj1.b1', '32.gg1.a1', '32.gq1.a2', '32.gx1.g1', '32.hf1.c1', '32.hk1.y1', '32.hk1.bd1', '32.hk1.cv1', '32.hk1.cy1', '32.hk1.dt1', '32.hk1.dw1', '32.hk1.eq1', '32.hk1.ev1'], 'contains': ['128.i1.d1', '128.k1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 2415, -1, 9218, -1, 2415, -1], 'generators': [161, 6], 'label': '256.30836.64.dm1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.g1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878863
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.c1', '32.eg1.b2', '32.fj1.b2', '32.gg1.a2', '32.gq1.a1', '32.gx1.g1', '32.hf1.c1', '32.hk1.z1', '32.hk1.bc1', '32.hk1.cu1', '32.hk1.cz1', '32.hk1.ds1', '32.hk1.dx1', '32.hk1.er1', '32.hk1.eu1'], 'contains': ['128.i1.d1', '128.k1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 2095, -1, 9218, -1, 2095, -1], 'generators': [41, 6], 'label': '256.30836.64.dm1.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.g2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.g2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878864
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.d1', '32.eg1.b1', '32.fj1.b1', '32.gg1.a2', '32.gq1.a1', '32.gx1.h1', '32.hf1.d1', '32.hk1.bb1', '32.hk1.be1', '32.hk1.cw1', '32.hk1.db1', '32.hk1.du1', '32.hk1.dz1', '32.hk1.et1', '32.hk1.ew1'], 'contains': ['128.i1.d1', '128.k1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 2486, -1, 9218, -1, 2491, -1], 'generators': [161, 38], 'label': '256.30836.64.dm1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.h1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878865
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dm1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cm1.d1', '32.eg1.b2', '32.fj1.b2', '32.gg1.a1', '32.gq1.a2', '32.gx1.h1', '32.hf1.d1', '32.hk1.ba1', '32.hk1.bf1', '32.hk1.cx1', '32.hk1.da1', '32.hk1.dv1', '32.hk1.dy1', '32.hk1.es1', '32.hk1.ex1'], 'contains': ['128.i1.d1', '128.k1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 2688, -1, 9218, -1, 2686, -1], 'generators': [41, 38], 'label': '256.30836.64.dm1.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dm1.h2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dm1.h2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878866
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.a1', '32.ei1.a1', '32.fl1.a1', '32.gh1.a1', '32.gr1.a1', '32.gz1.a1', '32.hh1.a1', '32.hk1.a1', '32.hk1.bb1', '32.hk1.bx1', '32.hk1.cf1', '32.hk1.co1', '32.hk1.dc1', '32.hk1.dn1', '32.hk1.es1'], 'contains': ['128.j1.a1', '128.m1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 2012, -1, 9271, -1, 2012, -1], 'generators': [3, 4], 'label': '256.30836.64.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878867
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.a1', '32.ei1.a2', '32.fl1.a3', '32.gh1.a1', '32.gr1.a2', '32.gz1.a1', '32.hh1.a2', '32.hk1.b1', '32.hk1.ba1', '32.hk1.bw1', '32.hk1.ce1', '32.hk1.cp1', '32.hk1.dd1', '32.hk1.dm1', '32.hk1.et1'], 'contains': ['128.j1.a1', '128.m1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 1943, -1, 9271, -1, 1943, -1], 'generators': [139, 4], 'label': '256.30836.64.dn1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.a2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878868
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.b1', '32.ei1.a1', '32.fl1.a4', '32.gh1.a1', '32.gr1.a2', '32.gz1.b1', '32.hh1.b2', '32.hk1.d1', '32.hk1.y1', '32.hk1.by1', '32.hk1.cg1', '32.hk1.cn1', '32.hk1.df1', '32.hk1.dk1', '32.hk1.er1'], 'contains': ['128.j1.a1', '128.m1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 1484, -1, 9271, -1, 1484, -1], 'generators': [163, 4], 'label': '256.30836.64.dn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878869
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.b1', '32.ei1.a2', '32.fl1.a2', '32.gh1.a1', '32.gr1.a1', '32.gz1.b1', '32.hh1.b1', '32.hk1.c1', '32.hk1.z1', '32.hk1.bz1', '32.hk1.ch1', '32.hk1.cm1', '32.hk1.de1', '32.hk1.dl1', '32.hk1.eq1'], 'contains': ['128.j1.a1', '128.m1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 1873, -1, 9271, -1, 1873, -1], 'generators': [43, 4], 'label': '256.30836.64.dn1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.b2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878870
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.a1', '32.ei1.a1', '32.fl1.a2', '32.gh1.b1', '32.gr1.b1', '32.gz1.c1', '32.hh1.a2', '32.hk1.j1', '32.hk1.s1', '32.hk1.bg1', '32.hk1.bp1', '32.hk1.cx1', '32.hk1.du1', '32.hk1.ea1', '32.hk1.el1'], 'contains': ['128.j1.a1', '128.m1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 1094, -1, 9271, -1, 1075, -1], 'generators': [131, 4], 'label': '256.30836.64.dn1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.c1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878871
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.a1', '32.ei1.a2', '32.fl1.a4', '32.gh1.b1', '32.gr1.b2', '32.gz1.c1', '32.hh1.a1', '32.hk1.i1', '32.hk1.t1', '32.hk1.bh1', '32.hk1.bo1', '32.hk1.cw1', '32.hk1.dv1', '32.hk1.eb1', '32.hk1.ek1'], 'contains': ['128.j1.a1', '128.m1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 927, -1, 9271, -1, 924, -1], 'generators': [11, 4], 'label': '256.30836.64.dn1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.c2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879435
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ey1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.gr1.a1', '8.gt1.a1'], 'contains': ['32.g1.a1', '32.dc1.a1', '32.df1.a1', '32.eh1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1453, -1, 5893, -1, 1453, -1, 5888, -1], 'generators': [1, 68, 136], 'label': '256.30836.16.ey1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.w1.a1', 'old_label': '16.ey1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ey1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878872
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ew1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.b1', '64.dj1.j1', '64.dj1.i1', '64.dj1.e1', '64.dj1.f1', '64.dj1.n1', '64.dj1.m1', '64.dj1.d1', '64.dj1.c1', '64.dj1.k1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.o1', '64.dj1.p1', '64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.d1', '64.dl1.o1', '64.dl1.k1', '64.dl1.h1', '64.dl1.g1', '64.dl1.l1', '64.dl1.p1', '64.dl1.c1', '64.dk1.a1', '64.dk1.d1', '64.dk1.c1', '64.dk1.b1', '64.dk1.k1', '64.dk1.j1', '64.dk1.i1', '64.dk1.l1', '64.dk1.g1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.n1', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.b2', '64.dm1.h1', '64.dm1.f2', '64.dm1.d1', '64.dm1.d2', '64.dm1.f1', '64.dm1.h2', '64.dm1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.x1.a1', '2.bc1.a1'], 'contains': ['8.cp1.a1', '8.cv1.a1', '8.cw1.a1', '8.ds1.a1', '8.dt1.a1', '8.fi1.a1', '8.fl1.a1'], 'core': '4.ew1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5162, 2539, 7233, 3753, 5164, 2538, 7227, 3761], 'generators': [3, 68, 80], 'label': '256.30836.4.ew1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ew1.a1', 'normal_contained_in': ['2.e1.a1', '2.x1.a1', '2.bc1.a1'], 'normal_contains': ['8.cp1.a1', '8.cv1.a1', '8.cw1.a1', '8.ds1.a1', '8.dt1.a1', '8.fi1.a1', '8.fl1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ew1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ew1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878873
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.b1', '32.ei1.a1', '32.fl1.a3', '32.gh1.b1', '32.gr1.b2', '32.gz1.d1', '32.hh1.b1', '32.hk1.k1', '32.hk1.r1', '32.hk1.bj1', '32.hk1.bq1', '32.hk1.cu1', '32.hk1.dt1', '32.hk1.ed1', '32.hk1.ei1'], 'contains': ['128.j1.a1', '128.m1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 773, -1, 9271, -1, 793, -1], 'generators': [35, 4], 'label': '256.30836.64.dn1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.d1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878874
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.b1', '32.ei1.a2', '32.fl1.a1', '32.gh1.b1', '32.gr1.b1', '32.gz1.d1', '32.hh1.b2', '32.hk1.l1', '32.hk1.q1', '32.hk1.bi1', '32.hk1.br1', '32.hk1.cv1', '32.hk1.ds1', '32.hk1.ec1', '32.hk1.ej1'], 'contains': ['128.j1.a1', '128.m1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 867, -1, 9271, -1, 862, -1], 'generators': [171, 4], 'label': '256.30836.64.dn1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.d2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.d2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878875
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.c1', '32.ei1.b1', '32.fl1.a2', '32.gh1.c1', '32.gr1.a2', '32.gz1.a1', '32.hh1.a1', '32.hk1.e1', '32.hk1.bf1', '32.hk1.cb1', '32.hk1.cj1', '32.hk1.cs1', '32.hk1.dg1', '32.hk1.dr1', '32.hk1.ew1'], 'contains': ['128.j1.b1', '128.m1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 2882, -1, 9271, -1, 2880, -1], 'generators': [139, 140], 'label': '256.30836.64.dn1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.e1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878876
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.c1', '32.ei1.b2', '32.fl1.a4', '32.gh1.c1', '32.gr1.a1', '32.gz1.a1', '32.hh1.a2', '32.hk1.f1', '32.hk1.be1', '32.hk1.ca1', '32.hk1.ci1', '32.hk1.ct1', '32.hk1.dh1', '32.hk1.dq1', '32.hk1.ex1'], 'contains': ['128.j1.b1', '128.m1.a1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 2910, -1, 9271, -1, 2908, -1], 'generators': [3, 140], 'label': '256.30836.64.dn1.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.e2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.e2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878877
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.d1', '32.ei1.b1', '32.fl1.a3', '32.gh1.c1', '32.gr1.a1', '32.gz1.b1', '32.hh1.b2', '32.hk1.h1', '32.hk1.bc1', '32.hk1.cc1', '32.hk1.ck1', '32.hk1.cr1', '32.hk1.dj1', '32.hk1.do1', '32.hk1.ev1'], 'contains': ['128.j1.b1', '128.m1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 2387, -1, 9271, -1, 2387, -1], 'generators': [43, 140], 'label': '256.30836.64.dn1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.f1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878878
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.d1', '32.ei1.b2', '32.fl1.a1', '32.gh1.c1', '32.gr1.a2', '32.gz1.b1', '32.hh1.b1', '32.hk1.g1', '32.hk1.bd1', '32.hk1.cd1', '32.hk1.cl1', '32.hk1.cq1', '32.hk1.di1', '32.hk1.dp1', '32.hk1.eu1'], 'contains': ['128.j1.b1', '128.m1.a1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 2401, -1, 9271, -1, 2401, -1], 'generators': [163, 140], 'label': '256.30836.64.dn1.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.f2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.f2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878879
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.c1', '32.ei1.b1', '32.fl1.a1', '32.gh1.d1', '32.gr1.b2', '32.gz1.c1', '32.hh1.a2', '32.hk1.n1', '32.hk1.w1', '32.hk1.bk1', '32.hk1.bt1', '32.hk1.db1', '32.hk1.dy1', '32.hk1.ee1', '32.hk1.ep1'], 'contains': ['128.j1.b1', '128.m1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 2151, -1, 9271, -1, 2151, -1], 'generators': [11, 140], 'label': '256.30836.64.dn1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.g1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878880
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.c1', '32.ei1.b2', '32.fl1.a3', '32.gh1.d1', '32.gr1.b1', '32.gz1.c1', '32.hh1.a1', '32.hk1.m1', '32.hk1.x1', '32.hk1.bl1', '32.hk1.bs1', '32.hk1.da1', '32.hk1.dz1', '32.hk1.ef1', '32.hk1.eo1'], 'contains': ['128.j1.b1', '128.m1.b1', '128.n1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 1971, -1, 9271, -1, 1970, -1], 'generators': [131, 140], 'label': '256.30836.64.dn1.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.g2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.g2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878881
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.d1', '32.ei1.b1', '32.fl1.a4', '32.gh1.d1', '32.gr1.b1', '32.gz1.d1', '32.hh1.b1', '32.hk1.o1', '32.hk1.v1', '32.hk1.bn1', '32.hk1.bu1', '32.hk1.cy1', '32.hk1.dx1', '32.hk1.eh1', '32.hk1.em1'], 'contains': ['128.j1.b1', '128.m1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 1609, -1, 9271, -1, 1609, -1], 'generators': [171, 140], 'label': '256.30836.64.dn1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.h1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878882
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.dn1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.co1.d1', '32.ei1.b2', '32.fl1.a2', '32.gh1.d1', '32.gr1.b2', '32.gz1.d1', '32.hh1.b2', '32.hk1.p1', '32.hk1.u1', '32.hk1.bm1', '32.hk1.bv1', '32.hk1.cz1', '32.hk1.dw1', '32.hk1.eg1', '32.hk1.en1'], 'contains': ['128.j1.b1', '128.m1.b1', '128.n1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9267, -1, 1886, -1, 9271, -1, 1887, -1], 'generators': [35, 140], 'label': '256.30836.64.dn1.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.dn1.h2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.dn1.h2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879436
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ey1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.gr1.b1', '8.gt1.b1'], 'contains': ['32.g1.b1', '32.dc1.a1', '32.df1.a1', '32.eh1.b1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1453, -1, 5920, -1, 1453, -1, 5915, -1], 'generators': [129, 68, 136], 'label': '256.30836.16.ey1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.w1.a1', 'old_label': '16.ey1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ey1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878884
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ex1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dm1.a1', '64.dm1.e2', '64.dm1.e1', '64.dm1.a2', '64.dm1.c1', '64.dm1.g2', '64.dm1.g1', '64.dm1.c2', '64.dm1.f2', '64.dm1.b1', '64.dm1.b2', '64.dm1.f1', '64.dm1.h2', '64.dm1.d1', '64.dm1.d2', '64.dm1.h1', '64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.h1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.e1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.k1', '64.dk1.l1', '64.dk1.j1', '64.dk1.i1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.m1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.z1.a1', '2.bd1.a1'], 'contains': ['8.cq1.a1', '8.ct1.a1', '8.cy1.a1', '8.dw1.a1', '8.ea1.a1', '8.eu1.a1', '8.fg1.a1'], 'core': '4.ex1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4029, 9856, 8678, 9465, 4031, 9853, 8671, 9485], 'generators': [17, 18, 64], 'label': '256.30836.4.ex1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ex1.a1', 'normal_contained_in': ['2.d1.a1', '2.z1.a1', '2.bd1.a1'], 'normal_contains': ['8.cq1.a1', '8.ct1.a1', '8.cy1.a1', '8.eu1.a1', '8.fg1.a1', '8.dw1.a1', '8.ea1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ex1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ex1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878885
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.a1', '32.ek1.a1', '32.fm1.a1', '32.gi1.a1', '32.gs1.a1', '32.ha1.a1', '32.hi1.a1', '32.hk1.a1', '32.hk1.bc1', '32.hk1.ca1', '32.hk1.ce1', '32.hk1.cq1', '32.hk1.dg1', '32.hk1.dk1', '32.hk1.eq1'], 'contains': ['128.k1.a1', '128.l1.a1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 2605, -1, 9111, -1, 2606, -1], 'generators': [5, 6], 'label': '256.30836.64.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878886
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.a2', '32.ek1.a3', '32.fm1.a2', '32.gi1.a1', '32.gs1.a2', '32.ha1.a1', '32.hi1.a1', '32.hk1.e1', '32.hk1.y1', '32.hk1.bw1', '32.hk1.ci1', '32.hk1.cm1', '32.hk1.dc1', '32.hk1.do1', '32.hk1.eu1'], 'contains': ['128.k1.a1', '128.l1.a1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 2573, -1, 9111, -1, 2571, -1], 'generators': [165, 6], 'label': '256.30836.64.do1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.a2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878887
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.a1', '32.ek1.a4', '32.fm1.a2', '32.gi1.b1', '32.gs1.b2', '32.ha1.b1', '32.hi1.a1', '32.hk1.i1', '32.hk1.u1', '32.hk1.bg1', '32.hk1.bs1', '32.hk1.cy1', '32.hk1.ds1', '32.hk1.ee1', '32.hk1.ei1'], 'contains': ['128.k1.a1', '128.l1.a1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 1915, -1, 9111, -1, 1915, -1], 'generators': [13, 6], 'label': '256.30836.64.do1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878888
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.a2', '32.ek1.a2', '32.fm1.a1', '32.gi1.b1', '32.gs1.b1', '32.ha1.b1', '32.hi1.a1', '32.hk1.m1', '32.hk1.q1', '32.hk1.bk1', '32.hk1.bo1', '32.hk1.cu1', '32.hk1.dw1', '32.hk1.ea1', '32.hk1.em1'], 'contains': ['128.k1.a1', '128.l1.a1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 1762, -1, 9111, -1, 1762, -1], 'generators': [173, 6], 'label': '256.30836.64.do1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.b2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878889
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.a1', '32.ek1.a2', '32.fm1.b1', '32.gi1.c1', '32.gs1.a2', '32.ha1.a1', '32.hi1.b1', '32.hk1.b1', '32.hk1.bd1', '32.hk1.cb1', '32.hk1.cf1', '32.hk1.cr1', '32.hk1.dh1', '32.hk1.dl1', '32.hk1.er1'], 'contains': ['128.k1.a1', '128.l1.b1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 1748, -1, 9111, -1, 1748, -1], 'generators': [141, 6], 'label': '256.30836.64.do1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.c1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878890
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.a2', '32.ek1.a4', '32.fm1.b2', '32.gi1.c1', '32.gs1.a1', '32.ha1.a1', '32.hi1.b1', '32.hk1.f1', '32.hk1.z1', '32.hk1.bx1', '32.hk1.cj1', '32.hk1.cn1', '32.hk1.dd1', '32.hk1.dp1', '32.hk1.ev1'], 'contains': ['128.k1.a1', '128.l1.b1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 1720, -1, 9111, -1, 1720, -1], 'generators': [45, 6], 'label': '256.30836.64.do1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.c2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878891
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.a1', '32.ek1.a3', '32.fm1.b2', '32.gi1.d1', '32.gs1.b1', '32.ha1.b1', '32.hi1.b1', '32.hk1.j1', '32.hk1.v1', '32.hk1.bh1', '32.hk1.bt1', '32.hk1.cz1', '32.hk1.dt1', '32.hk1.ef1', '32.hk1.ej1'], 'contains': ['128.k1.a1', '128.l1.b1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 903, -1, 9111, -1, 899, -1], 'generators': [133, 6], 'label': '256.30836.64.do1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.d1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878892
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.a2', '32.ek1.a1', '32.fm1.b1', '32.gi1.d1', '32.gs1.b2', '32.ha1.b1', '32.hi1.b1', '32.hk1.n1', '32.hk1.r1', '32.hk1.bl1', '32.hk1.bp1', '32.hk1.cv1', '32.hk1.dx1', '32.hk1.eb1', '32.hk1.en1'], 'contains': ['128.k1.a1', '128.l1.b1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 962, -1, 9111, -1, 943, -1], 'generators': [37, 6], 'label': '256.30836.64.do1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.d2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.d2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878893
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.b1', '32.ek1.a2', '32.fm1.a2', '32.gi1.a1', '32.gs1.a1', '32.ha1.c1', '32.hi1.c1', '32.hk1.c1', '32.hk1.be1', '32.hk1.cc1', '32.hk1.cg1', '32.hk1.cs1', '32.hk1.di1', '32.hk1.dm1', '32.hk1.es1'], 'contains': ['128.k1.b1', '128.l1.a1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 2528, -1, 9111, -1, 2533, -1], 'generators': [173, 38], 'label': '256.30836.64.do1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.e1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878894
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.b2', '32.ek1.a4', '32.fm1.a1', '32.gi1.a1', '32.gs1.a2', '32.ha1.c1', '32.hi1.c1', '32.hk1.g1', '32.hk1.ba1', '32.hk1.by1', '32.hk1.ck1', '32.hk1.co1', '32.hk1.de1', '32.hk1.dq1', '32.hk1.ew1'], 'contains': ['128.k1.b1', '128.l1.a1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 2542, -1, 9111, -1, 2547, -1], 'generators': [13, 38], 'label': '256.30836.64.do1.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.e2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.e2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879450
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.co1.a1', '8.gq1.a1', '8.gq1.b1'], 'contains': ['32.cu1.a1', '32.de1.a1', '32.di1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2066, -1, 5422, -1, 2067, -1, 5417, -1], 'generators': [5, 82], 'label': '256.30836.16.fi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.co1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '16.fi1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878895
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ey1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.m1', '64.dk1.p1', '64.dk1.n1', '64.dk1.o1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.e1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.dk1.i1', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.c1', '64.dj1.d1', '64.dj1.p1', '64.dj1.o1', '64.dj1.g1', '64.dj1.h1', '64.dj1.l1', '64.dj1.k1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.z1.a1', '2.bb1.a1'], 'contains': ['8.cq1.a1', '8.cu1.a1', '8.da1.a1', '8.dx1.a1', '8.eb1.a1', '8.ez1.a1', '8.fh1.a1'], 'core': '4.ey1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6849, 5985, 8120, 5634, 6853, 5983, 8113, 5646], 'generators': [21, 22, 64], 'label': '256.30836.4.ey1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ey1.a1', 'normal_contained_in': ['2.f1.a1', '2.z1.a1', '2.bb1.a1'], 'normal_contains': ['8.cq1.a1', '8.cu1.a1', '8.da1.a1', '8.ez1.a1', '8.fh1.a1', '8.dx1.a1', '8.eb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ey1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ey1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878896
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.b1', '32.ek1.a3', '32.fm1.a1', '32.gi1.b1', '32.gs1.b2', '32.ha1.d1', '32.hi1.c1', '32.hk1.k1', '32.hk1.w1', '32.hk1.bi1', '32.hk1.bu1', '32.hk1.da1', '32.hk1.du1', '32.hk1.eg1', '32.hk1.ek1'], 'contains': ['128.k1.b1', '128.l1.a1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 1706, -1, 9111, -1, 1707, -1], 'generators': [165, 38], 'label': '256.30836.64.do1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.f1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878897
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.b2', '32.ek1.a1', '32.fm1.a2', '32.gi1.b1', '32.gs1.b1', '32.ha1.d1', '32.hi1.c1', '32.hk1.o1', '32.hk1.s1', '32.hk1.bm1', '32.hk1.bq1', '32.hk1.cw1', '32.hk1.dy1', '32.hk1.ec1', '32.hk1.eo1'], 'contains': ['128.k1.b1', '128.l1.a1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 1734, -1, 9111, -1, 1734, -1], 'generators': [5, 38], 'label': '256.30836.64.do1.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.f2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.f2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878898
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.b1', '32.ek1.a1', '32.fm1.b2', '32.gi1.c1', '32.gs1.a2', '32.ha1.c1', '32.hi1.d1', '32.hk1.d1', '32.hk1.bf1', '32.hk1.cd1', '32.hk1.ch1', '32.hk1.ct1', '32.hk1.dj1', '32.hk1.dn1', '32.hk1.et1'], 'contains': ['128.k1.b1', '128.l1.b1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 1679, -1, 9111, -1, 1679, -1], 'generators': [37, 38], 'label': '256.30836.64.do1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.g1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878899
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.b2', '32.ek1.a3', '32.fm1.b1', '32.gi1.c1', '32.gs1.a1', '32.ha1.c1', '32.hi1.d1', '32.hk1.h1', '32.hk1.bb1', '32.hk1.bz1', '32.hk1.cl1', '32.hk1.cp1', '32.hk1.df1', '32.hk1.dr1', '32.hk1.ex1'], 'contains': ['128.k1.b1', '128.l1.b1', '128.m1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 1665, -1, 9111, -1, 1665, -1], 'generators': [133, 38], 'label': '256.30836.64.do1.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.g2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.g2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878900
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.b1', '32.ek1.a4', '32.fm1.b1', '32.gi1.d1', '32.gs1.b1', '32.ha1.d1', '32.hi1.d1', '32.hk1.l1', '32.hk1.x1', '32.hk1.bj1', '32.hk1.bv1', '32.hk1.db1', '32.hk1.dv1', '32.hk1.eh1', '32.hk1.el1'], 'contains': ['128.k1.b1', '128.l1.b1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 846, -1, 9111, -1, 842, -1], 'generators': [45, 38], 'label': '256.30836.64.do1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.h1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878901
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '64.do1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.cp1.b2', '32.ek1.a2', '32.fm1.b2', '32.gi1.d1', '32.gs1.b2', '32.ha1.d1', '32.hi1.d1', '32.hk1.p1', '32.hk1.t1', '32.hk1.bn1', '32.hk1.br1', '32.hk1.cx1', '32.hk1.dz1', '32.hk1.ed1', '32.hk1.ep1'], 'contains': ['128.k1.b1', '128.l1.b1', '128.m1.b1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 884, -1, 9111, -1, 883, -1], 'generators': [141, 38], 'label': '256.30836.64.do1.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '64.do1.h2', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.do1.h2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878902
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '128.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.j1.a1', '64.j1.b1', '64.k1.a1', '64.k1.b1', '64.l1.a1', '64.l1.b1', '64.m1.a1', '64.m1.b1', '64.n1.a1', '64.o1.a1', '64.p1.a1', '64.p1.b1', '64.q1.a1', '64.r1.a1', '64.s1.a1', '64.t1.a1'], 'contains': ['256.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8097, 4731, 4282, 6071, 8101, 4711, 4279, 6084], 'generators': [128], 'label': '256.30836.128.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.b1.a1', '64.a1.a1', '64.c1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.2222', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2222', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878903
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '128.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.d1.a1', '64.e1.a1', '64.u1.a1', '64.u1.b1', '64.v1.a1', '64.v1.b1', '64.w1.a1', '64.w1.b1', '64.x1.a1', '64.y1.a1', '64.z1.a1', '64.ba1.a1', '64.bb1.a1', '64.bc1.a1', '64.bd1.a1', '64.be1.a1', '64.bf1.a1', '64.bg1.a1'], 'contains': ['256.a1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6676, 4759, 3563, 6128, 6679, 4739, 3553, 6142], 'generators': [32], 'label': '256.30836.128.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1.a1', 'normal_contained_in': ['64.e1.a1', '64.a1.a1', '64.d1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.b1.a1', 'projective_image': '128.2264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2264', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878904
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '128.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.d1.a1', '64.f1.a1', '64.bh1.a1', '64.bh1.b1', '64.bi1.a1', '64.bi1.b1', '64.bj1.a1', '64.bk1.a1', '64.bl1.a1', '64.bl1.b1', '64.bm1.a1', '64.bn1.a1', '64.bo1.a1', '64.bp1.a1', '64.bq1.a1', '64.br1.a1', '64.bs1.a1', '64.bt1.a1'], 'contains': ['256.a1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7103, 4786, 4270, 6185, 7107, 4766, 4267, 6199], 'generators': [168], 'label': '256.30836.128.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.c1.a1', 'normal_contained_in': ['64.b1.a1', '64.f1.a1', '64.d1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.c1.a1', 'projective_image': '128.2264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2264', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879213
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hg1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.bg1.d1', '16.il1.b1', '16.im1.b1', '16.ir1.b1', '16.is1.b1', '16.ix1.a1', '16.iy1.a1', '16.jd1.m1', '16.jd1.n1', '16.jd1.o1', '16.jd1.p1', '16.je1.f1', '16.je1.f2', '16.je1.g1', '16.je1.g2', '16.jf1.k1', '16.jf1.l1', '16.jf1.m1', '16.jf1.n1'], 'core': '16.bg1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9920, -1, 3143, -1, 9925, -1, 3137, -1], 'generators': [129, 130, 4, 160, 136], 'label': '256.30836.8.hg1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.hg1.d1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hg1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30878906
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ez1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.n1', '64.dj1.b1', '64.dj1.e1', '64.dj1.i1', '64.dj1.j1', '64.dj1.f1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.dj1.h1', '64.dl1.a1', '64.dl1.b1', '64.dl1.m1', '64.dl1.n1', '64.dl1.f1', '64.dl1.e1', '64.dl1.j1', '64.dl1.i1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.dk1.a1', '64.dk1.c1', '64.dk1.b1', '64.dk1.d1', '64.dk1.o1', '64.dk1.m1', '64.dk1.p1', '64.dk1.n1', '64.dk1.g1', '64.dk1.e1', '64.dk1.h1', '64.dk1.f1', '64.dk1.i1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.dm1.a1', '64.dm1.a2', '64.dm1.g1', '64.dm1.g2', '64.dm1.c1', '64.dm1.c2', '64.dm1.e1', '64.dm1.e2', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.x1.a1', '2.bd1.a1'], 'contains': ['8.cq1.a1', '8.cv1.a1', '8.cx1.a1', '8.dy1.a1', '8.dz1.a1', '8.fd1.a1', '8.ff1.a1'], 'core': '4.ez1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4829, 6456, 7909, 4454, 4831, 6454, 7902, 4463], 'generators': [3, 20, 64], 'label': '256.30836.4.ez1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ez1.a1', 'normal_contained_in': ['2.f1.a1', '2.x1.a1', '2.bd1.a1'], 'normal_contains': ['8.cq1.a1', '8.cv1.a1', '8.cx1.a1', '8.fd1.a1', '8.ff1.a1', '8.dy1.a1', '8.dz1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ez1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ez1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878907
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '128.e1', 'aut_quo_index': 32, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.e1.a1', '64.g1.a1', '64.h1.a1', '64.h1.b1', '64.h1.c1', '64.h1.d1', '64.cf1.a1', '64.cf1.b1', '64.cg1.a1', '64.ch1.a1', '64.ci1.a1', '64.cj1.a1', '64.cj1.b1', '64.ck1.a1', '64.cl1.a1', '64.cm1.a1', '64.cn1.a1', '64.co1.a1'], 'contains': ['256.a1.a1'], 'core': '128.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8121, 4814, 5197, 6219, 8124, 4794, 5192, 6233], 'generators': [40], 'label': '256.30836.128.e1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.e1.a1', 'normal_contained_in': ['64.g1.a1', '64.e1.a1', '64.b1.a1', '64.h1.a1', '64.h1.b1', '64.h1.c1', '64.h1.d1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.e1.a1', 'projective_image': '128.2182', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2182', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878908
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '128.f1', 'aut_quo_index': 32, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '64.d1.a1', '64.g1.a1', '64.i1.a1', '64.i1.b1', '64.i1.c1', '64.i1.d1', '64.cp1.a1', '64.cp1.b1', '64.cq1.a1', '64.cr1.a1', '64.cr1.b1', '64.cs1.a1', '64.ct1.a1', '64.ct1.b1', '64.cu1.a1', '64.cu1.b1', '64.cv1.a1', '64.cw1.a1'], 'contains': ['256.a1.a1'], 'core': '128.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8681, 4842, 4652, 7292, 8685, 4822, 4659, 7307], 'generators': [136], 'label': '256.30836.128.f1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.f1.a1', 'normal_contained_in': ['64.g1.a1', '64.d1.a1', '64.c1.a1', '64.i1.b1', '64.i1.c1', '64.i1.d1', '64.i1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.f1.a1', 'projective_image': '128.2201', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2201', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878909
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '128.g1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '64.e1.a1', '64.f1.a1', '64.cx1.a1', '64.cx1.b1', '64.cy1.a1', '64.cy1.b1', '64.cz1.a1', '64.da1.a1', '64.da1.b1', '64.db1.a1', '64.db1.b1', '64.dc1.a1', '64.dd1.a1', '64.dd1.b1', '64.de1.a1', '64.df1.a1', '64.dg1.a1', '64.dh1.a1'], 'contains': ['256.a1.a1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8548, 4703, 3737, 6157, 8552, 4683, 3734, 6170], 'generators': [8], 'label': '256.30836.128.g1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.g1.a1', 'normal_contained_in': ['64.e1.a1', '64.f1.a1', '64.c1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.g1.a1', 'projective_image': '128.2222', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2222', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878910
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.a1', '64.j1.a1', '64.u1.a1', '64.bh1.a1', '64.bu1.a1', '64.cp1.a1', '64.cx1.a1', '64.di1.a1', '64.di1.b1', '64.di1.c1', '64.di1.d1', '64.dj1.a1', '64.dj1.b1', '64.dj1.c1', '64.dj1.d1', '64.dk1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.d1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8634, -1, 2821, -1, 8638, -1, 2815, -1], 'generators': [2], 'label': '256.30836.128.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '128.h1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878911
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.b1', '64.j1.a1', '64.u1.b1', '64.bh1.a1', '64.bu1.b1', '64.cp1.b1', '64.cx1.b1', '64.di1.e1', '64.di1.h1', '64.di1.i1', '64.di1.j1', '64.dj1.e1', '64.dj1.f1', '64.dj1.g1', '64.dj1.h1', '64.dk1.e1', '64.dk1.f1', '64.dk1.g1', '64.dk1.h1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8634, -1, 2841, -1, 8638, -1, 2832, -1], 'generators': [170], 'label': '256.30836.128.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '128.h1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878912
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.c1', '64.j1.b1', '64.u1.a1', '64.bh1.b1', '64.bu1.b1', '64.cp1.b1', '64.cx1.a1', '64.di1.f1', '64.di1.k1', '64.di1.l1', '64.di1.m1', '64.dj1.i1', '64.dj1.j1', '64.dj1.k1', '64.dj1.l1', '64.dk1.i1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8634, -1, 2723, -1, 8638, -1, 2720, -1], 'generators': [34], 'label': '256.30836.128.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.h1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '128.h1.c1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878913
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.h1.d1', '64.j1.b1', '64.u1.b1', '64.bh1.b1', '64.bu1.a1', '64.cp1.a1', '64.cx1.b1', '64.di1.g1', '64.di1.n1', '64.di1.o1', '64.di1.p1', '64.dj1.m1', '64.dj1.n1', '64.dj1.o1', '64.dj1.p1', '64.dk1.m1', '64.dk1.n1', '64.dk1.o1', '64.dk1.p1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8634, -1, 2674, -1, 8638, -1, 2671, -1], 'generators': [138], 'label': '256.30836.128.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.h1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '128.h1.d1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.h1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878914
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.a1', '64.k1.a1', '64.v1.a1', '64.bi1.a1', '64.bv1.a1', '64.cf1.a1', '64.cy1.a1', '64.di1.a1', '64.di1.e1', '64.di1.f1', '64.di1.g1', '64.dl1.a1', '64.dl1.b1', '64.dl1.c1', '64.dl1.d1', '64.dm1.a1', '64.dm1.a2', '64.dm1.b1', '64.dm1.b2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8657, -1, 1846, -1, 8662, -1, 1846, -1], 'generators': [1], 'label': '256.30836.128.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '128.i1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878915
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.b1', '64.k1.a1', '64.v1.b1', '64.bi1.b1', '64.bv1.b1', '64.cf1.b1', '64.cy1.a1', '64.di1.b1', '64.di1.h1', '64.di1.k1', '64.di1.n1', '64.dl1.e1', '64.dl1.f1', '64.dl1.g1', '64.dl1.h1', '64.dm1.c1', '64.dm1.c2', '64.dm1.d1', '64.dm1.d2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8657, -1, 2929, -1, 8662, -1, 2931, -1], 'generators': [129], 'label': '256.30836.128.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '128.i1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879214
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.bg1.a1', '16.in1.a1', '16.iq1.a1', '16.it1.a1', '16.iv1.a1', '16.iz1.a1', '16.jc1.a1'], 'core': '16.bg1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9146, -1, 4020, -1, 9151, -1, 4016, -1], 'generators': [1, 2, 80], 'label': '256.30836.8.hh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.hh1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878917
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fa1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.d1', '64.dl1.o1', '64.dl1.p1', '64.dl1.c1', '64.dl1.g1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.d1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.m1', '64.dk1.p1', '64.dk1.n1', '64.dk1.o1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.e1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.dk1.i1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.ba1.a1', '2.be1.a1'], 'contains': ['8.cr1.a1', '8.cs1.a1', '8.cy1.a1', '8.ec1.a1', '8.ed1.a1', '8.em1.a1', '8.et1.a1'], 'core': '4.fa1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4562, 3298, 6986, 6246, 4564, 3297, 6980, 6260], 'generators': [65, 66, 16], 'label': '256.30836.4.fa1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fa1.a1', 'normal_contained_in': ['2.d1.a1', '2.ba1.a1', '2.be1.a1'], 'normal_contains': ['8.cr1.a1', '8.cs1.a1', '8.cy1.a1', '8.ed1.a1', '8.ec1.a1', '8.et1.a1', '8.em1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fa1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fa1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878918
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.i1.d1', '64.k1.b1', '64.v1.b1', '64.bi1.b1', '64.bv1.a1', '64.cf1.a1', '64.cy1.b1', '64.di1.d1', '64.di1.j1', '64.di1.m1', '64.di1.p1', '64.dl1.m1', '64.dl1.n1', '64.dl1.o1', '64.dl1.p1', '64.dm1.g1', '64.dm1.g2', '64.dm1.h1', '64.dm1.h2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8657, -1, 2881, -1, 8662, -1, 2887, -1], 'generators': [161], 'label': '256.30836.128.i1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.i1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '128.i1.d1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.i1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878919
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.l1.a1', '64.w1.a1', '64.bj1.a1', '64.bw1.a1', '64.cg1.a1', '64.cq1.a1', '64.cz1.a1', '64.dj1.a1', '64.dj1.b1', '64.dj1.e1', '64.dj1.f1', '64.dj1.i1', '64.dj1.j1', '64.dj1.m1', '64.dj1.n1', '64.dl1.a1', '64.dl1.b1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.m1', '64.dl1.n1', '64.dn1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.b2', '64.dn1.c1', '64.dn1.c2', '64.dn1.d1', '64.dn1.d2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8814, -1, 1754, -1, 8818, -1, 1761, -1], 'generators': [4], 'label': '256.30836.128.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '128.j1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878920
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.l1.b1', '64.w1.b1', '64.bj1.a1', '64.bw1.b1', '64.cg1.a1', '64.cq1.a1', '64.cz1.a1', '64.dj1.c1', '64.dj1.d1', '64.dj1.g1', '64.dj1.h1', '64.dj1.k1', '64.dj1.l1', '64.dj1.o1', '64.dj1.p1', '64.dl1.c1', '64.dl1.d1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.dl1.o1', '64.dl1.p1', '64.dn1.e1', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8814, -1, 2661, -1, 8818, -1, 2651, -1], 'generators': [140], 'label': '256.30836.128.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '128.j1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878921
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.m1.a1', '64.x1.a1', '64.bk1.a1', '64.bx1.a1', '64.ch1.a1', '64.cr1.a1', '64.da1.a1', '64.dj1.a1', '64.dj1.c1', '64.dj1.e1', '64.dj1.g1', '64.dj1.i1', '64.dj1.k1', '64.dj1.m1', '64.dj1.o1', '64.dm1.a1', '64.dm1.a2', '64.dm1.c1', '64.dm1.c2', '64.dm1.e1', '64.dm1.e2', '64.dm1.g1', '64.dm1.g2', '64.do1.a1', '64.do1.a2', '64.do1.b1', '64.do1.b2', '64.do1.c1', '64.do1.c2', '64.do1.d1', '64.do1.d2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8728, -1, 2135, -1, 8732, -1, 2133, -1], 'generators': [6], 'label': '256.30836.128.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '128.k1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878922
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.m1.b1', '64.x1.a1', '64.bk1.a1', '64.bx1.a1', '64.ch1.a1', '64.cr1.b1', '64.da1.b1', '64.dj1.b1', '64.dj1.d1', '64.dj1.f1', '64.dj1.h1', '64.dj1.j1', '64.dj1.l1', '64.dj1.n1', '64.dj1.p1', '64.dm1.b1', '64.dm1.b2', '64.dm1.d1', '64.dm1.d2', '64.dm1.f1', '64.dm1.f2', '64.dm1.h1', '64.dm1.h2', '64.do1.e1', '64.do1.e2', '64.do1.f1', '64.do1.f2', '64.do1.g1', '64.do1.g2', '64.do1.h1', '64.do1.h2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8728, -1, 2119, -1, 8732, -1, 2112, -1], 'generators': [38], 'label': '256.30836.128.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '128.k1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878923
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.n1.a1', '64.y1.a1', '64.bl1.a1', '64.by1.a1', '64.ci1.a1', '64.cs1.a1', '64.db1.a1', '64.dk1.a1', '64.dk1.b1', '64.dk1.e1', '64.dk1.f1', '64.dk1.i1', '64.dk1.j1', '64.dk1.m1', '64.dk1.n1', '64.dl1.a1', '64.dl1.c1', '64.dl1.e1', '64.dl1.g1', '64.dl1.i1', '64.dl1.k1', '64.dl1.m1', '64.dl1.o1', '64.do1.a1', '64.do1.a2', '64.do1.b1', '64.do1.b2', '64.do1.e1', '64.do1.e2', '64.do1.f1', '64.do1.f2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8751, -1, 2512, -1, 8755, -1, 2483, -1], 'generators': [5], 'label': '256.30836.128.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '128.l1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878924
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.n1.a1', '64.y1.a1', '64.bl1.b1', '64.by1.b1', '64.ci1.a1', '64.cs1.a1', '64.db1.b1', '64.dk1.c1', '64.dk1.d1', '64.dk1.g1', '64.dk1.h1', '64.dk1.k1', '64.dk1.l1', '64.dk1.o1', '64.dk1.p1', '64.dl1.b1', '64.dl1.d1', '64.dl1.f1', '64.dl1.h1', '64.dl1.j1', '64.dl1.l1', '64.dl1.n1', '64.dl1.p1', '64.do1.c1', '64.do1.c2', '64.do1.d1', '64.do1.d2', '64.do1.g1', '64.do1.g2', '64.do1.h1', '64.do1.h2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8751, -1, 1706, -1, 8755, -1, 1707, -1], 'generators': [141], 'label': '256.30836.128.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '128.l1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.l1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878925
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.o1.a1', '64.z1.a1', '64.bm1.a1', '64.bz1.a1', '64.cj1.a1', '64.ct1.a1', '64.dc1.a1', '64.di1.a1', '64.di1.d1', '64.di1.g1', '64.di1.h1', '64.di1.i1', '64.di1.k1', '64.di1.l1', '64.di1.p1', '64.dn1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e1', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2', '64.do1.a1', '64.do1.a2', '64.do1.c1', '64.do1.c2', '64.do1.e1', '64.do1.e2', '64.do1.g1', '64.do1.g2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8705, -1, 2444, -1, 8708, -1, 2439, -1], 'generators': [3], 'label': '256.30836.128.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '128.m1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878927
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.p1.a1', '64.ba1.a1', '64.bn1.a1', '64.ca1.a1', '64.ck1.a1', '64.cu1.a1', '64.dd1.a1', '64.dk1.a1', '64.dk1.c1', '64.dk1.e1', '64.dk1.g1', '64.dk1.i1', '64.dk1.k1', '64.dk1.m1', '64.dk1.o1', '64.dm1.a1', '64.dm1.a2', '64.dm1.c1', '64.dm1.c2', '64.dm1.f1', '64.dm1.f2', '64.dm1.h1', '64.dm1.h2', '64.dn1.a1', '64.dn1.a2', '64.dn1.c1', '64.dn1.c2', '64.dn1.e1', '64.dn1.e2', '64.dn1.g1', '64.dn1.g2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8840, -1, 2424, -1, 8845, -1, 2397, -1], 'generators': [7], 'label': '256.30836.128.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '128.n1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878928
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fb1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.b1', '64.dj1.j1', '64.dj1.i1', '64.dj1.e1', '64.dj1.f1', '64.dj1.n1', '64.dj1.m1', '64.dj1.d1', '64.dj1.c1', '64.dj1.k1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.o1', '64.dj1.p1', '64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.d1', '64.dl1.o1', '64.dl1.k1', '64.dl1.h1', '64.dl1.g1', '64.dl1.l1', '64.dl1.p1', '64.dl1.c1', '64.dk1.a1', '64.dk1.d1', '64.dk1.c1', '64.dk1.b1', '64.dk1.k1', '64.dk1.j1', '64.dk1.i1', '64.dk1.l1', '64.dk1.g1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.n1', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.b2', '64.dm1.h1', '64.dm1.f2', '64.dm1.d1', '64.dm1.d2', '64.dm1.f1', '64.dm1.h2', '64.dm1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.x1.a1', '2.be1.a1'], 'contains': ['8.cr1.a1', '8.cw1.a1', '8.cx1.a1', '8.ee1.a1', '8.eh1.a1', '8.fp1.a1', '8.fv1.a1'], 'core': '4.fb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3479, 4062, 7113, 6946, 3480, 4061, 7106, 6961], 'generators': [3, 68, 16], 'label': '256.30836.4.fb1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fb1.a1', 'normal_contained_in': ['2.g1.a1', '2.x1.a1', '2.be1.a1'], 'normal_contains': ['8.cr1.a1', '8.cx1.a1', '8.cw1.a1', '8.ee1.a1', '8.eh1.a1', '8.fv1.a1', '8.fp1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fb1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878929
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.n1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.p1.b1', '64.ba1.a1', '64.bn1.a1', '64.ca1.a1', '64.ck1.a1', '64.cu1.b1', '64.dd1.b1', '64.dk1.b1', '64.dk1.d1', '64.dk1.f1', '64.dk1.h1', '64.dk1.j1', '64.dk1.l1', '64.dk1.n1', '64.dk1.p1', '64.dm1.b1', '64.dm1.b2', '64.dm1.d1', '64.dm1.d2', '64.dm1.e1', '64.dm1.e2', '64.dm1.g1', '64.dm1.g2', '64.dn1.b1', '64.dn1.b2', '64.dn1.d1', '64.dn1.d2', '64.dn1.f1', '64.dn1.f2', '64.dn1.h1', '64.dn1.h2'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8840, -1, 2102, -1, 8845, -1, 2098, -1], 'generators': [39], 'label': '256.30836.128.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '128.n1.b1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.n1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878930
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '128.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.q1.a1', '64.bb1.a1', '64.bo1.a1', '64.cb1.a1', '64.cl1.a1', '64.cv1.a1', '64.de1.a1'], 'contains': ['256.a1.a1'], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4750, -1, 6174, -1, 4759, -1, 6169, -1], 'generators': [83], 'label': '256.30836.128.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.dp1.a1', 'old_label': '128.o1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878931
{'ambient': '256.30836', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '128.b1.a1', '128.c1.a1', '128.d1.a1', '128.e1.a1', '128.f1.a1', '128.g1.a1', '128.h1.a1', '128.h1.b1', '128.h1.c1', '128.h1.d1', '128.i1.a1', '128.i1.b1', '128.i1.c1', '128.i1.d1', '128.j1.a1', '128.j1.b1', '128.k1.a1', '128.k1.b1', '128.l1.a1', '128.l1.b1', '128.m1.a1', '128.m1.b1', '128.n1.a1', '128.n1.b1', '128.o1.a1'], 'contains': [], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8634, 4759, 2695, 6157, 8638, 4739, 2699, 6170], 'generators': [], 'label': '256.30836.256.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1.a1', 'normal_contained_in': ['128.e1.a1', '128.d1.a1', '128.b1.a1', '128.c1.a1', '128.f1.a1', '128.g1.a1', '128.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '256.a1.a1', 'projective_image': '256.30836', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30878932
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fc1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.o1', '64.dl1.d1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.c1', '64.dl1.p1', '64.dk1.a1', '64.dk1.d1', '64.dk1.c1', '64.dk1.b1', '64.dk1.k1', '64.dk1.j1', '64.dk1.i1', '64.dk1.l1', '64.dk1.g1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.n1', '64.dj1.a1', '64.dj1.b1', '64.dj1.j1', '64.dj1.i1', '64.dj1.e1', '64.dj1.f1', '64.dj1.n1', '64.dj1.m1', '64.dj1.c1', '64.dj1.d1', '64.dj1.l1', '64.dj1.k1', '64.dj1.g1', '64.dj1.h1', '64.dj1.p1', '64.dj1.o1', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.h1', '64.dm1.b2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dm1.d2', '64.dm1.b1', '64.dm1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.ba1.a1', '2.bb1.a1'], 'contains': ['8.cr1.a1', '8.cz1.a1', '8.da1.a1', '8.ef1.a1', '8.eg1.a1', '8.fx1.a1', '8.fy1.a1'], 'core': '4.fc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5263, 2899, 6852, 6410, 5265, 2898, 6846, 6424], 'generators': [69, 70, 16], 'label': '256.30836.4.fc1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fc1.a1', 'normal_contained_in': ['2.g1.a1', '2.ba1.a1', '2.bb1.a1'], 'normal_contains': ['8.cr1.a1', '8.cz1.a1', '8.da1.a1', '8.eg1.a1', '8.ef1.a1', '8.fy1.a1', '8.fx1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fc1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878933
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fd1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.b2', '64.dm1.h1', '64.dm1.h2', '64.dm1.b1', '64.dm1.d2', '64.dm1.f1', '64.dm1.f2', '64.dm1.d1', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.n1', '64.dk1.o1', '64.dk1.m1', '64.dk1.p1', '64.dk1.e1', '64.dk1.h1', '64.dk1.f1', '64.dk1.g1', '64.dk1.j1', '64.dk1.k1', '64.dk1.i1', '64.dk1.l1', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.c1', '64.dj1.d1', '64.dj1.p1', '64.dj1.o1', '64.dj1.g1', '64.dj1.h1', '64.dj1.l1', '64.dj1.k1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.y1.a1', '2.be1.a1'], 'contains': ['8.cs1.a1', '8.cu1.a1', '8.cx1.a1', '8.ei1.a1', '8.en1.a1', '8.ep1.a1', '8.es1.a1'], 'core': '4.fd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5216, 3521, 6781, 5527, 5218, 3520, 6774, 5539], 'generators': [65, 66, 84], 'label': '256.30836.4.fd1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fd1.a1', 'normal_contained_in': ['2.f1.a1', '2.y1.a1', '2.be1.a1'], 'normal_contains': ['8.cs1.a1', '8.cu1.a1', '8.cx1.a1', '8.ep1.a1', '8.es1.a1', '8.ei1.a1', '8.en1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fd1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878934
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fe1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.d1', '64.dl1.o1', '64.dl1.p1', '64.dl1.c1', '64.dl1.g1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.d1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.m1', '64.dk1.p1', '64.dk1.n1', '64.dk1.o1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.e1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.dk1.i1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.ba1.a1', '2.bc1.a1'], 'contains': ['8.cs1.a1', '8.cv1.a1', '8.da1.a1', '8.ej1.a1', '8.el1.a1', '8.eq1.a1', '8.er1.a1'], 'core': '4.fe1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5570, 1745, 8041, 852, 5573, 1744, 8034, 854], 'generators': [65, 66, 20], 'label': '256.30836.4.fe1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fe1.a1', 'normal_contained_in': ['2.f1.a1', '2.ba1.a1', '2.bc1.a1'], 'normal_contains': ['8.cv1.a1', '8.cs1.a1', '8.da1.a1', '8.eq1.a1', '8.ej1.a1', '8.er1.a1', '8.el1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fe1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fe1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878935
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ff1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.h1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dm1.a1', '64.dm1.e2', '64.dm1.e1', '64.dm1.a2', '64.dm1.c1', '64.dm1.g2', '64.dm1.g1', '64.dm1.c2', '64.dm1.b1', '64.dm1.f2', '64.dm1.f1', '64.dm1.b2', '64.dm1.d1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.e1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.k1', '64.dk1.l1', '64.dk1.j1', '64.dk1.i1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.m1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.z1.a1', '2.bc1.a1'], 'contains': ['8.ct1.a1', '8.cw1.a1', '8.da1.a1', '8.ev1.a1', '8.ey1.a1', '8.fn1.a1', '8.fu1.a1'], 'core': '4.ff1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4252, 9499, 7934, 7954, 4254, 9496, 7927, 7971], 'generators': [17, 18, 68], 'label': '256.30836.4.ff1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ff1.a1', 'normal_contained_in': ['2.g1.a1', '2.z1.a1', '2.bc1.a1'], 'normal_contains': ['8.ct1.a1', '8.da1.a1', '8.cw1.a1', '8.ev1.a1', '8.ey1.a1', '8.fu1.a1', '8.fn1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ff1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ff1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878936
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fg1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.f1', '64.dk1.e1', '64.dk1.g1', '64.dk1.h1', '64.dk1.j1', '64.dk1.i1', '64.dk1.k1', '64.dk1.l1', '64.dk1.m1', '64.dk1.n1', '64.dk1.p1', '64.dk1.o1', '64.dm1.a1', '64.dm1.e2', '64.dm1.e1', '64.dm1.a2', '64.dm1.c1', '64.dm1.g2', '64.dm1.g1', '64.dm1.c2', '64.dm1.b1', '64.dm1.f2', '64.dm1.f1', '64.dm1.b2', '64.dm1.d1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.h1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.y1.a1', '2.bd1.a1'], 'contains': ['8.ct1.a1', '8.cx1.a1', '8.cz1.a1', '8.ew1.a1', '8.ex1.a1', '8.fs1.a1', '8.ft1.a1'], 'core': '4.fg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2246, 9599, 7186, 8963, 2247, 9596, 7180, 8983], 'generators': [17, 18, 84], 'label': '256.30836.4.fg1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fg1.a1', 'normal_contained_in': ['2.g1.a1', '2.y1.a1', '2.bd1.a1'], 'normal_contains': ['8.ct1.a1', '8.cz1.a1', '8.cx1.a1', '8.ew1.a1', '8.ex1.a1', '8.ft1.a1', '8.fs1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fg1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878937
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.p1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.h1.a1', '128.h1.d1', '128.h1.c1', '128.h1.b1', '128.m1.a1', '128.m1.b1', '128.k1.a1', '128.k1.b1', '128.n1.a1', '128.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.bj1.a1', '4.bk1.a1', '4.bn1.a1', '4.bv1.a1', '4.bx1.a1', '4.ca1.a1', '4.cj1.a1', '4.cr1.a1', '4.cu1.a1', '4.cx1.a1', '4.dd1.a1', '4.ed1.a1', '4.eg1.a1', '4.ej1.a1', '4.ep1.a1'], 'core': '2.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3170, 7659, 6062, 2102, 3172, 7656, 6057, 2174], 'generators': [1, 18, 4, 64], 'label': '256.30836.2.p1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.p1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.bj1.a1', '4.bn1.a1', '4.bk1.a1', '4.bx1.a1', '4.bv1.a1', '4.ca1.a1', '4.cj1.a1', '4.cr1.a1', '4.cu1.a1', '4.dd1.a1', '4.cx1.a1', '4.eg1.a1', '4.ed1.a1', '4.ej1.a1', '4.ep1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.p1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.p1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878938
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fh1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.c1', '64.dj1.d1', '64.dj1.p1', '64.dj1.o1', '64.dj1.g1', '64.dj1.h1', '64.dj1.l1', '64.dj1.k1', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.n1', '64.dk1.o1', '64.dk1.m1', '64.dk1.p1', '64.dk1.e1', '64.dk1.h1', '64.dk1.f1', '64.dk1.g1', '64.dk1.j1', '64.dk1.k1', '64.dk1.i1', '64.dk1.l1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.z1.a1', '2.be1.a1'], 'contains': ['8.cu1.a1', '8.cw1.a1', '8.cy1.a1', '8.fb1.a1', '8.fc1.a1', '8.fo1.a1', '8.fw1.a1'], 'core': '4.fh1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7360, 3682, 6587, 8847, 7364, 3681, 6581, 8866], 'generators': [81, 82, 68], 'label': '256.30836.4.fh1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fh1.a1', 'normal_contained_in': ['2.e1.a1', '2.z1.a1', '2.be1.a1'], 'normal_contains': ['8.cu1.a1', '8.cw1.a1', '8.cy1.a1', '8.fc1.a1', '8.fb1.a1', '8.fw1.a1', '8.fo1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fh1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fh1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879451
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cr1.a1', '8.gp1.a1', '8.gp1.b1'], 'contains': ['32.cv1.a1', '32.cy1.a1', '32.dg1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1949, -1, 7332, -1, 1950, -1, 7326, -1], 'generators': [3, 16], 'label': '256.30836.16.fj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cr1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.fj1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878939
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fi1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dk1.a1', '64.dk1.d1', '64.dk1.b1', '64.dk1.c1', '64.dk1.m1', '64.dk1.p1', '64.dk1.n1', '64.dk1.o1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.e1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.dk1.i1', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.c1', '64.dj1.d1', '64.dj1.p1', '64.dj1.o1', '64.dj1.g1', '64.dj1.h1', '64.dj1.l1', '64.dj1.k1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.ba1.a1', '2.bd1.a1'], 'contains': ['8.cv1.a1', '8.cy1.a1', '8.cz1.a1', '8.fj1.a1', '8.fk1.a1', '8.fq1.a1', '8.fr1.a1'], 'core': '4.fi1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6536, 2248, 6520, 7526, 6539, 2247, 6514, 7542], 'generators': [81, 82, 20], 'label': '256.30836.4.fi1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fi1.a1', 'normal_contained_in': ['2.e1.a1', '2.ba1.a1', '2.bd1.a1'], 'normal_contains': ['8.cv1.a1', '8.cz1.a1', '8.cy1.a1', '8.fj1.a1', '8.fk1.a1', '8.fr1.a1', '8.fq1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fi1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fi1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878940
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fj1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.i1', '64.di1.e1', '64.di1.h1', '64.di1.j1', '64.di1.p1', '64.di1.n1', '64.di1.g1', '64.di1.o1', '64.di1.k1', '64.di1.m1', '64.di1.l1', '64.di1.f1', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.f1', '64.do1.e2', '64.do1.f2', '64.do1.e1', '64.do1.g1', '64.do1.h2', '64.do1.g2', '64.do1.h1', '64.dj1.a1', '64.dj1.f1', '64.dj1.n1', '64.dj1.i1', '64.dj1.e1', '64.dj1.b1', '64.dj1.j1', '64.dj1.m1', '64.dj1.d1', '64.dj1.g1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.c1', '64.dj1.k1', '64.dj1.p1', '64.dl1.a1', '64.dl1.i1', '64.dl1.m1', '64.dl1.e1', '64.dl1.f1', '64.dl1.n1', '64.dl1.j1', '64.dl1.b1', '64.dl1.k1', '64.dl1.c1', '64.dl1.g1', '64.dl1.o1', '64.dl1.p1', '64.dl1.h1', '64.dl1.d1', '64.dl1.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.l1.a1', '2.t1.a1', '2.x1.a1'], 'contains': ['8.db1.a1', '8.dc1.a1', '8.dj1.a1', '8.dn1.a1', '8.dt1.a1', '8.dz1.a1', '8.fv1.a1'], 'core': '4.fj1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4083, 4826, 8336, 4520, 4085, 4824, 8329, 4529], 'generators': [19, 20, 64], 'label': '256.30836.4.fj1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fj1.a1', 'normal_contained_in': ['2.t1.a1', '2.l1.a1', '2.x1.a1'], 'normal_contains': ['8.db1.a1', '8.dc1.a1', '8.dj1.a1', '8.dn1.a1', '8.dt1.a1', '8.dz1.a1', '8.fv1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fj1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878941
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fk1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.do1.a1', '64.do1.b2', '64.do1.d2', '64.do1.c1', '64.do1.d1', '64.do1.c2', '64.do1.a2', '64.do1.b1', '64.do1.f1', '64.do1.e2', '64.do1.g2', '64.do1.h1', '64.do1.g1', '64.do1.h2', '64.do1.f2', '64.do1.e1', '64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.h1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.k1', '64.dl1.c1', '64.dl1.d1', '64.dl1.l1', '64.dl1.p1', '64.dl1.h1', '64.dl1.g1', '64.dl1.o1'], 'conjugacy_class_count': 1, 'contained_in': ['2.m1.a1', '2.u1.a1', '2.x1.a1'], 'contains': ['8.db1.a1', '8.dd1.a1', '8.dh1.a1', '8.do1.a1', '8.ds1.a1', '8.ee1.a1', '8.fd1.a1'], 'core': '4.fk1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1254, 7867, 7696, 1029, 1255, 7864, 7690, 1031], 'generators': [67, 68, 16], 'label': '256.30836.4.fk1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fk1.a1', 'normal_contained_in': ['2.u1.a1', '2.m1.a1', '2.x1.a1'], 'normal_contains': ['8.db1.a1', '8.dh1.a1', '8.dd1.a1', '8.do1.a1', '8.ds1.a1', '8.fd1.a1', '8.ee1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fk1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fk1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878942
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fl1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.e1', '64.di1.i1', '64.di1.j1', '64.di1.h1', '64.di1.g1', '64.di1.o1', '64.di1.p1', '64.di1.n1', '64.di1.f1', '64.di1.l1', '64.di1.m1', '64.di1.k1', '64.dj1.a1', '64.dj1.f1', '64.dj1.n1', '64.dj1.i1', '64.dj1.e1', '64.dj1.b1', '64.dj1.j1', '64.dj1.m1', '64.dj1.g1', '64.dj1.d1', '64.dj1.l1', '64.dj1.o1', '64.dj1.c1', '64.dj1.h1', '64.dj1.p1', '64.dj1.k1', '64.dl1.a1', '64.dl1.i1', '64.dl1.m1', '64.dl1.e1', '64.dl1.f1', '64.dl1.n1', '64.dl1.j1', '64.dl1.b1', '64.dl1.c1', '64.dl1.k1', '64.dl1.o1', '64.dl1.g1', '64.dl1.h1', '64.dl1.p1', '64.dl1.l1', '64.dl1.d1', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.f1', '64.do1.e2', '64.do1.f2', '64.do1.e1', '64.do1.g1', '64.do1.h2', '64.do1.g2', '64.do1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.l1.a1', '2.u1.a1', '2.y1.a1'], 'contains': ['8.db1.a1', '8.de1.a1', '8.dg1.a1', '8.dp1.a1', '8.dr1.a1', '8.ei1.a1', '8.ew1.a1'], 'core': '4.fl1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1531, 4564, 6432, 1886, 1532, 4562, 6426, 1890], 'generators': [17, 66, 84], 'label': '256.30836.4.fl1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fl1.a1', 'normal_contained_in': ['2.u1.a1', '2.l1.a1', '2.y1.a1'], 'normal_contains': ['8.db1.a1', '8.dg1.a1', '8.de1.a1', '8.dp1.a1', '8.dr1.a1', '8.ew1.a1', '8.ei1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fl1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fl1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878965
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.h1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.l1.a1', '4.r1.a1', '4.t1.a1', '4.bc1.a1', '4.bf1.a1', '4.bg1.a1'], 'contains': ['16.a1.a1', '16.m1.a1', '16.ba1.a1', '16.cu1.a1', '16.cu1.b1', '16.es1.a1', '16.hg1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [931, 5955, 9017, 9691, 931, 5953, 9010, 9712], 'generators': [17, 2, 32, 128], 'label': '256.30836.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.d1.a1', '4.l1.a1', '4.r1.a1', '4.t1.a1', '4.bc1.a1', '4.bg1.a1', '4.bf1.a1'], 'normal_contains': ['16.a1.a1', '16.m1.a1', '16.ba1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878966
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.i1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.j1.a1', '4.r1.a1', '4.v1.a1', '4.y1.a1', '4.bd1.a1', '4.bh1.a1'], 'contains': ['16.a1.a1', '16.n1.a1', '16.s1.a1', '16.bl1.a1', '16.hh1.a1', '16.io1.a1', '16.io1.b1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9379, 5699, 4638, 4479, 9384, 5698, 4634, 4488], 'generators': [2, 20, 136, 128], 'label': '256.30836.8.i1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.e1.a1', '4.j1.a1', '4.r1.a1', '4.v1.a1', '4.bd1.a1', '4.y1.a1', '4.bh1.a1'], 'normal_contains': ['16.a1.a1', '16.n1.a1', '16.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878943
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fm1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.di1.i1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.l1', '64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.d1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.do1.a1', '64.do1.c2', '64.do1.a2', '64.do1.c1', '64.do1.d1', '64.do1.b2', '64.do1.d2', '64.do1.b1', '64.do1.e1', '64.do1.g2', '64.do1.e2', '64.do1.g1', '64.do1.h1', '64.do1.f2', '64.do1.h2', '64.do1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.m1.a1', '2.t1.a1', '2.y1.a1'], 'contains': ['8.db1.a1', '8.df1.a1', '8.dk1.a1', '8.dq1.a1', '8.du1.a1', '8.es1.a1', '8.fs1.a1'], 'core': '4.fm1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3239, 8848, 7964, 6670, 3241, 8845, 7957, 6685], 'generators': [65, 18, 84], 'label': '256.30836.4.fm1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fm1.a1', 'normal_contained_in': ['2.t1.a1', '2.m1.a1', '2.y1.a1'], 'normal_contains': ['8.db1.a1', '8.df1.a1', '8.dk1.a1', '8.dq1.a1', '8.du1.a1', '8.es1.a1', '8.fs1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fm1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878944
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fn1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.i1', '64.dj1.j1', '64.dj1.b1', '64.dj1.e1', '64.dj1.m1', '64.dj1.n1', '64.dj1.f1', '64.dj1.c1', '64.dj1.k1', '64.dj1.l1', '64.dj1.d1', '64.dj1.g1', '64.dj1.o1', '64.dj1.p1', '64.dj1.h1', '64.dl1.a1', '64.dl1.e1', '64.dl1.j1', '64.dl1.n1', '64.dl1.f1', '64.dl1.b1', '64.dl1.m1', '64.dl1.i1', '64.dl1.g1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.k1', '64.dl1.o1', '64.di1.a1', '64.di1.b1', '64.di1.c1', '64.di1.d1', '64.di1.k1', '64.di1.f1', '64.di1.m1', '64.di1.l1', '64.di1.h1', '64.di1.e1', '64.di1.j1', '64.di1.i1', '64.di1.g1', '64.di1.n1', '64.di1.o1', '64.di1.p1', '64.do1.a1', '64.do1.b1', '64.do1.d2', '64.do1.c2', '64.do1.d1', '64.do1.c1', '64.do1.a2', '64.do1.b2', '64.do1.f2', '64.do1.e2', '64.do1.g1', '64.do1.h1', '64.do1.g2', '64.do1.h2', '64.do1.f1', '64.do1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.n1.a1', '2.v1.a1', '2.x1.a1'], 'contains': ['8.dc1.a1', '8.dd1.a1', '8.di1.a1', '8.dv1.a1', '8.dy1.a1', '8.eh1.a1', '8.fi1.a1'], 'core': '4.fn1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4605, 1848, 7262, 4105, 4607, 1848, 7255, 4114], 'generators': [7, 16, 64], 'label': '256.30836.4.fn1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fn1.a1', 'normal_contained_in': ['2.v1.a1', '2.n1.a1', '2.x1.a1'], 'normal_contains': ['8.dd1.a1', '8.dc1.a1', '8.di1.a1', '8.dv1.a1', '8.eh1.a1', '8.dy1.a1', '8.fi1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fn1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878945
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fo1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.i1', '64.dl1.m1', '64.dl1.e1', '64.dl1.f1', '64.dl1.n1', '64.dl1.j1', '64.dl1.b1', '64.dl1.c1', '64.dl1.k1', '64.dl1.o1', '64.dl1.g1', '64.dl1.h1', '64.dl1.p1', '64.dl1.l1', '64.dl1.d1', '64.di1.a1', '64.di1.c1', '64.di1.d1', '64.di1.b1', '64.di1.i1', '64.di1.e1', '64.di1.h1', '64.di1.j1', '64.di1.p1', '64.di1.n1', '64.di1.g1', '64.di1.o1', '64.di1.k1', '64.di1.m1', '64.di1.l1', '64.di1.f1', '64.dj1.a1', '64.dj1.f1', '64.dj1.n1', '64.dj1.i1', '64.dj1.e1', '64.dj1.b1', '64.dj1.j1', '64.dj1.m1', '64.dj1.g1', '64.dj1.d1', '64.dj1.l1', '64.dj1.o1', '64.dj1.c1', '64.dj1.h1', '64.dj1.p1', '64.dj1.k1', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.e2', '64.do1.f1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.g1', '64.do1.h1', '64.do1.g2'], 'conjugacy_class_count': 1, 'contained_in': ['2.l1.a1', '2.v1.a1', '2.z1.a1'], 'contains': ['8.dc1.a1', '8.dg1.a1', '8.dm1.a1', '8.dw1.a1', '8.dx1.a1', '8.ey1.a1', '8.fc1.a1'], 'core': '4.fo1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6936, 4329, 8724, 6880, 6939, 4327, 8716, 6895], 'generators': [17, 22, 64], 'label': '256.30836.4.fo1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fo1.a1', 'normal_contained_in': ['2.v1.a1', '2.l1.a1', '2.z1.a1'], 'normal_contains': ['8.dg1.a1', '8.dc1.a1', '8.dm1.a1', '8.dw1.a1', '8.ey1.a1', '8.dx1.a1', '8.fc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fo1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fo1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878946
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fp1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.o1', '64.dl1.d1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.c1', '64.dl1.p1', '64.do1.a1', '64.do1.c2', '64.do1.d2', '64.do1.b1', '64.do1.d1', '64.do1.b2', '64.do1.a2', '64.do1.c1', '64.do1.g2', '64.do1.e1', '64.do1.f1', '64.do1.h2', '64.do1.f2', '64.do1.h1', '64.do1.g1', '64.do1.e2', '64.dj1.a1', '64.dj1.b1', '64.dj1.j1', '64.dj1.i1', '64.dj1.e1', '64.dj1.f1', '64.dj1.n1', '64.dj1.m1', '64.dj1.d1', '64.dj1.c1', '64.dj1.k1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.o1', '64.dj1.p1', '64.di1.a1', '64.di1.d1', '64.di1.c1', '64.di1.b1', '64.di1.l1', '64.di1.k1', '64.di1.f1', '64.di1.m1', '64.di1.h1', '64.di1.i1', '64.di1.j1', '64.di1.e1', '64.di1.p1', '64.di1.g1', '64.di1.n1', '64.di1.o1'], 'conjugacy_class_count': 1, 'contained_in': ['2.n1.a1', '2.t1.a1', '2.z1.a1'], 'contains': ['8.dc1.a1', '8.dk1.a1', '8.dl1.a1', '8.ea1.a1', '8.eb1.a1', '8.fu1.a1', '8.fw1.a1'], 'core': '4.fp1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6736, 8782, 7542, 8229, 6740, 8779, 7535, 8248], 'generators': [21, 18, 64], 'label': '256.30836.4.fp1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fp1.a1', 'normal_contained_in': ['2.t1.a1', '2.n1.a1', '2.z1.a1'], 'normal_contains': ['8.dc1.a1', '8.dk1.a1', '8.dl1.a1', '8.eb1.a1', '8.ea1.a1', '8.fw1.a1', '8.fu1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fp1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878967
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.j1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.l1.a1', '4.p1.a1', '4.w1.a1', '4.z1.a1', '4.be1.a1', '4.bi1.a1'], 'contains': ['16.a1.a1', '16.p1.a1', '16.z1.a1', '16.cv1.a1', '16.cv1.b1', '16.ga1.a1', '16.ga1.b1', '16.ip1.a1', '16.ip1.b1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3505, 7768, 8963, 6160, 3507, 7765, 8955, 6174], 'generators': [21, 2, 32, 128], 'label': '256.30836.8.j1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.e1.a1', '4.l1.a1', '4.p1.a1', '4.w1.a1', '4.be1.a1', '4.z1.a1', '4.bi1.a1'], 'normal_contains': ['16.a1.a1', '16.p1.a1', '16.z1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878968
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.k1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.m1.a1', '4.s1.a1', '4.x1.a1', '4.bc1.a1', '4.bh1.a1', '4.bi1.a1'], 'contains': ['16.a1.a1', '16.q1.a1', '16.v1.a1', '16.iq1.a1', '16.iq1.b1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8919, 106, 4609, 9300, 8923, 105, 4605, 9320], 'generators': [2, 80, 128], 'label': '256.30836.8.k1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.b1.a1', '4.m1.a1', '4.s1.a1', '4.bc1.a1', '4.x1.a1', '4.bi1.a1', '4.bh1.a1'], 'normal_contains': ['16.a1.a1', '16.q1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878947
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fq1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.b1', '64.dl1.j1', '64.dl1.i1', '64.dl1.f1', '64.dl1.e1', '64.dl1.m1', '64.dl1.n1', '64.dl1.c1', '64.dl1.d1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dl1.g1', '64.dl1.o1', '64.dl1.p1', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.g1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.e2', '64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.d1', '64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.n1.a1', '2.u1.a1', '2.ba1.a1'], 'contains': ['8.dd1.a1', '8.de1.a1', '8.dl1.a1', '8.ec1.a1', '8.eg1.a1', '8.ej1.a1', '8.fj1.a1'], 'core': '4.fq1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3632, 1094, 5656, 754, 3634, 1094, 5652, 755], 'generators': [69, 66, 16], 'label': '256.30836.4.fq1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fq1.a1', 'normal_contained_in': ['2.u1.a1', '2.n1.a1', '2.ba1.a1'], 'normal_contains': ['8.dd1.a1', '8.de1.a1', '8.dl1.a1', '8.ec1.a1', '8.eg1.a1', '8.ej1.a1', '8.fj1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fq1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878948
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.q1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.h1.a1', '128.h1.b1', '128.h1.d1', '128.h1.c1', '128.m1.a1', '128.m1.b1', '128.k1.a1', '128.k1.b1', '128.n1.a1', '128.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.bj1.a1', '4.bl1.a1', '4.bm1.a1', '4.bw1.a1', '4.by1.a1', '4.cd1.a1', '4.cg1.a1', '4.cs1.a1', '4.ct1.a1', '4.cy1.a1', '4.de1.a1', '4.ee1.a1', '4.ef1.a1', '4.ek1.a1', '4.eq1.a1'], 'core': '2.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3257, 5347, 8007, 2767, 3259, 5345, 8016, 2773], 'generators': [1, 66, 4, 16], 'label': '256.30836.2.q1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.q1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.bj1.a1', '4.bm1.a1', '4.bl1.a1', '4.bw1.a1', '4.by1.a1', '4.cg1.a1', '4.cd1.a1', '4.cs1.a1', '4.ct1.a1', '4.de1.a1', '4.cy1.a1', '4.ee1.a1', '4.ef1.a1', '4.eq1.a1', '4.ek1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.q1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.q1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878949
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fr1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.b1', '64.dl1.j1', '64.dl1.i1', '64.dl1.f1', '64.dl1.e1', '64.dl1.m1', '64.dl1.n1', '64.dl1.d1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.o1', '64.dj1.c1', '64.dj1.h1', '64.dj1.l1', '64.dj1.k1', '64.dj1.g1', '64.dj1.d1', '64.dj1.p1', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.g1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.m1.a1', '2.v1.a1', '2.ba1.a1'], 'contains': ['8.dd1.a1', '8.df1.a1', '8.dm1.a1', '8.ed1.a1', '8.ef1.a1', '8.eq1.a1', '8.fk1.a1'], 'core': '4.fr1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5490, 1797, 8409, 2662, 5492, 1796, 8402, 2667], 'generators': [65, 70, 16], 'label': '256.30836.4.fr1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fr1.a1', 'normal_contained_in': ['2.v1.a1', '2.m1.a1', '2.ba1.a1'], 'normal_contains': ['8.dd1.a1', '8.df1.a1', '8.dm1.a1', '8.ed1.a1', '8.ef1.a1', '8.eq1.a1', '8.fk1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fr1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fr1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878950
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fs1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.b1', '64.dl1.j1', '64.dl1.i1', '64.dl1.f1', '64.dl1.e1', '64.dl1.m1', '64.dl1.n1', '64.dl1.c1', '64.dl1.d1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dl1.g1', '64.dl1.o1', '64.dl1.p1', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.g1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.e2', '64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.d1', '64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.n1.a1', '2.w1.a1', '2.y1.a1'], 'contains': ['8.de1.a1', '8.di1.a1', '8.dk1.a1', '8.ek1.a1', '8.en1.a1', '8.fm1.a1', '8.ft1.a1'], 'core': '4.fs1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1671, 1514, 5633, 4586, 1672, 1513, 5629, 4596], 'generators': [69, 66, 80], 'label': '256.30836.4.fs1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fs1.a1', 'normal_contained_in': ['2.w1.a1', '2.n1.a1', '2.y1.a1'], 'normal_contains': ['8.de1.a1', '8.dk1.a1', '8.di1.a1', '8.en1.a1', '8.ek1.a1', '8.fm1.a1', '8.ft1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fs1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fs1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878951
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ft1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.p1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.f1', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.d1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.do1.a1', '64.do1.c2', '64.do1.a2', '64.do1.c1', '64.do1.d1', '64.do1.b2', '64.do1.d2', '64.do1.b1', '64.do1.g2', '64.do1.e1', '64.do1.g1', '64.do1.e2', '64.do1.f2', '64.do1.h1', '64.do1.f1', '64.do1.h2', '64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1'], 'conjugacy_class_count': 1, 'contained_in': ['2.l1.a1', '2.w1.a1', '2.ba1.a1'], 'contains': ['8.de1.a1', '8.dj1.a1', '8.dm1.a1', '8.el1.a1', '8.em1.a1', '8.fr1.a1', '8.fy1.a1'], 'core': '4.ft1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3059, 3161, 6957, 1696, 3061, 3160, 6951, 1700], 'generators': [81, 66, 20], 'label': '256.30836.4.ft1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ft1.a1', 'normal_contained_in': ['2.w1.a1', '2.l1.a1', '2.ba1.a1'], 'normal_contains': ['8.de1.a1', '8.dj1.a1', '8.dm1.a1', '8.el1.a1', '8.em1.a1', '8.fr1.a1', '8.fy1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ft1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ft1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879452
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ct1.a1', '8.gp1.a1', '8.gp1.b1'], 'contains': ['32.cv1.a1', '32.da1.a1', '32.dd1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1547, -1, 7542, -1, 1548, -1, 7535, -1], 'generators': [17, 18], 'label': '256.30836.16.fk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ct1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.fk1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878952
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fu1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.b1', '64.dl1.m1', '64.dl1.n1', '64.dl1.f1', '64.dl1.e1', '64.dl1.j1', '64.dl1.i1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.k1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.dj1.a1', '64.dj1.m1', '64.dj1.n1', '64.dj1.b1', '64.dj1.e1', '64.dj1.i1', '64.dj1.j1', '64.dj1.f1', '64.dj1.o1', '64.dj1.c1', '64.dj1.d1', '64.dj1.p1', '64.dj1.k1', '64.dj1.g1', '64.dj1.h1', '64.dj1.l1', '64.do1.a1', '64.do1.c1', '64.do1.a2', '64.do1.c2', '64.do1.d1', '64.do1.b1', '64.do1.d2', '64.do1.b2', '64.do1.e1', '64.do1.g1', '64.do1.e2', '64.do1.g2', '64.do1.h1', '64.do1.f1', '64.do1.h2', '64.do1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.o1.a1', '2.v1.a1', '2.y1.a1'], 'contains': ['8.df1.a1', '8.dg1.a1', '8.di1.a1', '8.eo1.a1', '8.ep1.a1', '8.ex1.a1', '8.fa1.a1'], 'core': '4.fu1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7516, 601, 6191, 8686, 7519, 600, 6185, 8705], 'generators': [65, 70, 80], 'label': '256.30836.4.fu1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fu1.a1', 'normal_contained_in': ['2.v1.a1', '2.o1.a1', '2.y1.a1'], 'normal_contains': ['8.df1.a1', '8.dg1.a1', '8.di1.a1', '8.eo1.a1', '8.ep1.a1', '8.ex1.a1', '8.fa1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fu1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878953
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fv1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.g1', '64.di1.p1', '64.di1.n1', '64.di1.o1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.k1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.dl1.a1', '64.dl1.b1', '64.dl1.m1', '64.dl1.n1', '64.dl1.f1', '64.dl1.e1', '64.dl1.j1', '64.dl1.i1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.do1.a1', '64.do1.c1', '64.do1.a2', '64.do1.c2', '64.do1.d1', '64.do1.b1', '64.do1.d2', '64.do1.b2', '64.do1.e1', '64.do1.g1', '64.do1.e2', '64.do1.g2', '64.do1.h1', '64.do1.f1', '64.do1.h2', '64.do1.f2', '64.dj1.a1', '64.dj1.m1', '64.dj1.n1', '64.dj1.b1', '64.dj1.e1', '64.dj1.i1', '64.dj1.j1', '64.dj1.f1', '64.dj1.o1', '64.dj1.c1', '64.dj1.d1', '64.dj1.p1', '64.dj1.k1', '64.dj1.g1', '64.dj1.h1', '64.dj1.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.o1.a1', '2.t1.a1', '2.ba1.a1'], 'contains': ['8.df1.a1', '8.dj1.a1', '8.dl1.a1', '8.er1.a1', '8.et1.a1', '8.fq1.a1', '8.fx1.a1'], 'core': '4.fv1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8147, 765, 6563, 9520, 8151, 765, 6557, 9540], 'generators': [65, 82, 20], 'label': '256.30836.4.fv1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fv1.a1', 'normal_contained_in': ['2.t1.a1', '2.o1.a1', '2.ba1.a1'], 'normal_contains': ['8.df1.a1', '8.dl1.a1', '8.dj1.a1', '8.er1.a1', '8.et1.a1', '8.fx1.a1', '8.fq1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fv1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fv1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878954
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fw1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.e1', '64.di1.i1', '64.di1.h1', '64.di1.j1', '64.di1.f1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.do1.a1', '64.do1.b2', '64.do1.d2', '64.do1.c1', '64.do1.d1', '64.do1.c2', '64.do1.a2', '64.do1.b1', '64.do1.e2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.h2', '64.do1.g1', '64.do1.e1', '64.do1.f2', '64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.g1', '64.dj1.d1', '64.dj1.p1', '64.dj1.k1', '64.dj1.c1', '64.dj1.h1', '64.dj1.l1', '64.dj1.o1'], 'conjugacy_class_count': 1, 'contained_in': ['2.o1.a1', '2.u1.a1', '2.z1.a1'], 'contains': ['8.dg1.a1', '8.dh1.a1', '8.dl1.a1', '8.eu1.a1', '8.ev1.a1', '8.ez1.a1', '8.fb1.a1'], 'core': '4.fw1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7242, 7294, 6118, 9070, 7245, 7292, 6112, 9089], 'generators': [17, 82, 68], 'label': '256.30836.4.fw1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fw1.a1', 'normal_contained_in': ['2.u1.a1', '2.o1.a1', '2.z1.a1'], 'normal_contains': ['8.dh1.a1', '8.dg1.a1', '8.dl1.a1', '8.eu1.a1', '8.ez1.a1', '8.ev1.a1', '8.fb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fw1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fw1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878955
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fx1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.c1', '64.di1.b1', '64.di1.d1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.h1', '64.di1.l1', '64.di1.f1', '64.di1.m1', '64.di1.k1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.p1', '64.do1.a1', '64.do1.b2', '64.do1.d2', '64.do1.c1', '64.do1.d1', '64.do1.c2', '64.do1.a2', '64.do1.b1', '64.do1.f1', '64.do1.e2', '64.do1.g2', '64.do1.h1', '64.do1.g1', '64.do1.h2', '64.do1.f2', '64.do1.e1', '64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.h1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.k1', '64.dl1.c1', '64.dl1.d1', '64.dl1.l1', '64.dl1.p1', '64.dl1.h1', '64.dl1.g1', '64.dl1.o1'], 'conjugacy_class_count': 1, 'contained_in': ['2.o1.a1', '2.w1.a1', '2.x1.a1'], 'contains': ['8.dh1.a1', '8.di1.a1', '8.dj1.a1', '8.fe1.a1', '8.ff1.a1', '8.fl1.a1', '8.fp1.a1'], 'core': '4.fx1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3586, 2839, 6093, 5058, 3588, 2838, 6088, 5069], 'generators': [67, 68, 80], 'label': '256.30836.4.fx1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fx1.a1', 'normal_contained_in': ['2.w1.a1', '2.o1.a1', '2.x1.a1'], 'normal_contains': ['8.dh1.a1', '8.dj1.a1', '8.di1.a1', '8.ff1.a1', '8.fe1.a1', '8.fl1.a1', '8.fp1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fx1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fx1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878969
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.l1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.i1.a1', '4.q1.a1', '4.w1.a1', '4.ba1.a1', '4.bf1.a1', '4.bh1.a1'], 'contains': ['16.a1.a1', '16.r1.a1', '16.w1.a1', '16.gb1.a1', '16.gb1.b1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7757, 8218, 7515, 8902, 7761, 8215, 7508, 8921], 'generators': [2, 68, 128], 'label': '256.30836.8.l1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.f1.a1', '4.i1.a1', '4.q1.a1', '4.w1.a1', '4.ba1.a1', '4.bf1.a1', '4.bh1.a1'], 'normal_contains': ['16.a1.a1', '16.w1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878970
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.g1.a1', '4.h1.a1', '4.m1.a1', '4.n1.a1', '4.s1.a1', '4.bj1.a1', '4.bo1.a1', '4.bp1.a1', '4.bt1.a1', '4.cl1.a1', '4.cq1.a1', '4.dh1.a1', '4.dm1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7159, 3061, 5553, 7871, 7163, 3053, 5548, 7889], 'generators': [1, 2, 4, 80], 'label': '256.30836.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.g1.a1', '4.bj1.a1', '4.bo1.a1', '4.bp1.a1', '4.bt1.a1', '4.h1.a1', '4.m1.a1', '4.n1.a1', '4.s1.a1', '4.cl1.a1', '4.cq1.a1', '4.dh1.a1', '4.dm1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878956
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.fy1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.di1.a1', '64.di1.d1', '64.di1.b1', '64.di1.c1', '64.di1.p1', '64.di1.g1', '64.di1.o1', '64.di1.n1', '64.di1.h1', '64.di1.i1', '64.di1.e1', '64.di1.j1', '64.di1.l1', '64.di1.k1', '64.di1.m1', '64.di1.f1', '64.do1.a1', '64.do1.c2', '64.do1.a2', '64.do1.c1', '64.do1.d1', '64.do1.b2', '64.do1.d2', '64.do1.b1', '64.do1.e1', '64.do1.g2', '64.do1.e2', '64.do1.g1', '64.do1.h1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.dj1.a1', '64.dj1.b1', '64.dj1.n1', '64.dj1.m1', '64.dj1.e1', '64.dj1.f1', '64.dj1.j1', '64.dj1.i1', '64.dj1.d1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1'], 'conjugacy_class_count': 1, 'contained_in': ['2.m1.a1', '2.w1.a1', '2.z1.a1'], 'contains': ['8.dh1.a1', '8.dk1.a1', '8.dm1.a1', '8.fg1.a1', '8.fh1.a1', '8.fn1.a1', '8.fo1.a1'], 'core': '4.fy1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1855, 9277, 8272, 4282, 1856, 9274, 8265, 4291], 'generators': [81, 18, 68], 'label': '256.30836.4.fy1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.fy1.a1', 'normal_contained_in': ['2.w1.a1', '2.m1.a1', '2.z1.a1'], 'normal_contains': ['8.dh1.a1', '8.dk1.a1', '8.dm1.a1', '8.fh1.a1', '8.fg1.a1', '8.fo1.a1', '8.fn1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.fy1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.fy1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878957
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.f1.a1', '16.bg1.a1', '16.bg1.b1', '16.bg1.c1', '16.bg1.d1', '16.bh1.a1', '16.co1.a1', '16.co1.b1', '16.dv1.a1', '16.dv1.b1', '16.eo1.a1', '16.eo1.b1', '16.fv1.a1', '16.fv1.b1', '16.hd1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9601, 8581, 3938, 9966, 9606, 8578, 3935, 9987], 'generators': [1, 2, 136, 128, 32], 'label': '256.30836.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.b1.a1', '16.a1.a1', '16.f1.a1', '16.bg1.b1', '16.bg1.d1', '16.bg1.a1', '16.bg1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878958
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.k1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.d1.a1', '16.bi1.a1', '16.bi1.b1', '16.cp1.a1', '16.cp1.b1', '16.dw1.a1', '16.dw1.b1', '16.ep1.a1', '16.fw1.a1', '16.fw1.b1', '16.he1.a1', '16.il1.a1', '16.il1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9628, 8488, 3911, 6386, 9632, 8485, 3908, 6399], 'generators': [2, 4, 136, 128, 32], 'label': '256.30836.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.h1.a1', '4.k1.a1', '4.j1.a1', '4.l1.a1', '4.i1.a1', '4.m1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878959
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.r1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.h1.a1', '128.h1.d1', '128.h1.c1', '128.h1.b1', '128.m1.a1', '128.m1.b1', '128.k1.a1', '128.k1.b1', '128.n1.a1', '128.n1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.bk1.a1', '4.bl1.a1', '4.bo1.a1', '4.bz1.a1', '4.cb1.a1', '4.cc1.a1', '4.ci1.a1', '4.cv1.a1', '4.cw1.a1', '4.cz1.a1', '4.dc1.a1', '4.eh1.a1', '4.ei1.a1', '4.el1.a1', '4.eo1.a1'], 'core': '2.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6189, 3488, 6310, 4999, 6192, 3487, 6310, 5010], 'generators': [1, 4, 16, 64], 'label': '256.30836.2.r1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.r1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.bl1.a1', '4.bk1.a1', '4.bo1.a1', '4.bz1.a1', '4.cc1.a1', '4.cb1.a1', '4.ci1.a1', '4.cz1.a1', '4.cv1.a1', '4.dc1.a1', '4.cw1.a1', '4.el1.a1', '4.eh1.a1', '4.eo1.a1', '4.ei1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.r1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.r1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878960
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.c1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.n1.a1', '4.o1.a1', '4.p1.a1', '4.q1.a1', '4.r1.a1', '4.s1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '16.g1.a1', '16.bj1.a1', '16.cq1.a1', '16.cq1.b1', '16.dx1.a1', '16.dx1.b1', '16.eq1.a1', '16.fx1.a1', '16.fx1.b1', '16.hf1.a1', '16.hf1.b1', '16.im1.a1', '16.im1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9654, 6001, 3897, 3901, 9659, 5999, 3894, 3909], 'generators': [5, 2, 136, 128, 32], 'label': '256.30836.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1', '4.n1.a1', '4.q1.a1', '4.p1.a1', '4.r1.a1', '4.o1.a1', '4.s1.a1'], 'normal_contains': ['16.a1.a1', '16.e1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878961
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.d1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.m1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.n1.a1', '4.t1.a1', '4.u1.a1', '4.v1.a1', '4.w1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '16.x1.a1', '16.cr1.a1', '16.cr1.b1', '16.fy1.a1', '16.fy1.b1', '16.in1.a1', '16.in1.b1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1850, 6265, 9478, 6562, 1851, 6264, 9471, 6576], 'generators': [81, 2, 32, 128], 'label': '256.30836.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1', '4.h1.a1', '4.n1.a1', '4.u1.a1', '4.w1.a1', '4.t1.a1', '4.v1.a1'], 'normal_contains': ['16.a1.a1', '16.h1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878962
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.e1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.t1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.o1.a1', '4.t1.a1', '4.x1.a1', '4.y1.a1', '4.z1.a1'], 'contains': ['16.a1.a1', '16.i1.a1', '16.k1.a1', '16.cs1.a1', '16.cs1.b1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4977, 5827, 9075, 2773, 4980, 5825, 9067, 2779], 'generators': [2, 64, 32], 'label': '256.30836.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.c1.a1', '4.i1.a1', '4.o1.a1', '4.t1.a1', '4.x1.a1', '4.z1.a1', '4.y1.a1'], 'normal_contains': ['16.a1.a1', '16.k1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878963
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.j1.a1', '4.p1.a1', '4.u1.a1', '4.x1.a1', '4.ba1.a1', '4.bb1.a1'], 'contains': ['16.a1.a1', '16.j1.a1', '16.t1.a1', '16.bk1.a1', '16.er1.a1', '16.fz1.a1', '16.fz1.b1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2367, 9580, 5996, 2660, 2368, 9576, 5991, 2665], 'generators': [2, 16, 136, 128], 'label': '256.30836.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.d1.a1', '4.j1.a1', '4.p1.a1', '4.u1.a1', '4.x1.a1', '4.bb1.a1', '4.ba1.a1'], 'normal_contains': ['16.a1.a1', '16.j1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878964
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.g1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.v1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.k1.a1', '4.q1.a1', '4.u1.a1', '4.bc1.a1', '4.bd1.a1', '4.be1.a1'], 'contains': ['16.a1.a1', '16.l1.a1', '16.o1.a1', '16.ct1.a1', '16.ct1.b1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3082, 8145, 9541, 2276, 3084, 8142, 9532, 2281], 'generators': [65, 2, 32], 'label': '256.30836.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.c1.a1', '4.k1.a1', '4.q1.a1', '4.u1.a1', '4.be1.a1', '4.bc1.a1', '4.bd1.a1'], 'normal_contains': ['16.a1.a1', '16.o1.a1', '16.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878971
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.s1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.h1.a1', '128.h1.b1', '128.h1.d1', '128.h1.c1', '128.m1.a1', '128.m1.b1', '128.k1.a1', '128.k1.b1', '128.n1.a1', '128.n1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.bm1.a1', '4.bn1.a1', '4.bo1.a1', '4.ce1.a1', '4.cf1.a1', '4.ch1.a1', '4.ck1.a1', '4.da1.a1', '4.db1.a1', '4.df1.a1', '4.dg1.a1', '4.em1.a1', '4.en1.a1', '4.er1.a1', '4.es1.a1'], 'core': '2.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6438, 3333, 7962, 2341, 6441, 3332, 7970, 2347], 'generators': [1, 66, 4, 80], 'label': '256.30836.2.s1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.s1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.bm1.a1', '4.bn1.a1', '4.bo1.a1', '4.ce1.a1', '4.cf1.a1', '4.ch1.a1', '4.ck1.a1', '4.dg1.a1', '4.df1.a1', '4.db1.a1', '4.da1.a1', '4.es1.a1', '4.er1.a1', '4.en1.a1', '4.em1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.s1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.s1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878972
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.m1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.m1.a1', '4.n1.a1', '4.y1.a1', '4.ba1.a1', '4.be1.a1', '4.bg1.a1'], 'contains': ['16.a1.a1', '16.u1.a1', '16.bb1.a1', '16.cw1.a1', '16.cw1.b1'], 'core': '8.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3144, 5237, 9509, 4194, 3145, 5235, 9500, 4203], 'generators': [2, 84, 32], 'label': '256.30836.8.m1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.m1.a1', 'normal_contained_in': ['4.g1.a1', '4.m1.a1', '4.n1.a1', '4.be1.a1', '4.ba1.a1', '4.bg1.a1', '4.y1.a1'], 'normal_contains': ['16.a1.a1', '16.u1.a1', '16.bb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.m1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878973
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.n1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.k1.a1', '4.o1.a1', '4.v1.a1', '4.bb1.a1', '4.bg1.a1', '4.bi1.a1'], 'contains': ['16.a1.a1', '16.y1.a1', '16.bd1.a1', '16.gc1.a1', '16.gc1.b1'], 'core': '8.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3266, 6053, 7158, 2479, 3267, 6051, 7152, 2485], 'generators': [69, 2, 128], 'label': '256.30836.8.n1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.n1.a1', 'normal_contained_in': ['4.f1.a1', '4.k1.a1', '4.o1.a1', '4.v1.a1', '4.bb1.a1', '4.bi1.a1', '4.bg1.a1'], 'normal_contains': ['16.a1.a1', '16.y1.a1', '16.bd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.n1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878974
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.o1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.n1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.h1.a1', '4.s1.a1', '4.z1.a1', '4.bb1.a1', '4.bd1.a1', '4.bf1.a1'], 'contains': ['16.a1.a1', '16.bc1.a1', '16.be1.a1', '16.gd1.a1', '16.gd1.b1'], 'core': '8.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3932, 7451, 6236, 8976, 3934, 7449, 6230, 8996], 'generators': [85, 2, 128], 'label': '256.30836.8.o1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.o1.a1', 'normal_contained_in': ['4.g1.a1', '4.h1.a1', '4.s1.a1', '4.bd1.a1', '4.bb1.a1', '4.z1.a1', '4.bf1.a1'], 'normal_contains': ['16.a1.a1', '16.bc1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.o1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878975
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.p1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bj1.a1', '4.bk1.a1', '4.bl1.a1', '4.bm1.a1', '4.bn1.a1', '4.bo1.a1'], 'contains': ['16.b1.a1', '16.c1.a1', '16.e1.a1', '16.bm1.a1', '16.bm1.b1', '16.cx1.a1', '16.dy1.a1', '16.dy1.b1', '16.et1.a1', '16.et1.b1', '16.ge1.a1', '16.hi1.a1', '16.hi1.b1', '16.ir1.a1', '16.ir1.b1'], 'core': '8.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9681, 6563, 3883, 709, 9685, 6560, 3880, 710], 'generators': [1, 4, 136, 128, 32], 'label': '256.30836.8.p1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.p1.a1', 'normal_contained_in': ['4.a1.a1', '4.bj1.a1', '4.bm1.a1', '4.bl1.a1', '4.bn1.a1', '4.bk1.a1', '4.bo1.a1'], 'normal_contains': ['16.b1.a1', '16.c1.a1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.p1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878976
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.q1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.bp1.a1', '4.bq1.a1', '4.br1.a1', '4.bs1.a1', '4.bt1.a1', '4.bu1.a1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.g1.a1', '16.bf1.a1', '16.bf1.b1', '16.bf1.c1', '16.bf1.d1', '16.bn1.a1', '16.cy1.a1', '16.eu1.a1', '16.eu1.b1', '16.gf1.a1', '16.hj1.a1', '16.is1.a1', '16.is1.b1'], 'core': '8.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9734, 8747, 3924, 9738, 9739, 8743, 3921, 9760], 'generators': [1, 6, 136, 128, 32], 'label': '256.30836.8.q1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.q1.a1', 'normal_contained_in': ['4.a1.a1', '4.bp1.a1', '4.bs1.a1', '4.br1.a1', '4.bq1.a1', '4.bu1.a1', '4.bt1.a1'], 'normal_contains': ['16.b1.a1', '16.d1.a1', '16.g1.a1', '16.bf1.a1', '16.bf1.b1', '16.bf1.c1', '16.bf1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.q1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878977
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.r1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bj1.a1', '4.bp1.a1', '4.bv1.a1', '4.bw1.a1', '4.bx1.a1', '4.by1.a1'], 'contains': ['16.b1.a1', '16.h1.a1', '16.v1.a1', '16.dz1.a1', '16.dz1.b1', '16.ev1.a1', '16.ev1.b1', '16.it1.a1', '16.it1.b1'], 'core': '8.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2692, 6863, 4697, 8834, 2694, 6861, 4692, 8853], 'generators': [1, 82, 32, 128], 'label': '256.30836.8.r1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.r1.a1', 'normal_contained_in': ['4.b1.a1', '4.bj1.a1', '4.bp1.a1', '4.bw1.a1', '4.bx1.a1', '4.bv1.a1', '4.by1.a1'], 'normal_contains': ['16.b1.a1', '16.h1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.r1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.r1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878978
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.s1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.s1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bk1.a1', '4.bq1.a1', '4.bv1.a1', '4.bz1.a1', '4.ca1.a1', '4.cb1.a1'], 'contains': ['16.b1.a1', '16.i1.a1', '16.l1.a1', '16.bo1.a1', '16.cz1.a1', '16.ea1.a1', '16.ea1.b1'], 'core': '8.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7874, 7828, 8529, 4939, 7878, 7826, 8522, 4950], 'generators': [1, 64, 136, 32], 'label': '256.30836.8.s1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.s1.a1', 'normal_contained_in': ['4.c1.a1', '4.bk1.a1', '4.bq1.a1', '4.bv1.a1', '4.bz1.a1', '4.ca1.a1', '4.cb1.a1'], 'normal_contains': ['16.b1.a1', '16.l1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.s1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878979
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.t1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.bl1.a1', '4.br1.a1', '4.bw1.a1', '4.bz1.a1', '4.cc1.a1', '4.cd1.a1'], 'contains': ['16.b1.a1', '16.j1.a1', '16.m1.a1', '16.ew1.a1', '16.ew1.b1'], 'core': '8.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1403, 6930, 7649, 8152, 1404, 6928, 7642, 8170], 'generators': [1, 16, 128], 'label': '256.30836.8.t1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.t1.a1', 'normal_contained_in': ['4.d1.a1', '4.bl1.a1', '4.br1.a1', '4.bw1.a1', '4.bz1.a1', '4.cc1.a1', '4.cd1.a1'], 'normal_contains': ['16.b1.a1', '16.j1.a1', '16.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.t1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878980
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.u1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.u1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bm1.a1', '4.bs1.a1', '4.bw1.a1', '4.ce1.a1', '4.cf1.a1', '4.cg1.a1'], 'contains': ['16.b1.a1', '16.k1.a1', '16.o1.a1', '16.da1.a1', '16.ex1.a1', '16.ex1.b1', '16.hk1.a1'], 'core': '8.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1286, 7268, 9452, 969, 1287, 7266, 9444, 970], 'generators': [1, 66, 32, 128], 'label': '256.30836.8.u1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.u1.a1', 'normal_contained_in': ['4.c1.a1', '4.bm1.a1', '4.bs1.a1', '4.bw1.a1', '4.ce1.a1', '4.cg1.a1', '4.cf1.a1'], 'normal_contains': ['16.b1.a1', '16.o1.a1', '16.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.u1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878981
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.v1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bn1.a1', '4.br1.a1', '4.bx1.a1', '4.ca1.a1', '4.ce1.a1', '4.ch1.a1'], 'contains': ['16.b1.a1', '16.n1.a1', '16.p1.a1', '16.iu1.a1', '16.iu1.b1'], 'core': '8.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8736, 7525, 5246, 3740, 8740, 7521, 5242, 3748], 'generators': [1, 22, 128], 'label': '256.30836.8.v1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.v1.a1', 'normal_contained_in': ['4.e1.a1', '4.bn1.a1', '4.br1.a1', '4.bx1.a1', '4.ce1.a1', '4.ca1.a1', '4.ch1.a1'], 'normal_contains': ['16.b1.a1', '16.p1.a1', '16.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.v1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878982
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.t1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.h1.a1', '128.h1.d1', '128.h1.c1', '128.h1.b1', '128.m1.a1', '128.m1.b1', '128.j1.a1', '128.j1.b1', '128.l1.a1', '128.l1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.bp1.a1', '4.bq1.a1', '4.bu1.a1', '4.bv1.a1', '4.by1.a1', '4.cb1.a1', '4.ck1.a1', '4.dn1.a1', '4.dq1.a1', '4.dt1.a1', '4.dz1.a1', '4.fj1.a1', '4.fm1.a1', '4.fp1.a1', '4.fv1.a1'], 'core': '2.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6395, 7713, 7597, 8308, 6398, 7711, 7590, 8325], 'generators': [1, 18, 20, 64], 'label': '256.30836.2.t1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.t1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.bp1.a1', '4.bq1.a1', '4.bu1.a1', '4.bv1.a1', '4.by1.a1', '4.cb1.a1', '4.ck1.a1', '4.dq1.a1', '4.dn1.a1', '4.dz1.a1', '4.dt1.a1', '4.fm1.a1', '4.fj1.a1', '4.fv1.a1', '4.fp1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.t1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.t1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878983
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.w1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.bo1.a1', '4.bt1.a1', '4.bz1.a1', '4.cf1.a1', '4.ch1.a1', '4.ci1.a1'], 'contains': ['16.b1.a1', '16.q1.a1', '16.x1.a1', '16.iv1.a1', '16.iv1.b1'], 'core': '8.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8981, 1378, 5119, 7929, 8985, 1378, 5114, 7946], 'generators': [1, 80, 128], 'label': '256.30836.8.w1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.w1.a1', 'normal_contained_in': ['4.b1.a1', '4.bo1.a1', '4.bt1.a1', '4.cf1.a1', '4.bz1.a1', '4.ch1.a1', '4.ci1.a1'], 'normal_contains': ['16.b1.a1', '16.q1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.w1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878984
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.x1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.x1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.bk1.a1', '4.bs1.a1', '4.bx1.a1', '4.cc1.a1', '4.ci1.a1', '4.cj1.a1'], 'contains': ['16.b1.a1', '16.r1.a1', '16.y1.a1', '16.bp1.a1', '16.ey1.a1', '16.ey1.b1', '16.gg1.a1'], 'core': '8.x1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1799, 8627, 4977, 4060, 1800, 8624, 4974, 4068], 'generators': [1, 68, 136, 128], 'label': '256.30836.8.x1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.x1.a1', 'normal_contained_in': ['4.f1.a1', '4.bk1.a1', '4.bs1.a1', '4.bx1.a1', '4.cc1.a1', '4.ci1.a1', '4.cj1.a1'], 'normal_contains': ['16.b1.a1', '16.y1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.x1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878985
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.y1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.bl1.a1', '4.bu1.a1', '4.by1.a1', '4.cb1.a1', '4.cg1.a1', '4.ci1.a1'], 'contains': ['16.b1.a1', '16.s1.a1', '16.z1.a1', '16.iw1.a1', '16.iw1.b1'], 'core': '8.y1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8431, 6615, 5522, 7367, 8435, 6612, 5517, 7383], 'generators': [1, 20, 128], 'label': '256.30836.8.y1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.y1.a1', 'normal_contained_in': ['4.e1.a1', '4.bl1.a1', '4.bu1.a1', '4.by1.a1', '4.cg1.a1', '4.cb1.a1', '4.ci1.a1'], 'normal_contains': ['16.b1.a1', '16.z1.a1', '16.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.y1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878986
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.z1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.bn1.a1', '4.bu1.a1', '4.bv1.a1', '4.cf1.a1', '4.cj1.a1', '4.ck1.a1'], 'contains': ['16.b1.a1', '16.t1.a1', '16.ba1.a1', '16.ez1.a1', '16.ez1.b1'], 'core': '8.z1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1343, 9258, 7254, 7780, 1343, 9255, 7247, 7797], 'generators': [1, 18, 128], 'label': '256.30836.8.z1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.z1.a1', 'normal_contained_in': ['4.d1.a1', '4.bn1.a1', '4.bu1.a1', '4.bv1.a1', '4.cf1.a1', '4.cj1.a1', '4.ck1.a1'], 'normal_contains': ['16.b1.a1', '16.ba1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.z1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878987
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ba1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.o1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bo1.a1', '4.bp1.a1', '4.cb1.a1', '4.cc1.a1', '4.ce1.a1', '4.ck1.a1'], 'contains': ['16.b1.a1', '16.u1.a1', '16.bc1.a1', '16.eb1.a1', '16.eb1.b1'], 'core': '8.ba1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8150, 7597, 6611, 7854, 8154, 7594, 6605, 7872], 'generators': [1, 84, 32], 'label': '256.30836.8.ba1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ba1.a1', 'normal_contained_in': ['4.g1.a1', '4.bo1.a1', '4.bp1.a1', '4.ce1.a1', '4.cc1.a1', '4.cb1.a1', '4.ck1.a1'], 'normal_contains': ['16.b1.a1', '16.bc1.a1', '16.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ba1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878988
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bb1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.bb1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.bm1.a1', '4.bq1.a1', '4.by1.a1', '4.cd1.a1', '4.ch1.a1', '4.ck1.a1'], 'contains': ['16.b1.a1', '16.w1.a1', '16.bd1.a1', '16.ec1.a1', '16.ec1.b1', '16.gh1.a1', '16.hl1.a1'], 'core': '8.bb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9036, 7135, 8811, 9443, 9041, 7132, 8803, 9463], 'generators': [1, 70, 32, 128], 'label': '256.30836.8.bb1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bb1.a1', 'normal_contained_in': ['4.f1.a1', '4.bm1.a1', '4.bq1.a1', '4.by1.a1', '4.cd1.a1', '4.ch1.a1', '4.ck1.a1'], 'normal_contains': ['16.b1.a1', '16.w1.a1', '16.bd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bb1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30878989
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bc1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.bj1.a1', '4.bt1.a1', '4.ca1.a1', '4.cd1.a1', '4.cg1.a1', '4.cj1.a1'], 'contains': ['16.b1.a1', '16.bb1.a1', '16.be1.a1', '16.fa1.a1', '16.fa1.b1'], 'core': '8.bc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1944, 6405, 6853, 5637, 1944, 6403, 6847, 5649], 'generators': [1, 86, 128], 'label': '256.30836.8.bc1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bc1.a1', 'normal_contained_in': ['4.g1.a1', '4.bj1.a1', '4.bt1.a1', '4.cg1.a1', '4.cd1.a1', '4.ca1.a1', '4.cj1.a1'], 'normal_contains': ['16.b1.a1', '16.bb1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bc1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878990
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bd1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.cl1.a1', '4.cm1.a1', '4.cn1.a1', '4.co1.a1', '4.cp1.a1', '4.cq1.a1'], 'contains': ['16.c1.a1', '16.f1.a1', '16.g1.a1', '16.bq1.a1', '16.bq1.b1', '16.db1.a1', '16.ed1.a1', '16.ed1.b1', '16.fb1.a1', '16.gi1.a1', '16.hm1.a1', '16.ix1.a1', '16.ix1.b1'], 'core': '8.bd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9707, 1474, 3855, 6759, 9712, 1474, 3852, 6774], 'generators': [3, 4, 136, 128, 32], 'label': '256.30836.8.bd1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bd1.a1', 'normal_contained_in': ['4.a1.a1', '4.cl1.a1', '4.cm1.a1', '4.cn1.a1', '4.co1.a1', '4.cp1.a1', '4.cq1.a1'], 'normal_contains': ['16.c1.a1', '16.f1.a1', '16.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bd1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30878991
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.be1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bj1.a1', '4.cl1.a1', '4.cr1.a1', '4.cs1.a1', '4.ct1.a1', '4.cu1.a1'], 'contains': ['16.c1.a1', '16.h1.a1', '16.be1.a1', '16.br1.a1', '16.br1.b1', '16.fc1.a1', '16.gj1.a1'], 'core': '8.be1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [521, 6517, 5551, 1947, 521, 6514, 5546, 1951], 'generators': [83, 4, 136, 128], 'label': '256.30836.8.be1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.be1.a1', 'normal_contained_in': ['4.bj1.a1', '4.h1.a1', '4.cl1.a1', '4.cs1.a1', '4.cr1.a1', '4.cu1.a1', '4.ct1.a1'], 'normal_contains': ['16.c1.a1', '16.h1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.be1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878992
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bf1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.bk1.a1', '4.cm1.a1', '4.cr1.a1', '4.cv1.a1', '4.cw1.a1', '4.cx1.a1'], 'contains': ['16.c1.a1', '16.i1.a1', '16.r1.a1', '16.bs1.a1', '16.bs1.b1'], 'core': '8.bf1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7485, 8000, 6470, 2090, 7489, 7997, 6464, 2095], 'generators': [4, 64, 136], 'label': '256.30836.8.bf1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bf1.a1', 'normal_contained_in': ['4.bk1.a1', '4.i1.a1', '4.cm1.a1', '4.cr1.a1', '4.cv1.a1', '4.cw1.a1', '4.cx1.a1'], 'normal_contains': ['16.c1.a1', '16.i1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bf1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878993
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.u1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.h1.a1', '128.h1.b1', '128.h1.c1', '128.h1.d1', '128.m1.a1', '128.m1.b1', '128.j1.a1', '128.j1.b1', '128.l1.a1', '128.l1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.bp1.a1', '4.br1.a1', '4.bs1.a1', '4.bw1.a1', '4.bx1.a1', '4.cc1.a1', '4.ce1.a1', '4.do1.a1', '4.dp1.a1', '4.du1.a1', '4.ea1.a1', '4.fk1.a1', '4.fl1.a1', '4.fq1.a1', '4.fw1.a1'], 'core': '2.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2923, 7380, 6355, 3054, 2943, 7377, 6355, 3061], 'generators': [1, 66, 68, 16], 'label': '256.30836.2.u1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.u1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.bp1.a1', '4.bs1.a1', '4.br1.a1', '4.bw1.a1', '4.bx1.a1', '4.ce1.a1', '4.cc1.a1', '4.do1.a1', '4.dp1.a1', '4.ea1.a1', '4.du1.a1', '4.fk1.a1', '4.fl1.a1', '4.fw1.a1', '4.fq1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.u1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.u1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30878994
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bg1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.bl1.a1', '4.cn1.a1', '4.cs1.a1', '4.cv1.a1', '4.cy1.a1', '4.cz1.a1'], 'contains': ['16.c1.a1', '16.j1.a1', '16.s1.a1', '16.bt1.a1', '16.bt1.b1'], 'core': '8.bg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7216, 2189, 5059, 656, 7220, 2188, 5054, 657], 'generators': [4, 16, 136], 'label': '256.30836.8.bg1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bg1.a1', 'normal_contained_in': ['4.bl1.a1', '4.j1.a1', '4.cn1.a1', '4.cs1.a1', '4.cz1.a1', '4.cy1.a1', '4.cv1.a1'], 'normal_contains': ['16.c1.a1', '16.j1.a1', '16.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bg1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878995
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bh1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.bm1.a1', '4.co1.a1', '4.ct1.a1', '4.cy1.a1', '4.da1.a1', '4.db1.a1'], 'contains': ['16.c1.a1', '16.k1.a1', '16.w1.a1', '16.hn1.a1'], 'core': '8.bh1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7967, 324, 7764, 506, 7971, 323, 7757, 507], 'generators': [66, 4, 128], 'label': '256.30836.8.bh1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bh1.a1', 'normal_contained_in': ['4.bm1.a1', '4.i1.a1', '4.co1.a1', '4.ct1.a1', '4.cy1.a1', '4.db1.a1', '4.da1.a1'], 'normal_contains': ['16.c1.a1', '16.k1.a1', '16.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bh1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878996
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bi1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.bk1.a1', '4.co1.a1', '4.cu1.a1', '4.cz1.a1', '4.dc1.a1', '4.dd1.a1'], 'contains': ['16.c1.a1', '16.l1.a1', '16.y1.a1', '16.bu1.a1', '16.bu1.b1'], 'core': '8.bi1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3388, 1035, 5439, 108, 3389, 1035, 5434, 109], 'generators': [65, 4, 136], 'label': '256.30836.8.bi1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bi1.a1', 'normal_contained_in': ['4.bk1.a1', '4.k1.a1', '4.co1.a1', '4.cu1.a1', '4.cz1.a1', '4.dd1.a1', '4.dc1.a1'], 'normal_contains': ['16.c1.a1', '16.l1.a1', '16.y1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bi1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878997
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bj1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.bl1.a1', '4.cp1.a1', '4.ct1.a1', '4.cw1.a1', '4.dc1.a1', '4.de1.a1'], 'contains': ['16.c1.a1', '16.m1.a1', '16.z1.a1', '16.dc1.a1'], 'core': '8.bj1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3022, 6333, 8559, 8004, 3023, 6330, 8551, 8021], 'generators': [17, 4, 32], 'label': '256.30836.8.bj1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bj1.a1', 'normal_contained_in': ['4.bl1.a1', '4.l1.a1', '4.cp1.a1', '4.ct1.a1', '4.de1.a1', '4.dc1.a1', '4.cw1.a1'], 'normal_contains': ['16.c1.a1', '16.m1.a1', '16.z1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bj1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878998
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bk1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.bn1.a1', '4.cp1.a1', '4.cu1.a1', '4.cx1.a1', '4.da1.a1', '4.df1.a1'], 'contains': ['16.c1.a1', '16.n1.a1', '16.t1.a1', '16.bv1.a1', '16.bv1.b1'], 'core': '8.bk1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8370, 9052, 4885, 1112, 8374, 9049, 4881, 1114], 'generators': [18, 4, 136], 'label': '256.30836.8.bk1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bk1.a1', 'normal_contained_in': ['4.bn1.a1', '4.j1.a1', '4.cp1.a1', '4.cu1.a1', '4.df1.a1', '4.da1.a1', '4.cx1.a1'], 'normal_contains': ['16.c1.a1', '16.n1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bk1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30878999
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bl1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.bm1.a1', '4.cm1.a1', '4.cs1.a1', '4.de1.a1', '4.df1.a1', '4.dg1.a1'], 'contains': ['16.c1.a1', '16.o1.a1', '16.bd1.a1', '16.ho1.a1'], 'core': '8.bl1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4781, 7067, 8914, 357, 4784, 7065, 8906, 358], 'generators': [67, 4, 128], 'label': '256.30836.8.bl1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bl1.a1', 'normal_contained_in': ['4.bm1.a1', '4.k1.a1', '4.cm1.a1', '4.cs1.a1', '4.dg1.a1', '4.de1.a1', '4.df1.a1'], 'normal_contains': ['16.c1.a1', '16.o1.a1', '16.bd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bl1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879000
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bm1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.bn1.a1', '4.cn1.a1', '4.cr1.a1', '4.db1.a1', '4.dd1.a1', '4.dg1.a1'], 'contains': ['16.c1.a1', '16.p1.a1', '16.ba1.a1', '16.dd1.a1'], 'core': '8.bm1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3205, 1599, 8142, 1186, 3206, 1599, 8135, 1189], 'generators': [19, 4, 32], 'label': '256.30836.8.bm1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bm1.a1', 'normal_contained_in': ['4.bn1.a1', '4.l1.a1', '4.cn1.a1', '4.cr1.a1', '4.dg1.a1', '4.dd1.a1', '4.db1.a1'], 'normal_contains': ['16.c1.a1', '16.p1.a1', '16.ba1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bm1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879001
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bn1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bo1.a1', '4.cl1.a1', '4.cv1.a1', '4.da1.a1', '4.dc1.a1', '4.dg1.a1'], 'contains': ['16.c1.a1', '16.q1.a1', '16.u1.a1', '16.bw1.a1', '16.bw1.b1'], 'core': '8.bn1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7818, 33, 4853, 4763, 7822, 33, 4849, 4773], 'generators': [4, 80, 136], 'label': '256.30836.8.bn1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bn1.a1', 'normal_contained_in': ['4.bo1.a1', '4.m1.a1', '4.cl1.a1', '4.dg1.a1', '4.cv1.a1', '4.dc1.a1', '4.da1.a1'], 'normal_contains': ['16.c1.a1', '16.u1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bn1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879002
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bo1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bj1.a1', '4.cq1.a1', '4.cx1.a1', '4.cy1.a1', '4.dd1.a1', '4.de1.a1'], 'contains': ['16.c1.a1', '16.v1.a1', '16.bb1.a1', '16.fd1.a1'], 'core': '8.bo1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6213, 251, 5580, 1742, 6216, 251, 5576, 1745], 'generators': [82, 4, 128], 'label': '256.30836.8.bo1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bo1.a1', 'normal_contained_in': ['4.bj1.a1', '4.m1.a1', '4.cq1.a1', '4.de1.a1', '4.cy1.a1', '4.dd1.a1', '4.cx1.a1'], 'normal_contains': ['16.c1.a1', '16.bb1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bo1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879003
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bp1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bo1.a1', '4.cq1.a1', '4.cw1.a1', '4.cz1.a1', '4.db1.a1', '4.df1.a1'], 'contains': ['16.c1.a1', '16.x1.a1', '16.bc1.a1', '16.gk1.a1'], 'core': '8.bp1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6813, 1527, 6358, 5380, 6816, 1526, 6353, 5392], 'generators': [81, 4, 128], 'label': '256.30836.8.bp1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bp1.a1', 'normal_contained_in': ['4.bo1.a1', '4.h1.a1', '4.cq1.a1', '4.df1.a1', '4.cz1.a1', '4.db1.a1', '4.cw1.a1'], 'normal_contains': ['16.c1.a1', '16.bc1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bp1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879215
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.i1.a1', '2.j1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.i1.a1', '8.bg1.a1', '8.bk1.a1', '8.bt1.a1', '8.bz1.a1', '8.ga1.a1', '8.ga1.b1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8607, 9665, 5117, 2089, 8612, 9662, 5113, 2094], 'generators': [2, 4, 16, 136], 'label': '256.30836.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.c1.a1', '2.i1.a1', '2.j1.a1'], 'normal_contains': ['8.b1.a1', '8.f1.a1', '8.i1.a1', '8.bg1.a1', '8.bk1.a1', '8.bt1.a1', '8.bz1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879004
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.v1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.j1.a1', '128.j1.b1', '128.l1.a1', '128.l1.b1', '128.h1.a1', '128.h1.d1', '128.h1.c1', '128.h1.b1', '128.m1.a1', '128.m1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.bq1.a1', '4.br1.a1', '4.bt1.a1', '4.bz1.a1', '4.ca1.a1', '4.cd1.a1', '4.ch1.a1', '4.dr1.a1', '4.ds1.a1', '4.dv1.a1', '4.dy1.a1', '4.fn1.a1', '4.fo1.a1', '4.fr1.a1', '4.fu1.a1'], 'core': '2.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6351, 3385, 7822, 6884, 6354, 3384, 7815, 6899], 'generators': [1, 6, 16, 64], 'label': '256.30836.2.v1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.v1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.br1.a1', '4.bq1.a1', '4.bt1.a1', '4.bz1.a1', '4.cd1.a1', '4.ca1.a1', '4.ch1.a1', '4.dv1.a1', '4.dr1.a1', '4.dy1.a1', '4.ds1.a1', '4.fr1.a1', '4.fn1.a1', '4.fu1.a1', '4.fo1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.v1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.v1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879005
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bq1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.dh1.a1', '4.di1.a1', '4.dj1.a1', '4.dk1.a1', '4.dl1.a1', '4.dm1.a1'], 'contains': ['16.d1.a1', '16.e1.a1', '16.f1.a1', '16.bx1.a1', '16.de1.a1', '16.ee1.a1', '16.ee1.b1', '16.fe1.a1', '16.gl1.a1', '16.hp1.a1', '16.hp1.b1', '16.iy1.a1', '16.iy1.b1'], 'core': '8.bq1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9188, 4878, 3869, 7607, 9193, 4877, 3866, 7623], 'generators': [5, 6, 136, 128, 32], 'label': '256.30836.8.bq1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bq1.a1', 'normal_contained_in': ['4.a1.a1', '4.dh1.a1', '4.di1.a1', '4.dj1.a1', '4.dl1.a1', '4.dk1.a1', '4.dm1.a1'], 'normal_contains': ['16.d1.a1', '16.e1.a1', '16.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bq1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879006
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.br1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bp1.a1', '4.dh1.a1', '4.dn1.a1', '4.do1.a1', '4.dp1.a1', '4.dq1.a1'], 'contains': ['16.d1.a1', '16.h1.a1', '16.bc1.a1', '16.ef1.a1', '16.ef1.b1', '16.gm1.a1', '16.hq1.a1'], 'core': '8.br1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5340, 8535, 6669, 6433, 5343, 8531, 6663, 6447], 'generators': [85, 6, 32, 128], 'label': '256.30836.8.br1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.br1.a1', 'normal_contained_in': ['4.bp1.a1', '4.h1.a1', '4.dh1.a1', '4.do1.a1', '4.dp1.a1', '4.dq1.a1', '4.dn1.a1'], 'normal_contains': ['16.d1.a1', '16.h1.a1', '16.bc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.br1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.br1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879007
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bs1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.bq1.a1', '4.di1.a1', '4.dn1.a1', '4.dr1.a1', '4.ds1.a1', '4.dt1.a1'], 'contains': ['16.d1.a1', '16.i1.a1', '16.w1.a1', '16.eg1.a1', '16.eg1.b1'], 'core': '8.bs1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8674, 8436, 7998, 8377, 8679, 8433, 7991, 8395], 'generators': [6, 64, 32], 'label': '256.30836.8.bs1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bs1.a1', 'normal_contained_in': ['4.bq1.a1', '4.i1.a1', '4.di1.a1', '4.dn1.a1', '4.dr1.a1', '4.ds1.a1', '4.dt1.a1'], 'normal_contains': ['16.d1.a1', '16.i1.a1', '16.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bs1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879008
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bt1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.br1.a1', '4.dj1.a1', '4.do1.a1', '4.dr1.a1', '4.du1.a1', '4.dv1.a1'], 'contains': ['16.d1.a1', '16.j1.a1', '16.n1.a1', '16.by1.a1'], 'core': '8.bt1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8089, 4543, 5349, 5232, 8093, 4541, 5344, 5242], 'generators': [6, 16, 136], 'label': '256.30836.8.bt1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bt1.a1', 'normal_contained_in': ['4.br1.a1', '4.j1.a1', '4.dj1.a1', '4.do1.a1', '4.dv1.a1', '4.du1.a1', '4.dr1.a1'], 'normal_contains': ['16.d1.a1', '16.j1.a1', '16.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bt1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879009
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bu1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.bs1.a1', '4.dk1.a1', '4.dp1.a1', '4.du1.a1', '4.dw1.a1', '4.dx1.a1'], 'contains': ['16.d1.a1', '16.k1.a1', '16.r1.a1', '16.ff1.a1'], 'core': '8.bu1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3686, 4680, 6326, 1816, 3687, 4679, 6321, 1820], 'generators': [66, 68, 128], 'label': '256.30836.8.bu1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bu1.a1', 'normal_contained_in': ['4.bs1.a1', '4.i1.a1', '4.dk1.a1', '4.dp1.a1', '4.du1.a1', '4.dx1.a1', '4.dw1.a1'], 'normal_contains': ['16.d1.a1', '16.k1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bu1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879010
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bv1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.bq1.a1', '4.dk1.a1', '4.dq1.a1', '4.dv1.a1', '4.dy1.a1', '4.dz1.a1'], 'contains': ['16.d1.a1', '16.l1.a1', '16.bd1.a1', '16.eh1.a1', '16.eh1.b1'], 'core': '8.bv1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5704, 4754, 8339, 5455, 5708, 4752, 8332, 5467], 'generators': [65, 6, 32], 'label': '256.30836.8.bv1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bv1.a1', 'normal_contained_in': ['4.bq1.a1', '4.k1.a1', '4.dk1.a1', '4.dq1.a1', '4.dv1.a1', '4.dy1.a1', '4.dz1.a1'], 'normal_contains': ['16.d1.a1', '16.l1.a1', '16.bd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bv1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879011
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bw1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.br1.a1', '4.dl1.a1', '4.dp1.a1', '4.ds1.a1', '4.dy1.a1', '4.ea1.a1'], 'contains': ['16.d1.a1', '16.m1.a1', '16.p1.a1', '16.df1.a1'], 'core': '8.bw1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3747, 8363, 8590, 8078, 3748, 8360, 8583, 8096], 'generators': [17, 6, 32], 'label': '256.30836.8.bw1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bw1.a1', 'normal_contained_in': ['4.br1.a1', '4.l1.a1', '4.dl1.a1', '4.dp1.a1', '4.ea1.a1', '4.dy1.a1', '4.ds1.a1'], 'normal_contains': ['16.d1.a1', '16.p1.a1', '16.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bw1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879012
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bx1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.bs1.a1', '4.di1.a1', '4.do1.a1', '4.ea1.a1', '4.eb1.a1', '4.ec1.a1'], 'contains': ['16.d1.a1', '16.o1.a1', '16.y1.a1', '16.fg1.a1'], 'core': '8.bx1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2005, 8798, 6547, 3074, 2005, 8795, 6542, 3081], 'generators': [69, 6, 128], 'label': '256.30836.8.bx1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bx1.a1', 'normal_contained_in': ['4.bs1.a1', '4.k1.a1', '4.di1.a1', '4.do1.a1', '4.ea1.a1', '4.eb1.a1', '4.ec1.a1'], 'normal_contains': ['16.d1.a1', '16.o1.a1', '16.y1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bx1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879013
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.by1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bt1.a1', '4.dh1.a1', '4.dr1.a1', '4.dw1.a1', '4.dy1.a1', '4.eb1.a1'], 'contains': ['16.d1.a1', '16.q1.a1', '16.bb1.a1', '16.hr1.a1'], 'core': '8.by1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6972, 621, 6153, 6047, 6975, 621, 6147, 6060], 'generators': [6, 80, 128], 'label': '256.30836.8.by1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.by1.a1', 'normal_contained_in': ['4.bt1.a1', '4.m1.a1', '4.dh1.a1', '4.eb1.a1', '4.dr1.a1', '4.dy1.a1', '4.dw1.a1'], 'normal_contains': ['16.d1.a1', '16.bb1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.by1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.by1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879014
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.bz1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.bu1.a1', '4.dl1.a1', '4.dq1.a1', '4.dt1.a1', '4.dw1.a1', '4.ec1.a1'], 'contains': ['16.d1.a1', '16.s1.a1', '16.t1.a1', '16.bz1.a1'], 'core': '8.bz1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6448, 9513, 5935, 4409, 6451, 9509, 5930, 4420], 'generators': [18, 20, 136], 'label': '256.30836.8.bz1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.bz1.a1', 'normal_contained_in': ['4.bu1.a1', '4.j1.a1', '4.dl1.a1', '4.dq1.a1', '4.ec1.a1', '4.dw1.a1', '4.dt1.a1'], 'normal_contains': ['16.d1.a1', '16.s1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.bz1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879216
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.bg1.b1', '16.in1.a1', '16.iq1.a1', '16.it1.b1', '16.iv1.b1', '16.iz1.b1', '16.jc1.b1'], 'core': '16.bg1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9146, -1, 3990, -1, 9151, -1, 3986, -1], 'generators': [129, 2, 80], 'label': '256.30836.8.hh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.hh1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hh1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879015
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.w1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.h1.a1', '128.h1.b1', '128.h1.c1', '128.h1.d1', '128.m1.a1', '128.m1.b1', '128.j1.a1', '128.j1.b1', '128.l1.a1', '128.l1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.bs1.a1', '4.bt1.a1', '4.bu1.a1', '4.cf1.a1', '4.cg1.a1', '4.ci1.a1', '4.cj1.a1', '4.dw1.a1', '4.dx1.a1', '4.eb1.a1', '4.ec1.a1', '4.fs1.a1', '4.ft1.a1', '4.fx1.a1', '4.fy1.a1'], 'core': '2.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2678, 3695, 6494, 4729, 2752, 3694, 6481, 4739], 'generators': [1, 66, 68, 80], 'label': '256.30836.2.w1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.w1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.bs1.a1', '4.bu1.a1', '4.bt1.a1', '4.cg1.a1', '4.cf1.a1', '4.ci1.a1', '4.cj1.a1', '4.eb1.a1', '4.ec1.a1', '4.dx1.a1', '4.dw1.a1', '4.fy1.a1', '4.fx1.a1', '4.fs1.a1', '4.ft1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.w1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.w1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879016
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ca1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '4.bp1.a1', '4.dm1.a1', '4.dt1.a1', '4.du1.a1', '4.dz1.a1', '4.ea1.a1'], 'contains': ['16.d1.a1', '16.u1.a1', '16.v1.a1', '16.ei1.a1', '16.ei1.b1'], 'core': '8.ca1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7033, 4470, 5381, 9225, 7036, 4469, 5375, 9245], 'generators': [82, 84, 32], 'label': '256.30836.8.ca1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ca1.a1', 'normal_contained_in': ['4.bp1.a1', '4.m1.a1', '4.dm1.a1', '4.ea1.a1', '4.du1.a1', '4.dz1.a1', '4.dt1.a1'], 'normal_contains': ['16.d1.a1', '16.u1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ca1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879017
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cb1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bt1.a1', '4.dm1.a1', '4.ds1.a1', '4.dv1.a1', '4.dx1.a1', '4.ec1.a1'], 'contains': ['16.d1.a1', '16.x1.a1', '16.be1.a1', '16.gn1.a1'], 'core': '8.cb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4260, 4398, 6391, 8615, 4263, 4396, 6384, 8634], 'generators': [81, 6, 128], 'label': '256.30836.8.cb1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cb1.a1', 'normal_contained_in': ['4.bt1.a1', '4.h1.a1', '4.dm1.a1', '4.ec1.a1', '4.dv1.a1', '4.ds1.a1', '4.dx1.a1'], 'normal_contains': ['16.d1.a1', '16.be1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cb1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879018
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cc1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '4.bu1.a1', '4.dj1.a1', '4.dn1.a1', '4.dx1.a1', '4.dz1.a1', '4.eb1.a1'], 'contains': ['16.d1.a1', '16.z1.a1', '16.ba1.a1', '16.dg1.a1'], 'core': '8.cc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4599, 4326, 7483, 9374, 4601, 4324, 7476, 9395], 'generators': [21, 6, 32], 'label': '256.30836.8.cc1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cc1.a1', 'normal_contained_in': ['4.bu1.a1', '4.l1.a1', '4.dj1.a1', '4.dn1.a1', '4.eb1.a1', '4.dz1.a1', '4.dx1.a1'], 'normal_contains': ['16.d1.a1', '16.z1.a1', '16.ba1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cc1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879019
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cd1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.bj1.a1', '4.dh1.a1', '4.ed1.a1', '4.ee1.a1', '4.ef1.a1', '4.eg1.a1'], 'contains': ['16.e1.a1', '16.h1.a1', '16.bb1.a1', '16.dh1.a1', '16.fh1.a1', '16.hs1.a1', '16.hs1.b1'], 'core': '8.cd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1514, 5061, 8471, 176, 1514, 5060, 8463, 177], 'generators': [5, 86, 32, 128], 'label': '256.30836.8.cd1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cd1.a1', 'normal_contained_in': ['4.bj1.a1', '4.n1.a1', '4.dh1.a1', '4.ee1.a1', '4.eg1.a1', '4.ef1.a1', '4.ed1.a1'], 'normal_contains': ['16.e1.a1', '16.h1.a1', '16.bb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cd1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879020
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ce1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '4.bk1.a1', '4.di1.a1', '4.ed1.a1', '4.eh1.a1', '4.ei1.a1', '4.ej1.a1'], 'contains': ['16.e1.a1', '16.i1.a1', '16.y1.a1', '16.ca1.a1'], 'core': '8.ce1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5532, 5499, 6294, 1410, 5534, 5497, 6289, 1413], 'generators': [5, 64, 136], 'label': '256.30836.8.ce1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ce1.a1', 'normal_contained_in': ['4.bk1.a1', '4.o1.a1', '4.di1.a1', '4.ed1.a1', '4.eh1.a1', '4.ej1.a1', '4.ei1.a1'], 'normal_contains': ['16.e1.a1', '16.i1.a1', '16.y1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ce1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879021
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cf1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.bl1.a1', '4.dj1.a1', '4.ee1.a1', '4.eh1.a1', '4.ek1.a1', '4.el1.a1'], 'contains': ['16.e1.a1', '16.j1.a1', '16.z1.a1', '16.go1.a1'], 'core': '8.cf1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5174, 3511, 6089, 3398, 5176, 3510, 6084, 3405], 'generators': [5, 16, 128], 'label': '256.30836.8.cf1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cf1.a1', 'normal_contained_in': ['4.bl1.a1', '4.p1.a1', '4.dj1.a1', '4.ee1.a1', '4.el1.a1', '4.ek1.a1', '4.eh1.a1'], 'normal_contains': ['16.e1.a1', '16.j1.a1', '16.z1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cf1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879022
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cg1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '4.bm1.a1', '4.dk1.a1', '4.ef1.a1', '4.ek1.a1', '4.em1.a1', '4.en1.a1'], 'contains': ['16.e1.a1', '16.k1.a1', '16.bd1.a1', '16.ht1.a1', '16.ht1.b1'], 'core': '8.cg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5075, 3322, 8500, 34, 5078, 3320, 8492, 34], 'generators': [5, 66, 128], 'label': '256.30836.8.cg1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cg1.a1', 'normal_contained_in': ['4.bm1.a1', '4.o1.a1', '4.dk1.a1', '4.ef1.a1', '4.ek1.a1', '4.en1.a1', '4.em1.a1'], 'normal_contains': ['16.e1.a1', '16.k1.a1', '16.bd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cg1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879023
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ch1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.bk1.a1', '4.dk1.a1', '4.eg1.a1', '4.el1.a1', '4.eo1.a1', '4.ep1.a1'], 'contains': ['16.e1.a1', '16.l1.a1', '16.r1.a1', '16.cb1.a1'], 'core': '8.ch1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6152, 4252, 6204, 1592, 6155, 4251, 6199, 1595], 'generators': [65, 68, 136], 'label': '256.30836.8.ch1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ch1.a1', 'normal_contained_in': ['4.bk1.a1', '4.q1.a1', '4.dk1.a1', '4.eg1.a1', '4.el1.a1', '4.eo1.a1', '4.ep1.a1'], 'normal_contains': ['16.e1.a1', '16.l1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ch1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879024
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ci1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '4.bl1.a1', '4.dl1.a1', '4.ef1.a1', '4.ei1.a1', '4.eo1.a1', '4.eq1.a1'], 'contains': ['16.e1.a1', '16.m1.a1', '16.s1.a1', '16.hu1.a1', '16.hu1.b1'], 'core': '8.ci1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6092, 4995, 7059, 5306, 6094, 4993, 7053, 5317], 'generators': [17, 20, 128], 'label': '256.30836.8.ci1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ci1.a1', 'normal_contained_in': ['4.bl1.a1', '4.r1.a1', '4.dl1.a1', '4.ef1.a1', '4.eq1.a1', '4.eo1.a1', '4.ei1.a1'], 'normal_contains': ['16.e1.a1', '16.m1.a1', '16.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ci1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879025
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cj1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '4.bn1.a1', '4.dj1.a1', '4.ed1.a1', '4.em1.a1', '4.ep1.a1', '4.er1.a1'], 'contains': ['16.e1.a1', '16.n1.a1', '16.ba1.a1', '16.hv1.a1', '16.hv1.b1'], 'core': '8.cj1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8028, 3394, 6058, 5156, 8032, 3393, 6052, 5168], 'generators': [5, 22, 128], 'label': '256.30836.8.cj1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cj1.a1', 'normal_contained_in': ['4.bn1.a1', '4.r1.a1', '4.dj1.a1', '4.ed1.a1', '4.er1.a1', '4.ep1.a1', '4.em1.a1'], 'normal_contains': ['16.e1.a1', '16.n1.a1', '16.ba1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cj1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879217
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.bg1.c1', '16.in1.b1', '16.iq1.b1', '16.it1.a1', '16.iv1.a1', '16.iz1.b1', '16.jc1.b1'], 'core': '16.bg1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9146, -1, 3960, -1, 9151, -1, 3957, -1], 'generators': [1, 130, 80], 'label': '256.30836.8.hh1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.hh1.c1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hh1.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879026
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.x1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.h1.a1', '128.h1.d1', '128.h1.c1', '128.h1.b1', '128.i1.a1', '128.i1.c1', '128.i1.b1', '128.i1.d1', '128.k1.a1', '128.k1.b1', '128.l1.a1', '128.l1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.cl1.a1', '4.cm1.a1', '4.cn1.a1', '4.cr1.a1', '4.cs1.a1', '4.cv1.a1', '4.dg1.a1', '4.et1.a1', '4.ew1.a1', '4.ez1.a1', '4.fb1.a1', '4.fj1.a1', '4.fk1.a1', '4.fn1.a1', '4.fx1.a1'], 'core': '2.x1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4224, 3540, 7401, 4139, 4227, 3539, 7395, 4203], 'generators': [3, 4, 16, 64], 'label': '256.30836.2.x1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.x1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.cl1.a1', '4.cm1.a1', '4.cn1.a1', '4.cs1.a1', '4.cr1.a1', '4.dg1.a1', '4.cv1.a1', '4.et1.a1', '4.ew1.a1', '4.ez1.a1', '4.fb1.a1', '4.fk1.a1', '4.fj1.a1', '4.fx1.a1', '4.fn1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.x1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.x1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879027
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ck1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.bm1.a1', '4.di1.a1', '4.ee1.a1', '4.eq1.a1', '4.er1.a1', '4.es1.a1'], 'contains': ['16.e1.a1', '16.o1.a1', '16.w1.a1', '16.hw1.a1', '16.hw1.b1'], 'core': '8.ck1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7333, 7201, 8307, 1666, 7337, 7199, 8300, 1670], 'generators': [5, 70, 128], 'label': '256.30836.8.ck1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ck1.a1', 'normal_contained_in': ['4.bm1.a1', '4.q1.a1', '4.di1.a1', '4.ee1.a1', '4.es1.a1', '4.eq1.a1', '4.er1.a1'], 'normal_contains': ['16.e1.a1', '16.o1.a1', '16.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ck1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879028
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cl1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.bn1.a1', '4.dl1.a1', '4.eg1.a1', '4.ej1.a1', '4.en1.a1', '4.es1.a1'], 'contains': ['16.e1.a1', '16.p1.a1', '16.t1.a1', '16.gp1.a1'], 'core': '8.cl1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4109, 8980, 6821, 581, 4111, 8976, 6815, 582], 'generators': [5, 18, 128], 'label': '256.30836.8.cl1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cl1.a1', 'normal_contained_in': ['4.bn1.a1', '4.p1.a1', '4.dl1.a1', '4.eg1.a1', '4.es1.a1', '4.en1.a1', '4.ej1.a1'], 'normal_contains': ['16.e1.a1', '16.p1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cl1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879029
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cm1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '4.bo1.a1', '4.dh1.a1', '4.eh1.a1', '4.en1.a1', '4.eo1.a1', '4.er1.a1'], 'contains': ['16.e1.a1', '16.q1.a1', '16.bc1.a1', '16.hx1.a1', '16.hx1.b1'], 'core': '8.cm1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8211, 396, 5732, 5082, 8215, 396, 5726, 5093], 'generators': [5, 80, 128], 'label': '256.30836.8.cm1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cm1.a1', 'normal_contained_in': ['4.bo1.a1', '4.s1.a1', '4.dh1.a1', '4.er1.a1', '4.eh1.a1', '4.en1.a1', '4.eo1.a1'], 'normal_contains': ['16.e1.a1', '16.bc1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cm1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879030
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cn1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.bo1.a1', '4.dm1.a1', '4.ei1.a1', '4.el1.a1', '4.em1.a1', '4.es1.a1'], 'contains': ['16.e1.a1', '16.u1.a1', '16.x1.a1', '16.di1.a1'], 'core': '8.cn1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5471, 3710, 8110, 4548, 5473, 3708, 8103, 4557], 'generators': [81, 84, 32], 'label': '256.30836.8.cn1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cn1.a1', 'normal_contained_in': ['4.bo1.a1', '4.n1.a1', '4.dm1.a1', '4.es1.a1', '4.el1.a1', '4.ei1.a1', '4.em1.a1'], 'normal_contains': ['16.e1.a1', '16.u1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cn1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879031
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.co1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '4.bj1.a1', '4.dm1.a1', '4.ej1.a1', '4.ek1.a1', '4.ep1.a1', '4.eq1.a1'], 'contains': ['16.e1.a1', '16.v1.a1', '16.be1.a1', '16.fi1.a1'], 'core': '8.co1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4720, 3205, 5027, 6630, 4723, 3204, 5022, 6645], 'generators': [5, 82, 128], 'label': '256.30836.8.co1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.co1.a1', 'normal_contained_in': ['4.bj1.a1', '4.s1.a1', '4.dm1.a1', '4.eq1.a1', '4.ek1.a1', '4.ej1.a1', '4.ep1.a1'], 'normal_contains': ['16.e1.a1', '16.be1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.co1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.co1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879032
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cp1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.cl1.a1', '4.dh1.a1', '4.et1.a1', '4.eu1.a1', '4.ev1.a1', '4.ew1.a1'], 'contains': ['16.f1.a1', '16.h1.a1', '16.q1.a1', '16.cc1.a1', '16.hy1.a1', '16.iz1.a1', '16.iz1.b1'], 'core': '8.cp1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5587, 1250, 5410, 7112, 5590, 1250, 5405, 7128], 'generators': [3, 80, 136, 128], 'label': '256.30836.8.cp1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cp1.a1', 'normal_contained_in': ['4.b1.a1', '4.cl1.a1', '4.dh1.a1', '4.et1.a1', '4.ew1.a1', '4.eu1.a1', '4.ev1.a1'], 'normal_contains': ['16.f1.a1', '16.h1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cp1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879033
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cq1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.cm1.a1', '4.di1.a1', '4.et1.a1', '4.ex1.a1', '4.ey1.a1', '4.ez1.a1'], 'contains': ['16.f1.a1', '16.i1.a1', '16.o1.a1', '16.dj1.a1'], 'core': '8.cq1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6274, 8072, 8718, 5778, 6277, 8070, 8710, 5791], 'generators': [3, 64, 32], 'label': '256.30836.8.cq1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cq1.a1', 'normal_contained_in': ['4.c1.a1', '4.cm1.a1', '4.di1.a1', '4.et1.a1', '4.ez1.a1', '4.ex1.a1', '4.ey1.a1'], 'normal_contains': ['16.f1.a1', '16.o1.a1', '16.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cq1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879034
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cr1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.cn1.a1', '4.dj1.a1', '4.et1.a1', '4.fa1.a1', '4.fb1.a1', '4.fc1.a1'], 'contains': ['16.f1.a1', '16.j1.a1', '16.ba1.a1', '16.fj1.a1'], 'core': '8.cr1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4048, 3088, 7000, 7441, 4050, 3087, 6995, 7458], 'generators': [3, 16, 128], 'label': '256.30836.8.cr1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cr1.a1', 'normal_contained_in': ['4.d1.a1', '4.cn1.a1', '4.dj1.a1', '4.et1.a1', '4.fa1.a1', '4.fc1.a1', '4.fb1.a1'], 'normal_contains': ['16.f1.a1', '16.j1.a1', '16.ba1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cr1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879035
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cs1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.co1.a1', '4.dk1.a1', '4.eu1.a1', '4.fa1.a1', '4.fd1.a1', '4.fe1.a1'], 'contains': ['16.f1.a1', '16.k1.a1', '16.l1.a1', '16.dk1.a1'], 'core': '8.cs1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5817, 1841, 7815, 2847, 5820, 1841, 7808, 2854], 'generators': [65, 66, 32], 'label': '256.30836.8.cs1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cs1.a1', 'normal_contained_in': ['4.c1.a1', '4.co1.a1', '4.dk1.a1', '4.eu1.a1', '4.fa1.a1', '4.fe1.a1', '4.fd1.a1'], 'normal_contains': ['16.f1.a1', '16.l1.a1', '16.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cs1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879036
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ct1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.cp1.a1', '4.dl1.a1', '4.eu1.a1', '4.ex1.a1', '4.ff1.a1', '4.fg1.a1'], 'contains': ['16.f1.a1', '16.m1.a1', '16.t1.a1', '16.fk1.a1'], 'core': '8.ct1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2257, 9689, 7700, 9622, 2258, 9687, 7693, 9643], 'generators': [17, 18, 128], 'label': '256.30836.8.ct1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ct1.a1', 'normal_contained_in': ['4.d1.a1', '4.cp1.a1', '4.dl1.a1', '4.eu1.a1', '4.ex1.a1', '4.fg1.a1', '4.ff1.a1'], 'normal_contains': ['16.f1.a1', '16.m1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ct1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879218
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.bg1.d1', '16.in1.b1', '16.iq1.b1', '16.it1.b1', '16.iv1.b1', '16.iz1.a1', '16.jc1.a1'], 'core': '16.bg1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9146, -1, 4049, -1, 9151, -1, 4045, -1], 'generators': [129, 130, 80], 'label': '256.30836.8.hh1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.hh1.d1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hh1.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879037
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.y1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.d1', '128.i1.b1', '128.i1.c1', '128.h1.a1', '128.h1.d1', '128.h1.b1', '128.h1.c1', '128.l1.a1', '128.l1.b1', '128.k1.a1', '128.k1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.cl1.a1', '4.co1.a1', '4.cp1.a1', '4.ct1.a1', '4.cu1.a1', '4.da1.a1', '4.dc1.a1', '4.eu1.a1', '4.ev1.a1', '4.fd1.a1', '4.fg1.a1', '4.fl1.a1', '4.fm1.a1', '4.fs1.a1', '4.fu1.a1'], 'core': '2.y1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3851, 3120, 6434, 5895, 3839, 3119, 6431, 5840], 'generators': [65, 66, 4, 80], 'label': '256.30836.2.y1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.y1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.cl1.a1', '4.co1.a1', '4.cp1.a1', '4.cu1.a1', '4.ct1.a1', '4.dc1.a1', '4.da1.a1', '4.eu1.a1', '4.ev1.a1', '4.fd1.a1', '4.fg1.a1', '4.fm1.a1', '4.fl1.a1', '4.fu1.a1', '4.fs1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.y1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.y1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879038
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cu1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.cp1.a1', '4.dj1.a1', '4.ev1.a1', '4.ey1.a1', '4.fd1.a1', '4.fh1.a1'], 'contains': ['16.f1.a1', '16.n1.a1', '16.z1.a1', '16.ja1.a1', '16.ja1.b1'], 'core': '8.cu1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8309, 3782, 5214, 8302, 8313, 3780, 5210, 8320], 'generators': [21, 22, 128], 'label': '256.30836.8.cu1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cu1.a1', 'normal_contained_in': ['4.e1.a1', '4.cp1.a1', '4.dj1.a1', '4.ev1.a1', '4.ey1.a1', '4.fd1.a1', '4.fh1.a1'], 'normal_contains': ['16.f1.a1', '16.n1.a1', '16.z1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cu1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879039
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cv1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.cn1.a1', '4.dl1.a1', '4.ew1.a1', '4.ez1.a1', '4.fe1.a1', '4.fi1.a1'], 'contains': ['16.f1.a1', '16.p1.a1', '16.s1.a1', '16.jb1.a1', '16.jb1.b1'], 'core': '8.cv1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6509, 2516, 6579, 4335, 6512, 2515, 6573, 4345], 'generators': [3, 20, 128], 'label': '256.30836.8.cv1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cv1.a1', 'normal_contained_in': ['4.e1.a1', '4.cn1.a1', '4.dl1.a1', '4.ew1.a1', '4.ez1.a1', '4.fe1.a1', '4.fi1.a1'], 'normal_contains': ['16.f1.a1', '16.p1.a1', '16.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cv1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879040
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cw1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.cm1.a1', '4.dk1.a1', '4.ew1.a1', '4.fb1.a1', '4.ff1.a1', '4.fh1.a1'], 'contains': ['16.f1.a1', '16.r1.a1', '16.bd1.a1', '16.gq1.a1'], 'core': '8.cw1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6387, 4826, 7432, 6903, 6390, 4824, 7425, 6918], 'generators': [3, 68, 128], 'label': '256.30836.8.cw1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cw1.a1', 'normal_contained_in': ['4.f1.a1', '4.cm1.a1', '4.dk1.a1', '4.ew1.a1', '4.fb1.a1', '4.ff1.a1', '4.fh1.a1'], 'normal_contains': ['16.f1.a1', '16.bd1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cw1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879041
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cx1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.cl1.a1', '4.dm1.a1', '4.ez1.a1', '4.fb1.a1', '4.fd1.a1', '4.fg1.a1'], 'contains': ['16.f1.a1', '16.u1.a1', '16.be1.a1', '16.cd1.a1'], 'core': '8.cx1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4880, 4028, 6789, 8541, 4882, 4026, 6783, 8560], 'generators': [3, 84, 136], 'label': '256.30836.8.cx1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cx1.a1', 'normal_contained_in': ['4.g1.a1', '4.cl1.a1', '4.dm1.a1', '4.ez1.a1', '4.fb1.a1', '4.fd1.a1', '4.fg1.a1'], 'normal_contains': ['16.f1.a1', '16.u1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cx1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879042
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cy1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.cq1.a1', '4.dm1.a1', '4.ex1.a1', '4.fa1.a1', '4.fh1.a1', '4.fi1.a1'], 'contains': ['16.f1.a1', '16.v1.a1', '16.x1.a1', '16.jc1.a1', '16.jc1.b1'], 'core': '8.cy1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7094, 2589, 5671, 9912, 7097, 2588, 5666, 9934], 'generators': [81, 82, 128], 'label': '256.30836.8.cy1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cy1.a1', 'normal_contained_in': ['4.b1.a1', '4.cq1.a1', '4.dm1.a1', '4.ex1.a1', '4.fa1.a1', '4.fi1.a1', '4.fh1.a1'], 'normal_contains': ['16.f1.a1', '16.x1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cy1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879043
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.cz1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.co1.a1', '4.di1.a1', '4.ev1.a1', '4.fc1.a1', '4.fg1.a1', '4.fi1.a1'], 'contains': ['16.f1.a1', '16.w1.a1', '16.y1.a1', '16.gr1.a1'], 'core': '8.cz1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6874, 2734, 6758, 8227, 6877, 2733, 6751, 8245], 'generators': [69, 70, 128], 'label': '256.30836.8.cz1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.cz1.a1', 'normal_contained_in': ['4.f1.a1', '4.co1.a1', '4.di1.a1', '4.ev1.a1', '4.fc1.a1', '4.fi1.a1', '4.fg1.a1'], 'normal_contains': ['16.f1.a1', '16.y1.a1', '16.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.cz1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879044
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.da1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.cq1.a1', '4.dh1.a1', '4.ey1.a1', '4.fc1.a1', '4.fe1.a1', '4.ff1.a1'], 'contains': ['16.f1.a1', '16.bb1.a1', '16.bc1.a1', '16.hz1.a1'], 'core': '8.da1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6752, 2306, 7399, 7660, 6755, 2305, 7393, 7677], 'generators': [85, 86, 128], 'label': '256.30836.8.da1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.da1.a1', 'normal_contained_in': ['4.g1.a1', '4.cq1.a1', '4.dh1.a1', '4.ey1.a1', '4.fc1.a1', '4.fe1.a1', '4.ff1.a1'], 'normal_contains': ['16.f1.a1', '16.bc1.a1', '16.bb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.da1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.da1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879045
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.db1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.bp1.a1', '4.cl1.a1', '4.fj1.a1', '4.fk1.a1', '4.fl1.a1', '4.fm1.a1'], 'contains': ['16.g1.a1', '16.h1.a1', '16.u1.a1', '16.ce1.a1', '16.dl1.a1', '16.ej1.a1', '16.ej1.b1'], 'core': '8.db1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2641, 5894, 7030, 3854, 2643, 5892, 7024, 3862], 'generators': [83, 84, 136, 32], 'label': '256.30836.8.db1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.db1.a1', 'normal_contained_in': ['4.bp1.a1', '4.n1.a1', '4.cl1.a1', '4.fk1.a1', '4.fm1.a1', '4.fl1.a1', '4.fj1.a1'], 'normal_contains': ['16.g1.a1', '16.h1.a1', '16.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.db1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.db1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879046
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dc1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '4.bq1.a1', '4.cm1.a1', '4.fj1.a1', '4.fn1.a1', '4.fo1.a1', '4.fp1.a1'], 'contains': ['16.g1.a1', '16.i1.a1', '16.bd1.a1', '16.ek1.a1', '16.ek1.b1'], 'core': '8.dc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7659, 5426, 8654, 5007, 7663, 5425, 8646, 5018], 'generators': [7, 64, 32], 'label': '256.30836.8.dc1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dc1.a1', 'normal_contained_in': ['4.bq1.a1', '4.o1.a1', '4.cm1.a1', '4.fj1.a1', '4.fn1.a1', '4.fo1.a1', '4.fp1.a1'], 'normal_contains': ['16.g1.a1', '16.i1.a1', '16.bd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dc1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879047
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dd1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.br1.a1', '4.cn1.a1', '4.fk1.a1', '4.fn1.a1', '4.fq1.a1', '4.fr1.a1'], 'contains': ['16.g1.a1', '16.j1.a1', '16.p1.a1', '16.gs1.a1'], 'core': '8.dd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4659, 2443, 5966, 2015, 4662, 2443, 5961, 2020], 'generators': [7, 16, 128], 'label': '256.30836.8.dd1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dd1.a1', 'normal_contained_in': ['4.br1.a1', '4.p1.a1', '4.cn1.a1', '4.fk1.a1', '4.fr1.a1', '4.fq1.a1', '4.fn1.a1'], 'normal_contains': ['16.g1.a1', '16.j1.a1', '16.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dd1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879219
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.bg1.a1', '16.io1.a1', '16.ip1.a1', '16.iu1.a1', '16.iw1.a1', '16.ja1.a1', '16.jb1.a1'], 'core': '16.bg1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9556, -1, 4143, -1, 9562, -1, 4140, -1], 'generators': [1, 2, 20], 'label': '256.30836.8.hi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.hi1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879048
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.z1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.c1', '128.i1.b1', '128.i1.d1', '128.h1.a1', '128.h1.b1', '128.h1.c1', '128.h1.d1', '128.l1.a1', '128.l1.b1', '128.k1.a1', '128.k1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.cm1.a1', '4.cp1.a1', '4.cq1.a1', '4.cw1.a1', '4.cx1.a1', '4.de1.a1', '4.df1.a1', '4.ex1.a1', '4.ey1.a1', '4.ff1.a1', '4.fh1.a1', '4.fo1.a1', '4.fp1.a1', '4.fw1.a1', '4.fy1.a1'], 'core': '2.z1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6307, 7767, 7798, 7297, 6311, 7764, 7792, 7228], 'generators': [17, 18, 4, 64], 'label': '256.30836.2.z1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.z1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.cm1.a1', '4.cp1.a1', '4.cq1.a1', '4.de1.a1', '4.df1.a1', '4.cw1.a1', '4.cx1.a1', '4.ex1.a1', '4.ey1.a1', '4.ff1.a1', '4.fh1.a1', '4.fw1.a1', '4.fy1.a1', '4.fo1.a1', '4.fp1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.z1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879049
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.de1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '4.bs1.a1', '4.co1.a1', '4.fl1.a1', '4.fq1.a1', '4.fs1.a1', '4.ft1.a1'], 'contains': ['16.g1.a1', '16.k1.a1', '16.y1.a1', '16.fl1.a1'], 'core': '8.de1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1570, 1979, 5639, 431, 1571, 1978, 5634, 433], 'generators': [69, 66, 128], 'label': '256.30836.8.de1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.de1.a1', 'normal_contained_in': ['4.bs1.a1', '4.o1.a1', '4.co1.a1', '4.fl1.a1', '4.fq1.a1', '4.fs1.a1', '4.ft1.a1'], 'normal_contains': ['16.g1.a1', '16.k1.a1', '16.y1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.de1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.de1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879050
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.df1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.bq1.a1', '4.co1.a1', '4.fm1.a1', '4.fr1.a1', '4.fu1.a1', '4.fv1.a1'], 'contains': ['16.g1.a1', '16.l1.a1', '16.w1.a1', '16.el1.a1', '16.el1.b1'], 'core': '8.df1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8614, 963, 7731, 6705, 8618, 962, 7725, 6720], 'generators': [65, 70, 32], 'label': '256.30836.8.df1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.df1.a1', 'normal_contained_in': ['4.bq1.a1', '4.q1.a1', '4.co1.a1', '4.fm1.a1', '4.fr1.a1', '4.fu1.a1', '4.fv1.a1'], 'normal_contains': ['16.g1.a1', '16.l1.a1', '16.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.df1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.df1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879051
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dg1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '4.br1.a1', '4.cp1.a1', '4.fl1.a1', '4.fo1.a1', '4.fu1.a1', '4.fw1.a1'], 'contains': ['16.g1.a1', '16.m1.a1', '16.n1.a1', '16.ia1.a1'], 'core': '8.dg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8553, 5310, 5278, 8765, 8557, 5308, 5273, 8784], 'generators': [17, 22, 128], 'label': '256.30836.8.dg1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dg1.a1', 'normal_contained_in': ['4.br1.a1', '4.r1.a1', '4.cp1.a1', '4.fl1.a1', '4.fw1.a1', '4.fu1.a1', '4.fo1.a1'], 'normal_contains': ['16.g1.a1', '16.m1.a1', '16.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dg1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879052
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dh1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.bs1.a1', '4.cm1.a1', '4.fk1.a1', '4.fw1.a1', '4.fx1.a1', '4.fy1.a1'], 'contains': ['16.g1.a1', '16.o1.a1', '16.r1.a1', '16.fm1.a1'], 'core': '8.dh1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2586, 8693, 6885, 3211, 2587, 8691, 6879, 3218], 'generators': [67, 68, 128], 'label': '256.30836.8.dh1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dh1.a1', 'normal_contained_in': ['4.bs1.a1', '4.q1.a1', '4.cm1.a1', '4.fk1.a1', '4.fw1.a1', '4.fy1.a1', '4.fx1.a1'], 'normal_contains': ['16.g1.a1', '16.o1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dh1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879053
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.di1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '4.bt1.a1', '4.cl1.a1', '4.fn1.a1', '4.fs1.a1', '4.fu1.a1', '4.fx1.a1'], 'contains': ['16.g1.a1', '16.q1.a1', '16.be1.a1', '16.cf1.a1'], 'core': '8.di1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5643, 178, 4948, 7181, 5646, 178, 4944, 7197], 'generators': [7, 80, 136], 'label': '256.30836.8.di1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.di1.a1', 'normal_contained_in': ['4.bt1.a1', '4.s1.a1', '4.cl1.a1', '4.fx1.a1', '4.fn1.a1', '4.fu1.a1', '4.fs1.a1'], 'normal_contains': ['16.g1.a1', '16.q1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.di1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.di1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879054
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dj1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '4.bu1.a1', '4.cn1.a1', '4.fj1.a1', '4.ft1.a1', '4.fv1.a1', '4.fx1.a1'], 'contains': ['16.g1.a1', '16.s1.a1', '16.ba1.a1', '16.ib1.a1'], 'core': '8.dj1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7598, 2661, 6121, 5927, 7602, 2660, 6116, 5940], 'generators': [19, 20, 128], 'label': '256.30836.8.dj1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dj1.a1', 'normal_contained_in': ['4.bu1.a1', '4.r1.a1', '4.cn1.a1', '4.fj1.a1', '4.fx1.a1', '4.fv1.a1', '4.ft1.a1'], 'normal_contains': ['16.g1.a1', '16.s1.a1', '16.ba1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dj1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879055
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dk1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.bu1.a1', '4.cp1.a1', '4.fm1.a1', '4.fp1.a1', '4.fs1.a1', '4.fy1.a1'], 'contains': ['16.g1.a1', '16.t1.a1', '16.z1.a1', '16.gt1.a1'], 'core': '8.dk1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4322, 9332, 6025, 7043, 4324, 9328, 6020, 7059], 'generators': [21, 18, 128], 'label': '256.30836.8.dk1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dk1.a1', 'normal_contained_in': ['4.bu1.a1', '4.p1.a1', '4.cp1.a1', '4.fm1.a1', '4.fy1.a1', '4.fs1.a1', '4.fp1.a1'], 'normal_contains': ['16.g1.a1', '16.z1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dk1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879056
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dl1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '4.bp1.a1', '4.cq1.a1', '4.fp1.a1', '4.fq1.a1', '4.fv1.a1', '4.fw1.a1'], 'contains': ['16.g1.a1', '16.v1.a1', '16.bc1.a1', '16.em1.a1', '16.em1.b1'], 'core': '8.dl1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8858, 693, 4917, 9838, 8862, 694, 4913, 9859], 'generators': [85, 82, 32], 'label': '256.30836.8.dl1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dl1.a1', 'normal_contained_in': ['4.bp1.a1', '4.s1.a1', '4.cq1.a1', '4.fw1.a1', '4.fq1.a1', '4.fv1.a1', '4.fp1.a1'], 'normal_contains': ['16.g1.a1', '16.bc1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dl1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879057
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dm1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.bt1.a1', '4.cq1.a1', '4.fo1.a1', '4.fr1.a1', '4.ft1.a1', '4.fy1.a1'], 'contains': ['16.g1.a1', '16.x1.a1', '16.bb1.a1', '16.dm1.a1'], 'core': '8.dm1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5915, 2051, 8781, 4622, 5918, 2051, 8774, 4632], 'generators': [81, 86, 32], 'label': '256.30836.8.dm1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dm1.a1', 'normal_contained_in': ['4.bt1.a1', '4.n1.a1', '4.cq1.a1', '4.fy1.a1', '4.fr1.a1', '4.fo1.a1', '4.ft1.a1'], 'normal_contains': ['16.g1.a1', '16.bb1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dm1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879058
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dn1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.m1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.co1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bo1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.cq1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.cj1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.eo1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.bd1', '32.hk1.n1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.e1', '32.hk1.f1', '32.hk1.v1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.di1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dq1', '32.hk1.bu1'], 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bv1.a1', '4.cr1.a1', '4.dn1.a1', '4.ed1.a1', '4.et1.a1', '4.fj1.a1'], 'contains': ['16.h1.a1', '16.i1.a1', '16.ba1.a1', '16.dn1.a1'], 'core': '8.dn1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1078, 6199, 8622, 5853, 1078, 6197, 8615, 5866], 'generators': [19, 64, 32], 'label': '256.30836.8.dn1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dn1.a1', 'normal_contained_in': ['4.bv1.a1', '4.t1.a1', '4.cr1.a1', '4.dn1.a1', '4.ed1.a1', '4.et1.a1', '4.fj1.a1'], 'normal_contains': ['16.h1.a1', '16.i1.a1', '16.ba1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dn1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879059
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.ba1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.d1', '128.i1.b1', '128.i1.c1', '128.h1.a1', '128.h1.d1', '128.h1.b1', '128.h1.c1', '128.l1.a1', '128.l1.b1', '128.k1.a1', '128.k1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.cn1.a1', '4.co1.a1', '4.cq1.a1', '4.cy1.a1', '4.cz1.a1', '4.db1.a1', '4.dd1.a1', '4.fa1.a1', '4.fc1.a1', '4.fe1.a1', '4.fi1.a1', '4.fq1.a1', '4.fr1.a1', '4.ft1.a1', '4.fv1.a1'], 'core': '2.ba1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5718, 1771, 6633, 2820, 5721, 1770, 6628, 2827], 'generators': [65, 66, 4, 16], 'label': '256.30836.2.ba1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.ba1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.cn1.a1', '4.co1.a1', '4.cq1.a1', '4.cz1.a1', '4.cy1.a1', '4.dd1.a1', '4.db1.a1', '4.fa1.a1', '4.fc1.a1', '4.fe1.a1', '4.fi1.a1', '4.fr1.a1', '4.fq1.a1', '4.fv1.a1', '4.ft1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.ba1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879060
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.do1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.k1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.co1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bo1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.cq1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.cj1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.eo1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.bd1', '32.hk1.n1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.e1', '32.hk1.f1', '32.hk1.v1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.di1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dq1', '32.hk1.bu1'], 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '4.bw1.a1', '4.cs1.a1', '4.do1.a1', '4.ee1.a1', '4.et1.a1', '4.fk1.a1'], 'contains': ['16.h1.a1', '16.j1.a1', '16.o1.a1', '16.fn1.a1'], 'core': '8.do1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [465, 7379, 8686, 762, 464, 7376, 8678, 764], 'generators': [67, 16, 128], 'label': '256.30836.8.do1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.do1.a1', 'normal_contained_in': ['4.bw1.a1', '4.u1.a1', '4.cs1.a1', '4.do1.a1', '4.ee1.a1', '4.et1.a1', '4.fk1.a1'], 'normal_contains': ['16.h1.a1', '16.o1.a1', '16.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.do1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.do1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879061
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dp1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.dp1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.c1', '32.hk1.s1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1'], 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bw1.a1', '4.ct1.a1', '4.dp1.a1', '4.ef1.a1', '4.eu1.a1', '4.fl1.a1'], 'contains': ['16.h1.a1', '16.k1.a1', '16.m1.a1', '16.do1.a1', '16.fo1.a1', '16.ic1.a1'], 'core': '8.dp1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [327, 5639, 9570, 2411, 327, 5637, 9561, 2416], 'generators': [17, 66, 32, 128], 'label': '256.30836.8.dp1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dp1.a1', 'normal_contained_in': ['4.bw1.a1', '4.t1.a1', '4.ct1.a1', '4.dp1.a1', '4.ef1.a1', '4.eu1.a1', '4.fl1.a1'], 'normal_contains': ['16.h1.a1', '16.m1.a1', '16.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dp1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879062
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dq1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.y1', '32.hk1.z1', '32.hk1.j1', '32.hk1.i1', '32.hk1.r1', '32.hk1.q1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.es1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.c1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.t1', '32.hk1.s1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.de1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ct1'], 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '4.bv1.a1', '4.cu1.a1', '4.dq1.a1', '4.eg1.a1', '4.eu1.a1', '4.fm1.a1'], 'contains': ['16.h1.a1', '16.l1.a1', '16.t1.a1', '16.cg1.a1'], 'core': '8.dq1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [577, 9186, 8049, 1037, 577, 9183, 8043, 1039], 'generators': [65, 18, 136], 'label': '256.30836.8.dq1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dq1.a1', 'normal_contained_in': ['4.bv1.a1', '4.u1.a1', '4.cu1.a1', '4.dq1.a1', '4.eg1.a1', '4.eu1.a1', '4.fm1.a1'], 'normal_contains': ['16.h1.a1', '16.l1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dq1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879063
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dr1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.r1', '32.hk1.q1', '32.hk1.j1', '32.hk1.i1', '32.hk1.y1', '32.hk1.z1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.es1', '32.hk1.et1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.ca1', '32.hk1.cb1', '32.hk1.en1', '32.hk1.em1', '32.hk1.ef1', '32.hk1.ee1', '32.hk1.eu1', '32.hk1.ev1', '32.hk1.e1', '32.hk1.f1', '32.hk1.v1', '32.hk1.u1', '32.hk1.n1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.bd1', '32.hk1.bm1', '32.hk1.bn1', '32.hk1.ct1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.ck1', '32.hk1.da1', '32.hk1.db1', '32.hk1.bu1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dq1', '32.hk1.dj1', '32.hk1.di1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.bs1', '32.hk1.bt1', '32.hk1.dp1', '32.hk1.do1', '32.hk1.dh1', '32.hk1.dg1', '32.hk1.dw1', '32.hk1.dx1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cq1', '32.hk1.cj1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.cz1', '32.hk1.g1', '32.hk1.h1', '32.hk1.x1', '32.hk1.w1', '32.hk1.p1', '32.hk1.o1', '32.hk1.be1', '32.hk1.bf1', '32.hk1.cc1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.eo1', '32.hk1.eh1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.ex1'], 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '4.bx1.a1', '4.cu1.a1', '4.do1.a1', '4.ed1.a1', '4.ev1.a1', '4.fl1.a1'], 'contains': ['16.h1.a1', '16.n1.a1', '16.y1.a1', '16.ch1.a1'], 'core': '8.dr1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1139, 6126, 5471, 899, 1139, 6124, 5466, 902], 'generators': [69, 22, 136], 'label': '256.30836.8.dr1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dr1.a1', 'normal_contained_in': ['4.bx1.a1', '4.v1.a1', '4.cu1.a1', '4.do1.a1', '4.ed1.a1', '4.ev1.a1', '4.fl1.a1'], 'normal_contains': ['16.h1.a1', '16.n1.a1', '16.y1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dr1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879064
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ds1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.i1', '32.hk1.r1', '32.hk1.z1', '32.hk1.j1', '32.hk1.b1', '32.hk1.y1', '32.hk1.q1', '32.hk1.dc1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.dn1', '32.hk1.dv1', '32.hk1.bq1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.br1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.k1', '32.hk1.c1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.l1', '32.hk1.cf1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cm1', '32.hk1.bg1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cv1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.es1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.et1', '32.hk1.by1', '32.hk1.ec1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.bi1', '32.hk1.m1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.dh1', '32.hk1.bt1', '32.hk1.dw1', '32.hk1.do1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.g1', '32.hk1.o1', '32.hk1.be1', '32.hk1.w1', '32.hk1.p1', '32.hk1.h1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.ef1', '32.hk1.cb1', '32.hk1.eu1', '32.hk1.em1', '32.hk1.ca1', '32.hk1.ee1', '32.hk1.en1', '32.hk1.ev1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.bn1', '32.hk1.ct1', '32.hk1.db1', '32.hk1.bm1', '32.hk1.ck1'], 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '4.bx1.a1', '4.cr1.a1', '4.dp1.a1', '4.eg1.a1', '4.ew1.a1', '4.fk1.a1'], 'contains': ['16.h1.a1', '16.p1.a1', '16.r1.a1', '16.gu1.a1'], 'core': '8.ds1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [637, 8290, 8402, 1260, 638, 8288, 8395, 1263], 'generators': [83, 68, 128], 'label': '256.30836.8.ds1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ds1.a1', 'normal_contained_in': ['4.bx1.a1', '4.w1.a1', '4.cr1.a1', '4.dp1.a1', '4.eg1.a1', '4.ew1.a1', '4.fk1.a1'], 'normal_contains': ['16.h1.a1', '16.p1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ds1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879065
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dt1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.y1', '32.hk1.i1', '32.hk1.j1', '32.hk1.z1', '32.hk1.r1', '32.hk1.b1', '32.hk1.co1', '32.hk1.bi1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dk1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.c1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.ei1', '32.hk1.bw1', '32.hk1.w1', '32.hk1.g1', '32.hk1.o1', '32.hk1.be1', '32.hk1.bf1', '32.hk1.p1', '32.hk1.h1', '32.hk1.x1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.ee1', '32.hk1.eu1', '32.hk1.em1', '32.hk1.ca1', '32.hk1.cb1', '32.hk1.en1', '32.hk1.ev1', '32.hk1.ef1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.db1', '32.hk1.cl1', '32.hk1.bn1', '32.hk1.ct1', '32.hk1.cs1', '32.hk1.bm1', '32.hk1.ck1', '32.hk1.da1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.f1', '32.hk1.e1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.bt1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.dh1', '32.hk1.dg1', '32.hk1.dw1', '32.hk1.do1', '32.hk1.bs1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.eo1'], 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '4.by1.a1', '4.cs1.a1', '4.dq1.a1', '4.ef1.a1', '4.ew1.a1', '4.fj1.a1'], 'contains': ['16.h1.a1', '16.s1.a1', '16.bd1.a1', '16.id1.a1'], 'core': '8.dt1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3326, 5572, 8371, 1335, 3328, 5570, 8364, 1338], 'generators': [83, 20, 128], 'label': '256.30836.8.dt1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dt1.a1', 'normal_contained_in': ['4.by1.a1', '4.v1.a1', '4.cs1.a1', '4.dq1.a1', '4.ef1.a1', '4.ew1.a1', '4.fj1.a1'], 'normal_contains': ['16.h1.a1', '16.s1.a1', '16.bd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dt1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879453
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.de1.a1', '8.gr1.a1', '8.gr1.b1'], 'contains': ['32.cw1.a1', '32.cz1.a1', '32.df1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1753, -1, 6148, -1, 1754, -1, 6142, -1], 'generators': [69, 66], 'label': '256.30836.16.fl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.de1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bs1.a1', 'old_label': '16.fl1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fl1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879066
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.du1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.r1', '32.hk1.i1', '32.hk1.j1', '32.hk1.q1', '32.hk1.y1', '32.hk1.b1', '32.hk1.c1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.k1', '32.hk1.l1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.br1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.by1', '32.hk1.et1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.bx1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.be1', '32.hk1.h1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.cy1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.eu1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ca1', '32.hk1.ev1'], 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '4.by1.a1', '4.ct1.a1', '4.dn1.a1', '4.ee1.a1', '4.ev1.a1', '4.fm1.a1'], 'contains': ['16.h1.a1', '16.w1.a1', '16.z1.a1', '16.gv1.a1'], 'core': '8.du1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2102, 6732, 8749, 8691, 2103, 6729, 8742, 8709], 'generators': [21, 70, 128], 'label': '256.30836.8.du1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.du1.a1', 'normal_contained_in': ['4.by1.a1', '4.w1.a1', '4.ct1.a1', '4.dn1.a1', '4.ee1.a1', '4.ev1.a1', '4.fm1.a1'], 'normal_contains': ['16.h1.a1', '16.z1.a1', '16.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.du1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.du1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879067
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dv1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.dv1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.r1', '32.hk1.q1', '32.hk1.j1', '32.hk1.i1', '32.hk1.y1', '32.hk1.z1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.es1', '32.hk1.et1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.f1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.h1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '4.bz1.a1', '4.cv1.a1', '4.dr1.a1', '4.eh1.a1', '4.et1.a1', '4.fn1.a1'], 'contains': ['16.i1.a1', '16.j1.a1', '16.q1.a1', '16.ci1.a1'], 'core': '8.dv1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6331, 1312, 6499, 4832, 6334, 1311, 6493, 4842], 'generators': [16, 64, 136], 'label': '256.30836.8.dv1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dv1.a1', 'normal_contained_in': ['4.bz1.a1', '4.x1.a1', '4.cv1.a1', '4.dr1.a1', '4.eh1.a1', '4.et1.a1', '4.fn1.a1'], 'normal_contains': ['16.j1.a1', '16.i1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dv1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879068
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dw1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.dw1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.c1', '32.hk1.s1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1'], 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bz1.a1', '4.cw1.a1', '4.ds1.a1', '4.ei1.a1', '4.ex1.a1', '4.fo1.a1'], 'contains': ['16.i1.a1', '16.m1.a1', '16.x1.a1', '16.dp1.a1'], 'core': '8.dw1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4542, 5760, 9160, 9090, 4544, 5758, 9151, 9110], 'generators': [17, 64, 32], 'label': '256.30836.8.dw1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dw1.a1', 'normal_contained_in': ['4.bz1.a1', '4.t1.a1', '4.cw1.a1', '4.ds1.a1', '4.ei1.a1', '4.ex1.a1', '4.fo1.a1'], 'normal_contains': ['16.m1.a1', '16.i1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dw1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879069
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dx1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.l1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.y1', '32.hk1.z1', '32.hk1.j1', '32.hk1.i1', '32.hk1.r1', '32.hk1.q1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.es1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.c1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.t1', '32.hk1.s1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.de1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1'], 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '4.ca1.a1', '4.cx1.a1', '4.dr1.a1', '4.ed1.a1', '4.ey1.a1', '4.fo1.a1'], 'contains': ['16.i1.a1', '16.n1.a1', '16.bb1.a1'], 'core': '8.dx1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6923, 5115, 8215, 3272, 6926, 5113, 8208, 3279], 'generators': [22, 64], 'label': '256.30836.8.dx1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dx1.a1', 'normal_contained_in': ['4.ca1.a1', '4.y1.a1', '4.cx1.a1', '4.dr1.a1', '4.ed1.a1', '4.ey1.a1', '4.fo1.a1'], 'normal_contains': ['16.i1.a1', '16.n1.a1', '16.bb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dx1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.dx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879070
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.bb1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.j1.a1', '128.j1.b1', '128.i1.a1', '128.i1.b1', '128.i1.c1', '128.i1.d1', '128.h1.a1', '128.h1.c1', '128.h1.b1', '128.h1.d1', '128.n1.a1', '128.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.dh1.a1', '4.di1.a1', '4.dj1.a1', '4.dn1.a1', '4.do1.a1', '4.dr1.a1', '4.eb1.a1', '4.ed1.a1', '4.ee1.a1', '4.eh1.a1', '4.er1.a1', '4.et1.a1', '4.ev1.a1', '4.ey1.a1', '4.fc1.a1'], 'core': '2.bb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5675, 3643, 6922, 5336, 5677, 3642, 6915, 5348], 'generators': [5, 6, 16, 64], 'label': '256.30836.2.bb1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.bb1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.dh1.a1', '4.di1.a1', '4.dj1.a1', '4.do1.a1', '4.dn1.a1', '4.eb1.a1', '4.dr1.a1', '4.ee1.a1', '4.ed1.a1', '4.er1.a1', '4.eh1.a1', '4.et1.a1', '4.ev1.a1', '4.ey1.a1', '4.fc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.bb1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879071
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dy1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.l1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.y1', '32.hk1.b1', '32.hk1.j1', '32.hk1.q1', '32.hk1.r1', '32.hk1.i1', '32.hk1.bb1', '32.hk1.c1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.t1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.by1', '32.hk1.et1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.br1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.bo1', '32.hk1.be1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.f1', '32.hk1.bc1', '32.hk1.bd1', '32.hk1.e1', '32.hk1.m1', '32.hk1.v1', '32.hk1.u1', '32.hk1.n1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ex1', '32.hk1.cc1', '32.hk1.cd1', '32.hk1.ew1', '32.hk1.eo1', '32.hk1.eh1', '32.hk1.eg1', '32.hk1.ep1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.ci1', '32.hk1.cr1', '32.hk1.cq1', '32.hk1.cj1', '32.hk1.bl1', '32.hk1.cy1', '32.hk1.cz1', '32.hk1.bk1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.dq1', '32.hk1.dj1', '32.hk1.di1', '32.hk1.dr1', '32.hk1.dz1', '32.hk1.bu1', '32.hk1.bv1', '32.hk1.dy1'], 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '4.ca1.a1', '4.cr1.a1', '4.ds1.a1', '4.ej1.a1', '4.ez1.a1', '4.fn1.a1'], 'contains': ['16.i1.a1', '16.p1.a1', '16.be1.a1'], 'core': '8.dy1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3549, 7716, 8253, 3800, 3551, 7713, 8246, 3808], 'generators': [23, 64], 'label': '256.30836.8.dy1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dy1.a1', 'normal_contained_in': ['4.ca1.a1', '4.z1.a1', '4.cr1.a1', '4.ds1.a1', '4.ej1.a1', '4.ez1.a1', '4.fn1.a1'], 'normal_contains': ['16.p1.a1', '16.i1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dy1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.dy1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879072
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.dz1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.y1', '32.hk1.z1', '32.hk1.j1', '32.hk1.i1', '32.hk1.r1', '32.hk1.q1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.es1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.c1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.t1', '32.hk1.s1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.de1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ct1'], 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '4.cb1.a1', '4.cv1.a1', '4.dt1.a1', '4.ei1.a1', '4.ez1.a1', '4.fj1.a1'], 'contains': ['16.i1.a1', '16.s1.a1', '16.u1.a1', '16.cj1.a1'], 'core': '8.dz1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6658, 5169, 7845, 4124, 6661, 5167, 7838, 4133], 'generators': [20, 64, 136], 'label': '256.30836.8.dz1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.dz1.a1', 'normal_contained_in': ['4.cb1.a1', '4.y1.a1', '4.cv1.a1', '4.dt1.a1', '4.ei1.a1', '4.ez1.a1', '4.fj1.a1'], 'normal_contains': ['16.i1.a1', '16.s1.a1', '16.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.dz1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.dz1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879220
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.bg1.b1', '16.io1.a1', '16.ip1.a1', '16.iu1.b1', '16.iw1.b1', '16.ja1.b1', '16.jb1.b1'], 'core': '16.bg1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9556, -1, 4112, -1, 9562, -1, 4108, -1], 'generators': [129, 2, 20], 'label': '256.30836.8.hi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.hi1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hi1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879073
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ea1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.j1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.r1', '32.hk1.i1', '32.hk1.j1', '32.hk1.q1', '32.hk1.y1', '32.hk1.b1', '32.hk1.c1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.k1', '32.hk1.l1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.br1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.by1', '32.hk1.et1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.bx1', '32.hk1.h1', '32.hk1.be1', '32.hk1.w1', '32.hk1.p1', '32.hk1.o1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.g1', '32.hk1.f1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.n1', '32.hk1.m1', '32.hk1.v1', '32.hk1.bd1', '32.hk1.e1', '32.hk1.bt1', '32.hk1.dw1', '32.hk1.do1', '32.hk1.dh1', '32.hk1.dg1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.bs1', '32.hk1.bv1', '32.hk1.dy1', '32.hk1.dq1', '32.hk1.dj1', '32.hk1.di1', '32.hk1.dr1', '32.hk1.dz1', '32.hk1.bu1', '32.hk1.bn1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.ck1', '32.hk1.ct1', '32.hk1.db1', '32.hk1.bm1', '32.hk1.bl1', '32.hk1.cy1', '32.hk1.cq1', '32.hk1.cj1', '32.hk1.ci1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.bk1', '32.hk1.cb1', '32.hk1.eu1', '32.hk1.em1', '32.hk1.ef1', '32.hk1.ee1', '32.hk1.en1', '32.hk1.ev1', '32.hk1.ca1', '32.hk1.cd1', '32.hk1.ew1', '32.hk1.eo1', '32.hk1.eh1', '32.hk1.eg1', '32.hk1.ep1', '32.hk1.ex1', '32.hk1.cc1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '4.bv1.a1', '4.cx1.a1', '4.dt1.a1', '4.ej1.a1', '4.ex1.a1', '4.fp1.a1'], 'contains': ['16.i1.a1', '16.t1.a1', '16.v1.a1'], 'core': '8.ea1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4929, 8856, 7279, 7720, 4931, 8854, 7273, 7737], 'generators': [18, 64], 'label': '256.30836.8.ea1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ea1.a1', 'normal_contained_in': ['4.bv1.a1', '4.x1.a1', '4.cx1.a1', '4.dt1.a1', '4.ej1.a1', '4.ex1.a1', '4.fp1.a1'], 'normal_contains': ['16.i1.a1', '16.t1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ea1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ea1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879074
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.eb1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.y1', '32.hk1.b1', '32.hk1.j1', '32.hk1.q1', '32.hk1.r1', '32.hk1.i1', '32.hk1.c1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.l1', '32.hk1.s1', '32.hk1.t1', '32.hk1.k1', '32.hk1.by1', '32.hk1.et1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.dc1', '32.hk1.be1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.eu1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.cy1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dq1'], 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '4.cb1.a1', '4.cw1.a1', '4.dn1.a1', '4.eh1.a1', '4.ey1.a1', '4.fp1.a1'], 'contains': ['16.i1.a1', '16.z1.a1', '16.bc1.a1'], 'core': '8.eb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6557, 7321, 8428, 7307, 6561, 7318, 8421, 7323], 'generators': [21, 64], 'label': '256.30836.8.eb1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.eb1.a1', 'normal_contained_in': ['4.cb1.a1', '4.z1.a1', '4.cw1.a1', '4.dn1.a1', '4.eh1.a1', '4.ey1.a1', '4.fp1.a1'], 'normal_contains': ['16.i1.a1', '16.z1.a1', '16.bc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.eb1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.eb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879075
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ec1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.ec1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.c1', '32.hk1.s1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '4.bw1.a1', '4.cy1.a1', '4.du1.a1', '4.ek1.a1', '4.fa1.a1', '4.fq1.a1'], 'contains': ['16.j1.a1', '16.k1.a1', '16.v1.a1', '16.fp1.a1'], 'core': '8.ec1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3629, 1731, 6265, 1884, 3631, 1730, 6260, 1888], 'generators': [66, 16, 128], 'label': '256.30836.8.ec1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ec1.a1', 'normal_contained_in': ['4.bw1.a1', '4.x1.a1', '4.cy1.a1', '4.du1.a1', '4.ek1.a1', '4.fa1.a1', '4.fq1.a1'], 'normal_contains': ['16.j1.a1', '16.k1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ec1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ec1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879076
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ed1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.i1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.r1', '32.hk1.q1', '32.hk1.j1', '32.hk1.i1', '32.hk1.y1', '32.hk1.z1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.es1', '32.hk1.et1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.f1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.h1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1'], 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '4.bz1.a1', '4.cz1.a1', '4.dv1.a1', '4.el1.a1', '4.fa1.a1', '4.fr1.a1'], 'contains': ['16.j1.a1', '16.l1.a1', '16.x1.a1'], 'core': '8.ed1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5124, 2792, 7559, 4005, 5127, 2791, 7553, 4014], 'generators': [65, 16], 'label': '256.30836.8.ed1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ed1.a1', 'normal_contained_in': ['4.bz1.a1', '4.u1.a1', '4.cz1.a1', '4.dv1.a1', '4.el1.a1', '4.fa1.a1', '4.fr1.a1'], 'normal_contains': ['16.j1.a1', '16.l1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ed1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ed1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879077
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ee1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.r1', '32.hk1.q1', '32.hk1.j1', '32.hk1.i1', '32.hk1.y1', '32.hk1.z1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.es1', '32.hk1.et1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.f1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.h1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1'], 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '4.cc1.a1', '4.cv1.a1', '4.du1.a1', '4.el1.a1', '4.fb1.a1', '4.fk1.a1'], 'contains': ['16.j1.a1', '16.r1.a1', '16.u1.a1', '16.ck1.a1'], 'core': '8.ee1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2964, 4612, 6440, 3328, 2965, 4610, 6434, 3334], 'generators': [68, 16, 136], 'label': '256.30836.8.ee1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ee1.a1', 'normal_contained_in': ['4.cc1.a1', '4.ba1.a1', '4.cv1.a1', '4.du1.a1', '4.el1.a1', '4.fb1.a1', '4.fk1.a1'], 'normal_contains': ['16.j1.a1', '16.u1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ee1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ee1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879078
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ef1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.i1', '32.hk1.r1', '32.hk1.z1', '32.hk1.j1', '32.hk1.b1', '32.hk1.y1', '32.hk1.q1', '32.hk1.bo1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dk1', '32.hk1.bq1', '32.hk1.de1', '32.hk1.dn1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dm1', '32.hk1.c1', '32.hk1.k1', '32.hk1.t1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.bg1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cv1', '32.hk1.cf1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cm1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.ei1', '32.hk1.by1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.bz1', '32.hk1.es1', '32.hk1.ek1', '32.hk1.bi1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.co1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.dh1', '32.hk1.bt1', '32.hk1.dw1', '32.hk1.do1', '32.hk1.e1', '32.hk1.m1', '32.hk1.v1', '32.hk1.bd1', '32.hk1.n1', '32.hk1.f1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.g1', '32.hk1.o1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.p1', '32.hk1.h1', '32.hk1.be1', '32.hk1.w1', '32.hk1.bu1', '32.hk1.di1', '32.hk1.dr1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.bv1', '32.hk1.dy1', '32.hk1.dq1', '32.hk1.ca1', '32.hk1.ee1', '32.hk1.en1', '32.hk1.ev1', '32.hk1.ef1', '32.hk1.cb1', '32.hk1.eu1', '32.hk1.em1', '32.hk1.bk1', '32.hk1.ci1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.cj1', '32.hk1.bl1', '32.hk1.cy1', '32.hk1.cq1', '32.hk1.bm1', '32.hk1.ck1', '32.hk1.ct1', '32.hk1.db1', '32.hk1.cl1', '32.hk1.bn1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ep1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.cd1', '32.hk1.ew1', '32.hk1.eo1'], 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '4.cd1.a1', '4.cy1.a1', '4.dr1.a1', '4.ee1.a1', '4.fc1.a1', '4.fr1.a1'], 'contains': ['16.j1.a1', '16.w1.a1', '16.bb1.a1'], 'core': '8.ef1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5026, 2247, 7973, 2540, 5029, 2247, 7966, 2545], 'generators': [70, 16], 'label': '256.30836.8.ef1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ef1.a1', 'normal_contained_in': ['4.cd1.a1', '4.ba1.a1', '4.cy1.a1', '4.dr1.a1', '4.ee1.a1', '4.fc1.a1', '4.fr1.a1'], 'normal_contains': ['16.j1.a1', '16.w1.a1', '16.bb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ef1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ef1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879079
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.eg1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.i1', '32.hk1.r1', '32.hk1.z1', '32.hk1.j1', '32.hk1.b1', '32.hk1.y1', '32.hk1.q1', '32.hk1.bo1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dk1', '32.hk1.bq1', '32.hk1.de1', '32.hk1.dn1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dm1', '32.hk1.c1', '32.hk1.k1', '32.hk1.t1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.bg1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cv1', '32.hk1.cf1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cm1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.ei1', '32.hk1.by1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.bz1', '32.hk1.es1', '32.hk1.ek1', '32.hk1.bi1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.co1', '32.hk1.m1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.o1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.w1', '32.hk1.be1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ee1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.eu1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.da1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '4.cc1.a1', '4.cz1.a1', '4.do1.a1', '4.eh1.a1', '4.fc1.a1', '4.fq1.a1'], 'contains': ['16.j1.a1', '16.y1.a1', '16.bc1.a1', '16.gw1.a1'], 'core': '8.eg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2910, 2890, 5702, 2206, 2911, 2889, 5696, 2210], 'generators': [69, 16, 128], 'label': '256.30836.8.eg1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.eg1.a1', 'normal_contained_in': ['4.cc1.a1', '4.bb1.a1', '4.cz1.a1', '4.do1.a1', '4.eh1.a1', '4.fc1.a1', '4.fq1.a1'], 'normal_contains': ['16.j1.a1', '16.y1.a1', '16.bc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.eg1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.eg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879221
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.bg1.c1', '16.io1.b1', '16.ip1.b1', '16.iu1.a1', '16.iw1.a1', '16.ja1.b1', '16.jb1.b1'], 'core': '16.bg1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9556, -1, 4080, -1, 9562, -1, 4076, -1], 'generators': [1, 130, 20], 'label': '256.30836.8.hi1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.hi1.c1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hi1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879080
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.eh1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.i1', '32.hk1.r1', '32.hk1.z1', '32.hk1.j1', '32.hk1.b1', '32.hk1.y1', '32.hk1.q1', '32.hk1.dc1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.dn1', '32.hk1.dv1', '32.hk1.bq1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.br1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.k1', '32.hk1.c1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.l1', '32.hk1.cf1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cm1', '32.hk1.bg1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cv1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.es1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.et1', '32.hk1.by1', '32.hk1.ec1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.bi1', '32.hk1.m1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.dh1', '32.hk1.bt1', '32.hk1.dw1', '32.hk1.do1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.g1', '32.hk1.o1', '32.hk1.be1', '32.hk1.w1', '32.hk1.p1', '32.hk1.h1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.ef1', '32.hk1.cb1', '32.hk1.eu1', '32.hk1.em1', '32.hk1.ca1', '32.hk1.ee1', '32.hk1.en1', '32.hk1.ev1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.bn1', '32.hk1.ct1', '32.hk1.db1', '32.hk1.bm1', '32.hk1.ck1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '4.cd1.a1', '4.cs1.a1', '4.dv1.a1', '4.ek1.a1', '4.fb1.a1', '4.fn1.a1'], 'contains': ['16.j1.a1', '16.bd1.a1', '16.be1.a1', '16.gx1.a1'], 'core': '8.eh1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2528, 3959, 7369, 3670, 2529, 3957, 7363, 3677], 'generators': [71, 16, 128], 'label': '256.30836.8.eh1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.eh1.a1', 'normal_contained_in': ['4.cd1.a1', '4.bb1.a1', '4.cs1.a1', '4.dv1.a1', '4.ek1.a1', '4.fb1.a1', '4.fn1.a1'], 'normal_contains': ['16.j1.a1', '16.bd1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.eh1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.eh1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879081
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '16.b1.a1', 'complements': ['128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.f1.a1', '4.i1.a1', '4.k1.a1', '4.o1.a1', '4.q1.a1', '4.bk1.a1', '4.bm1.a1', '4.bq1.a1', '4.bs1.a1', '4.cm1.a1', '4.co1.a1', '4.di1.a1', '4.dk1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6979, 7597, 7159, 2938, 7060, 7594, 7153, 2944], 'generators': [1, 2, 4, 64], 'label': '256.30836.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.f1.a1', '4.bm1.a1', '4.bk1.a1', '4.bs1.a1', '4.bq1.a1', '4.k1.a1', '4.i1.a1', '4.q1.a1', '4.o1.a1', '4.cm1.a1', '4.co1.a1', '4.di1.a1', '4.dk1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879082
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.bc1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.d1', '128.i1.b1', '128.i1.c1', '128.h1.a1', '128.h1.d1', '128.h1.b1', '128.h1.c1', '128.j1.a1', '128.j1.b1', '128.n1.a1', '128.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.dh1.a1', '4.dk1.a1', '4.dl1.a1', '4.dp1.a1', '4.dq1.a1', '4.dw1.a1', '4.dy1.a1', '4.ef1.a1', '4.eg1.a1', '4.en1.a1', '4.eo1.a1', '4.eu1.a1', '4.ew1.a1', '4.fe1.a1', '4.ff1.a1'], 'core': '2.bc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4673, 3592, 7548, 2714, 4675, 3591, 7541, 2720], 'generators': [65, 66, 68, 80], 'label': '256.30836.2.bc1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.bc1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.dh1.a1', '4.dl1.a1', '4.dk1.a1', '4.dp1.a1', '4.dq1.a1', '4.dy1.a1', '4.dw1.a1', '4.eg1.a1', '4.ef1.a1', '4.en1.a1', '4.eo1.a1', '4.ew1.a1', '4.eu1.a1', '4.fe1.a1', '4.ff1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.bc1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879083
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ei1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.o1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.c1', '32.hk1.s1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1'], 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '4.ce1.a1', '4.da1.a1', '4.du1.a1', '4.em1.a1', '4.fd1.a1', '4.fl1.a1'], 'contains': ['16.k1.a1', '16.n1.a1', '16.u1.a1'], 'core': '8.ei1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5866, 3263, 7085, 1470, 5869, 3262, 7079, 1473], 'generators': [66, 84], 'label': '256.30836.8.ei1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ei1.a1', 'normal_contained_in': ['4.ce1.a1', '4.y1.a1', '4.da1.a1', '4.du1.a1', '4.em1.a1', '4.fd1.a1', '4.fl1.a1'], 'normal_contains': ['16.k1.a1', '16.n1.a1', '16.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ei1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ei1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879084
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ej1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.o1.a1', 'complements': ['32.hk1.a1', '32.hk1.i1', '32.hk1.y1', '32.hk1.q1', '32.hk1.j1', '32.hk1.b1', '32.hk1.r1', '32.hk1.z1', '32.hk1.dc1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.es1', '32.hk1.ek1', '32.hk1.by1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.bz1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cf1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cv1', '32.hk1.bg1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cm1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.dn1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dm1', '32.hk1.bq1', '32.hk1.de1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.c1', '32.hk1.m1', '32.hk1.e1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dw1', '32.hk1.do1', '32.hk1.dh1', '32.hk1.bt1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.bm1', '32.hk1.ck1', '32.hk1.ct1', '32.hk1.db1', '32.hk1.cl1', '32.hk1.bn1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ef1', '32.hk1.cb1', '32.hk1.en1', '32.hk1.ev1', '32.hk1.ca1', '32.hk1.ee1', '32.hk1.eu1', '32.hk1.em1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.p1', '32.hk1.h1', '32.hk1.be1', '32.hk1.w1', '32.hk1.g1', '32.hk1.o1'], 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '4.ce1.a1', '4.db1.a1', '4.dp1.a1', '4.en1.a1', '4.fe1.a1', '4.fq1.a1'], 'contains': ['16.k1.a1', '16.p1.a1', '16.bc1.a1'], 'core': '8.ej1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4158, 1093, 8447, 297, 4160, 1093, 8440, 298], 'generators': [85, 66], 'label': '256.30836.8.ej1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ej1.a1', 'normal_contained_in': ['4.ce1.a1', '4.z1.a1', '4.db1.a1', '4.dp1.a1', '4.en1.a1', '4.fe1.a1', '4.fq1.a1'], 'normal_contains': ['16.p1.a1', '16.k1.a1', '16.bc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ej1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ej1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879085
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ek1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.j1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.y1', '32.hk1.i1', '32.hk1.j1', '32.hk1.z1', '32.hk1.r1', '32.hk1.b1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.c1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.d1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.g1', '32.hk1.w1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.h1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.e1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.f1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.cd1'], 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '4.cf1.a1', '4.da1.a1', '4.dw1.a1', '4.en1.a1', '4.eu1.a1', '4.fs1.a1'], 'contains': ['16.k1.a1', '16.q1.a1', '16.t1.a1'], 'core': '8.ek1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2828, 860, 6522, 2713, 2829, 860, 6516, 2719], 'generators': [66, 80], 'label': '256.30836.8.ek1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ek1.a1', 'normal_contained_in': ['4.cf1.a1', '4.x1.a1', '4.da1.a1', '4.dw1.a1', '4.en1.a1', '4.eu1.a1', '4.fs1.a1'], 'normal_contains': ['16.k1.a1', '16.q1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ek1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ek1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879086
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.el1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.y1', '32.hk1.i1', '32.hk1.j1', '32.hk1.z1', '32.hk1.r1', '32.hk1.b1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.c1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.d1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.g1', '32.hk1.w1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.h1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.e1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.f1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.cd1'], 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '4.cg1.a1', '4.cy1.a1', '4.dw1.a1', '4.ef1.a1', '4.fe1.a1', '4.ft1.a1'], 'contains': ['16.k1.a1', '16.s1.a1', '16.bb1.a1', '16.ie1.a1'], 'core': '8.el1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3990, 1910, 8277, 242, 3992, 1909, 8270, 242], 'generators': [66, 20, 128], 'label': '256.30836.8.el1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.el1.a1', 'normal_contained_in': ['4.cg1.a1', '4.y1.a1', '4.cy1.a1', '4.dw1.a1', '4.ef1.a1', '4.fe1.a1', '4.ft1.a1'], 'normal_contains': ['16.k1.a1', '16.s1.a1', '16.bb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.el1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.el1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879143
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.co1.a1', '16.cp1.a1', '16.cq1.a1', '16.cx1.a1', '16.cy1.a1', '16.db1.a1', '16.de1.a1', '16.en1.a1', '16.en1.b1', '16.en1.c1', '16.en1.d1', '16.en1.e1', '16.en1.f1', '16.en1.g1', '16.en1.h1', '16.ik1.a1', '16.ik1.a2', '16.ik1.b1', '16.ik1.b2', '16.ik1.c1', '16.ik1.c2', '16.ik1.d1', '16.ik1.d2', '16.je1.a1', '16.je1.a2', '16.je1.b1', '16.je1.b2', '16.je1.c1', '16.je1.c2', '16.je1.f1', '16.je1.f2'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9787, -1, 2156, -1, 9792, -1, 2158, -1], 'generators': [1, 2, 4, 128, 168], 'label': '256.30836.8.gf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.gf1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879087
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.em1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.m1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.r1', '32.hk1.i1', '32.hk1.j1', '32.hk1.q1', '32.hk1.y1', '32.hk1.b1', '32.hk1.bb1', '32.hk1.c1', '32.hk1.k1', '32.hk1.t1', '32.hk1.s1', '32.hk1.l1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dt1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.bi1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.by1', '32.hk1.et1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.er1', '32.hk1.bw1', '32.hk1.h1', '32.hk1.be1', '32.hk1.w1', '32.hk1.p1', '32.hk1.o1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.g1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.do1', '32.hk1.dh1', '32.hk1.bt1', '32.hk1.dw1', '32.hk1.dx1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dp1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.ck1', '32.hk1.ct1', '32.hk1.db1', '32.hk1.bm1', '32.hk1.bn1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.ev1', '32.hk1.ca1', '32.hk1.ee1', '32.hk1.en1', '32.hk1.em1', '32.hk1.ef1', '32.hk1.cb1', '32.hk1.eu1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.cd1'], 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.cf1.a1', '4.db1.a1', '4.dx1.a1', '4.em1.a1', '4.fa1.a1', '4.ft1.a1'], 'contains': ['16.k1.a1', '16.x1.a1', '16.ba1.a1', '16.dq1.a1'], 'core': '8.em1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1746, 3019, 8990, 4265, 1747, 3018, 8982, 4274], 'generators': [81, 66, 32], 'label': '256.30836.8.em1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.em1.a1', 'normal_contained_in': ['4.cf1.a1', '4.t1.a1', '4.db1.a1', '4.dx1.a1', '4.em1.a1', '4.fa1.a1', '4.ft1.a1'], 'normal_contains': ['16.k1.a1', '16.ba1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.em1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.em1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879088
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.en1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.y1', '32.hk1.b1', '32.hk1.j1', '32.hk1.q1', '32.hk1.r1', '32.hk1.i1', '32.hk1.c1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.l1', '32.hk1.s1', '32.hk1.t1', '32.hk1.k1', '32.hk1.by1', '32.hk1.et1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.dc1', '32.hk1.be1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.eu1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.cy1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dq1'], 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '4.cg1.a1', '4.ct1.a1', '4.dx1.a1', '4.ek1.a1', '4.fd1.a1', '4.fs1.a1'], 'contains': ['16.k1.a1', '16.z1.a1', '16.be1.a1'], 'core': '8.en1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1188, 3147, 7458, 4886, 1188, 3145, 7451, 4896], 'generators': [21, 66], 'label': '256.30836.8.en1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.en1.a1', 'normal_contained_in': ['4.cg1.a1', '4.z1.a1', '4.ct1.a1', '4.dx1.a1', '4.ek1.a1', '4.fd1.a1', '4.fs1.a1'], 'normal_contains': ['16.k1.a1', '16.z1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.en1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.en1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879089
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.eo1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.i1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.y1', '32.hk1.z1', '32.hk1.j1', '32.hk1.i1', '32.hk1.r1', '32.hk1.q1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.es1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.c1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.t1', '32.hk1.s1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.de1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ct1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '4.bz1.a1', '4.dc1.a1', '4.dy1.a1', '4.eo1.a1', '4.eu1.a1', '4.fu1.a1'], 'contains': ['16.l1.a1', '16.m1.a1', '16.q1.a1'], 'core': '8.eo1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4461, 519, 7674, 7568, 4464, 519, 7668, 7584], 'generators': [65, 80], 'label': '256.30836.8.eo1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.eo1.a1', 'normal_contained_in': ['4.bz1.a1', '4.bc1.a1', '4.dc1.a1', '4.dy1.a1', '4.eo1.a1', '4.eu1.a1', '4.fu1.a1'], 'normal_contains': ['16.l1.a1', '16.m1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.eo1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.eo1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879090
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ep1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.ep1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.y1', '32.hk1.z1', '32.hk1.j1', '32.hk1.i1', '32.hk1.r1', '32.hk1.q1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.es1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.c1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.t1', '32.hk1.s1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.de1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '4.ca1.a1', '4.cu1.a1', '4.dv1.a1', '4.ep1.a1', '4.fd1.a1', '4.fu1.a1'], 'contains': ['16.l1.a1', '16.n1.a1', '16.be1.a1', '16.cl1.a1'], 'core': '8.ep1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5761, 3578, 5808, 5523, 5764, 3576, 5803, 5536], 'generators': [65, 22, 136], 'label': '256.30836.8.ep1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ep1.a1', 'normal_contained_in': ['4.ca1.a1', '4.bd1.a1', '4.cu1.a1', '4.dv1.a1', '4.ep1.a1', '4.fd1.a1', '4.fu1.a1'], 'normal_contains': ['16.l1.a1', '16.n1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ep1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ep1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879091
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.eq1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.eq1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.co1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bo1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.w1', '32.hk1.g1', '32.hk1.h1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.p1', '32.hk1.o1', '32.hk1.be1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.bt1', '32.hk1.dp1', '32.hk1.do1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dw1', '32.hk1.dx1', '32.hk1.dh1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.f1', '32.hk1.db1', '32.hk1.cl1', '32.hk1.ck1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.bm1', '32.hk1.bn1', '32.hk1.ct1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.ee1', '32.hk1.eu1', '32.hk1.ev1', '32.hk1.ef1', '32.hk1.cb1', '32.hk1.en1', '32.hk1.em1', '32.hk1.ca1'], 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '4.ca1.a1', '4.dd1.a1', '4.dy1.a1', '4.eg1.a1', '4.fe1.a1', '4.fr1.a1'], 'contains': ['16.l1.a1', '16.p1.a1', '16.bb1.a1', '16.dr1.a1'], 'core': '8.eq1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3803, 1146, 8838, 831, 3804, 1145, 8830, 833], 'generators': [65, 86, 32], 'label': '256.30836.8.eq1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.eq1.a1', 'normal_contained_in': ['4.ca1.a1', '4.be1.a1', '4.dd1.a1', '4.dy1.a1', '4.eg1.a1', '4.fe1.a1', '4.fr1.a1'], 'normal_contains': ['16.p1.a1', '16.l1.a1', '16.bb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.eq1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.eq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879092
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.er1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.n1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.y1', '32.hk1.b1', '32.hk1.j1', '32.hk1.q1', '32.hk1.r1', '32.hk1.i1', '32.hk1.c1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.l1', '32.hk1.s1', '32.hk1.t1', '32.hk1.k1', '32.hk1.by1', '32.hk1.et1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.dc1', '32.hk1.h1', '32.hk1.be1', '32.hk1.bf1', '32.hk1.g1', '32.hk1.o1', '32.hk1.x1', '32.hk1.w1', '32.hk1.p1', '32.hk1.f1', '32.hk1.bc1', '32.hk1.bd1', '32.hk1.e1', '32.hk1.m1', '32.hk1.v1', '32.hk1.u1', '32.hk1.n1', '32.hk1.cb1', '32.hk1.eu1', '32.hk1.ev1', '32.hk1.ca1', '32.hk1.ee1', '32.hk1.en1', '32.hk1.em1', '32.hk1.ef1', '32.hk1.cd1', '32.hk1.ew1', '32.hk1.ex1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ep1', '32.hk1.eo1', '32.hk1.eh1', '32.hk1.bn1', '32.hk1.da1', '32.hk1.db1', '32.hk1.bm1', '32.hk1.ck1', '32.hk1.ct1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.bl1', '32.hk1.cy1', '32.hk1.cz1', '32.hk1.bk1', '32.hk1.ci1', '32.hk1.cr1', '32.hk1.cq1', '32.hk1.cj1', '32.hk1.bt1', '32.hk1.dw1', '32.hk1.dx1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dp1', '32.hk1.do1', '32.hk1.dh1', '32.hk1.bv1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.bu1', '32.hk1.di1', '32.hk1.dr1', '32.hk1.dq1', '32.hk1.dj1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '4.cb1.a1', '4.cz1.a1', '4.dq1.a1', '4.eo1.a1', '4.fe1.a1', '4.fv1.a1'], 'contains': ['16.l1.a1', '16.s1.a1', '16.bc1.a1'], 'core': '8.er1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6703, 1436, 6910, 2970, 6706, 1436, 6904, 2976], 'generators': [65, 20], 'label': '256.30836.8.er1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.er1.a1', 'normal_contained_in': ['4.cb1.a1', '4.bd1.a1', '4.cz1.a1', '4.dq1.a1', '4.eo1.a1', '4.fe1.a1', '4.fv1.a1'], 'normal_contains': ['16.l1.a1', '16.bc1.a1', '16.s1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.er1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.er1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879093
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.bd1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.c1', '128.i1.b1', '128.i1.d1', '128.h1.a1', '128.h1.b1', '128.h1.c1', '128.h1.d1', '128.j1.a1', '128.j1.b1', '128.n1.a1', '128.n1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.di1.a1', '4.dl1.a1', '4.dm1.a1', '4.ds1.a1', '4.dt1.a1', '4.ea1.a1', '4.ec1.a1', '4.ei1.a1', '4.ej1.a1', '4.eq1.a1', '4.es1.a1', '4.ex1.a1', '4.ez1.a1', '4.fg1.a1', '4.fi1.a1'], 'core': '2.bd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4739, 7970, 7186, 7067, 4741, 7995, 7180, 7082], 'generators': [17, 18, 20, 64], 'label': '256.30836.2.bd1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.bd1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.di1.a1', '4.dl1.a1', '4.dm1.a1', '4.ea1.a1', '4.ec1.a1', '4.ds1.a1', '4.dt1.a1', '4.es1.a1', '4.eq1.a1', '4.ej1.a1', '4.ei1.a1', '4.ez1.a1', '4.ex1.a1', '4.fi1.a1', '4.fg1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.bd1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879222
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.bg1.d1', '16.io1.b1', '16.ip1.b1', '16.iu1.b1', '16.iw1.b1', '16.ja1.a1', '16.jb1.a1'], 'core': '16.bg1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9556, -1, 4175, -1, 9562, -1, 4172, -1], 'generators': [129, 130, 20], 'label': '256.30836.8.hi1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.hi1.d1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hi1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879094
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.es1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.r1', '32.hk1.i1', '32.hk1.j1', '32.hk1.q1', '32.hk1.y1', '32.hk1.b1', '32.hk1.c1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.k1', '32.hk1.l1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.br1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.by1', '32.hk1.et1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.bx1', '32.hk1.be1', '32.hk1.h1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.cy1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.eu1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.ex1'], 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '4.cb1.a1', '4.dc1.a1', '4.dz1.a1', '4.el1.a1', '4.fd1.a1', '4.fm1.a1'], 'contains': ['16.l1.a1', '16.u1.a1', '16.z1.a1', '16.ds1.a1'], 'core': '8.es1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4380, 3640, 8172, 6225, 4382, 3639, 8165, 6238], 'generators': [65, 84, 32], 'label': '256.30836.8.es1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.es1.a1', 'normal_contained_in': ['4.cb1.a1', '4.be1.a1', '4.dc1.a1', '4.dz1.a1', '4.el1.a1', '4.fd1.a1', '4.fm1.a1'], 'normal_contains': ['16.l1.a1', '16.z1.a1', '16.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.es1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.es1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879095
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.et1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.y1', '32.hk1.z1', '32.hk1.j1', '32.hk1.i1', '32.hk1.r1', '32.hk1.q1', '32.hk1.bx1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.es1', '32.hk1.et1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.c1', '32.hk1.s1', '32.hk1.t1', '32.hk1.k1', '32.hk1.l1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.bi1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.ca1', '32.hk1.cb1', '32.hk1.eu1', '32.hk1.ev1', '32.hk1.ef1', '32.hk1.ee1', '32.hk1.en1', '32.hk1.em1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.be1', '32.hk1.bf1', '32.hk1.g1', '32.hk1.h1', '32.hk1.x1', '32.hk1.w1', '32.hk1.p1', '32.hk1.o1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.dh1', '32.hk1.dg1', '32.hk1.dp1', '32.hk1.do1', '32.hk1.bs1', '32.hk1.bt1', '32.hk1.dw1', '32.hk1.dx1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.ct1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.ck1', '32.hk1.da1', '32.hk1.db1', '32.hk1.bm1', '32.hk1.bn1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '4.bv1.a1', '4.dd1.a1', '4.dz1.a1', '4.ep1.a1', '4.fa1.a1', '4.fv1.a1'], 'contains': ['16.l1.a1', '16.v1.a1', '16.ba1.a1'], 'core': '8.et1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4425, 1783, 7346, 8481, 4427, 1782, 7339, 8500], 'generators': [65, 82], 'label': '256.30836.8.et1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.et1.a1', 'normal_contained_in': ['4.bv1.a1', '4.bc1.a1', '4.dd1.a1', '4.dz1.a1', '4.ep1.a1', '4.fa1.a1', '4.fv1.a1'], 'normal_contains': ['16.l1.a1', '16.ba1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.et1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.et1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879096
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.eu1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.k1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.c1', '32.hk1.s1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '4.bw1.a1', '4.de1.a1', '4.ea1.a1', '4.eq1.a1', '4.ex1.a1', '4.fw1.a1'], 'contains': ['16.m1.a1', '16.o1.a1', '16.v1.a1', '16.fq1.a1'], 'core': '8.eu1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1628, 6999, 8884, 9155, 1628, 6996, 8876, 9174], 'generators': [17, 82, 128], 'label': '256.30836.8.eu1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.eu1.a1', 'normal_contained_in': ['4.bw1.a1', '4.bc1.a1', '4.de1.a1', '4.ea1.a1', '4.eq1.a1', '4.ex1.a1', '4.fw1.a1'], 'normal_contains': ['16.o1.a1', '16.m1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.eu1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.eu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879097
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ev1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.c1', '32.hk1.s1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bf1.a1', '4.cc1.a1', '4.cw1.a1', '4.dp1.a1', '4.eo1.a1', '4.ff1.a1', '4.fw1.a1'], 'contains': ['16.m1.a1', '16.r1.a1', '16.bc1.a1'], 'core': '8.ev1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3846, 7942, 7540, 9036, 3848, 7939, 7534, 9056], 'generators': [17, 68], 'label': '256.30836.8.ev1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ev1.a1', 'normal_contained_in': ['4.cc1.a1', '4.bf1.a1', '4.cw1.a1', '4.dp1.a1', '4.eo1.a1', '4.ff1.a1', '4.fw1.a1'], 'normal_contains': ['16.m1.a1', '16.bc1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ev1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ev1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879098
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ew1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.y1', '32.hk1.i1', '32.hk1.j1', '32.hk1.z1', '32.hk1.r1', '32.hk1.b1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.c1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.d1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.g1', '32.hk1.w1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.h1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.e1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.f1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.cd1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bg1.a1', '4.cc1.a1', '4.dc1.a1', '4.ea1.a1', '4.ei1.a1', '4.fg1.a1', '4.fl1.a1'], 'contains': ['16.m1.a1', '16.u1.a1', '16.y1.a1'], 'core': '8.ew1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [974, 5369, 7326, 6280, 975, 5366, 7320, 6294], 'generators': [17, 84], 'label': '256.30836.8.ew1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ew1.a1', 'normal_contained_in': ['4.cc1.a1', '4.bg1.a1', '4.dc1.a1', '4.ea1.a1', '4.ei1.a1', '4.fg1.a1', '4.fl1.a1'], 'normal_contains': ['16.m1.a1', '16.y1.a1', '16.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ew1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ew1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879099
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ex1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.y1', '32.hk1.i1', '32.hk1.j1', '32.hk1.z1', '32.hk1.r1', '32.hk1.b1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.c1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.d1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.g1', '32.hk1.w1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.h1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.e1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.f1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.bt1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bf1.a1', '4.cd1.a1', '4.ct1.a1', '4.ds1.a1', '4.eq1.a1', '4.fg1.a1', '4.fu1.a1'], 'contains': ['16.m1.a1', '16.w1.a1', '16.be1.a1'], 'core': '8.ex1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1894, 6463, 8024, 9777, 1895, 6461, 8017, 9799], 'generators': [17, 70], 'label': '256.30836.8.ex1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ex1.a1', 'normal_contained_in': ['4.cd1.a1', '4.bf1.a1', '4.ct1.a1', '4.ds1.a1', '4.eq1.a1', '4.fg1.a1', '4.fu1.a1'], 'normal_contains': ['16.m1.a1', '16.w1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ex1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ex1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879100
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ey1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.y1', '32.hk1.i1', '32.hk1.j1', '32.hk1.z1', '32.hk1.r1', '32.hk1.b1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.c1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.d1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.g1', '32.hk1.w1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.h1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.e1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.f1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.bt1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bg1.a1', '4.cd1.a1', '4.de1.a1', '4.dy1.a1', '4.ef1.a1', '4.ff1.a1', '4.fo1.a1'], 'contains': ['16.m1.a1', '16.bb1.a1', '16.bd1.a1', '16.if1.a1'], 'core': '8.ey1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2315, 4927, 9187, 6335, 2316, 4924, 9179, 6350], 'generators': [17, 86, 128], 'label': '256.30836.8.ey1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ey1.a1', 'normal_contained_in': ['4.cd1.a1', '4.bg1.a1', '4.de1.a1', '4.dy1.a1', '4.ef1.a1', '4.ff1.a1', '4.fo1.a1'], 'normal_contains': ['16.m1.a1', '16.bb1.a1', '16.bd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ey1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ey1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879454
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dh1.a1', '8.gr1.a1', '8.gr1.b1'], 'contains': ['32.cw1.a1', '32.db1.a1', '32.dc1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1789, -1, 6239, -1, 1790, -1, 6234, -1], 'generators': [67, 68], 'label': '256.30836.16.fm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dh1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bs1.a1', 'old_label': '16.fm1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fm1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879101
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ez1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.ez1.a1', 'complements': ['32.hk1.a1', '32.hk1.i1', '32.hk1.y1', '32.hk1.q1', '32.hk1.j1', '32.hk1.b1', '32.hk1.r1', '32.hk1.z1', '32.hk1.dc1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.es1', '32.hk1.ek1', '32.hk1.by1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.bz1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cf1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cv1', '32.hk1.bg1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cm1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.dn1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dm1', '32.hk1.bq1', '32.hk1.de1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.c1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.e1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.n1', '32.hk1.f1', '32.hk1.v1', '32.hk1.bd1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.ew1', '32.hk1.eo1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ep1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.cd1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.eu1', '32.hk1.cj1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.bk1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.cq1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.w1', '32.hk1.be1', '32.hk1.o1', '32.hk1.g1', '32.hk1.dr1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.bv1', '32.hk1.dy1', '32.hk1.dq1', '32.hk1.bu1', '32.hk1.di1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '4.ce1.a1', '4.df1.a1', '4.do1.a1', '4.er1.a1', '4.ey1.a1', '4.fw1.a1'], 'contains': ['16.n1.a1', '16.o1.a1', '16.bc1.a1', '16.ig1.a1'], 'core': '8.ez1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7542, 7663, 6933, 2917, 7545, 7661, 6927, 2922], 'generators': [85, 22, 128], 'label': '256.30836.8.ez1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ez1.a1', 'normal_contained_in': ['4.ce1.a1', '4.bd1.a1', '4.df1.a1', '4.do1.a1', '4.er1.a1', '4.ey1.a1', '4.fw1.a1'], 'normal_contains': ['16.o1.a1', '16.n1.a1', '16.bc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ez1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ez1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879102
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fa1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.i1', '32.hk1.y1', '32.hk1.q1', '32.hk1.j1', '32.hk1.b1', '32.hk1.r1', '32.hk1.z1', '32.hk1.bo1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dt1', '32.hk1.by1', '32.hk1.ec1', '32.hk1.es1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.et1', '32.hk1.bi1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.bg1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cm1', '32.hk1.cf1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cv1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.er1', '32.hk1.bq1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.br1', '32.hk1.dn1', '32.hk1.dv1', '32.hk1.c1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.l1', '32.hk1.d1', '32.hk1.t1', '32.hk1.bb1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dw1', '32.hk1.do1', '32.hk1.dh1', '32.hk1.bt1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.e1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.n1', '32.hk1.f1', '32.hk1.v1', '32.hk1.bd1', '32.hk1.bm1', '32.hk1.ck1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.bn1', '32.hk1.ct1', '32.hk1.db1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.eo1', '32.hk1.eh1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.ex1', '32.hk1.ca1', '32.hk1.ee1', '32.hk1.eu1', '32.hk1.em1', '32.hk1.ef1', '32.hk1.cb1', '32.hk1.en1', '32.hk1.ev1', '32.hk1.bk1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.cq1', '32.hk1.cj1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.g1', '32.hk1.o1', '32.hk1.be1', '32.hk1.w1', '32.hk1.p1', '32.hk1.h1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.bu1', '32.hk1.di1', '32.hk1.dy1', '32.hk1.dq1', '32.hk1.dj1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dz1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bh1.a1', '4.ch1.a1', '4.da1.a1', '4.dr1.a1', '4.er1.a1', '4.ev1.a1', '4.fu1.a1'], 'contains': ['16.n1.a1', '16.q1.a1', '16.w1.a1', '16.ih1.a1'], 'core': '8.fa1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9228, 465, 5762, 7252, 9233, 465, 5757, 7267], 'generators': [70, 80, 128], 'label': '256.30836.8.fa1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fa1.a1', 'normal_contained_in': ['4.ch1.a1', '4.bh1.a1', '4.da1.a1', '4.dr1.a1', '4.er1.a1', '4.ev1.a1', '4.fu1.a1'], 'normal_contains': ['16.n1.a1', '16.w1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fa1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fa1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879103
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fb1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.r1', '32.hk1.q1', '32.hk1.j1', '32.hk1.i1', '32.hk1.y1', '32.hk1.z1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.es1', '32.hk1.et1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.f1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.h1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bh1.a1', '4.bx1.a1', '4.cx1.a1', '4.du1.a1', '4.ep1.a1', '4.fh1.a1', '4.fw1.a1'], 'contains': ['16.n1.a1', '16.r1.a1', '16.v1.a1'], 'core': '8.fb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7708, 4194, 5001, 6843, 7712, 4193, 4997, 6857], 'generators': [82, 68], 'label': '256.30836.8.fb1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fb1.a1', 'normal_contained_in': ['4.bx1.a1', '4.bh1.a1', '4.cx1.a1', '4.du1.a1', '4.ep1.a1', '4.fh1.a1', '4.fw1.a1'], 'normal_contains': ['16.n1.a1', '16.r1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fb1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879104
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.be1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.d1', '128.i1.b1', '128.i1.c1', '128.h1.a1', '128.h1.d1', '128.h1.b1', '128.h1.c1', '128.j1.a1', '128.j1.b1', '128.n1.a1', '128.n1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.dj1.a1', '4.dk1.a1', '4.dm1.a1', '4.du1.a1', '4.dv1.a1', '4.dx1.a1', '4.dz1.a1', '4.ek1.a1', '4.el1.a1', '4.em1.a1', '4.ep1.a1', '4.fa1.a1', '4.fb1.a1', '4.fd1.a1', '4.fh1.a1'], 'core': '2.be1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5287, 3799, 6898, 6010, 5289, 3798, 6891, 5973], 'generators': [65, 66, 68, 16], 'label': '256.30836.2.be1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.be1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.dj1.a1', '4.dk1.a1', '4.dm1.a1', '4.dv1.a1', '4.du1.a1', '4.dz1.a1', '4.dx1.a1', '4.el1.a1', '4.ek1.a1', '4.ep1.a1', '4.em1.a1', '4.fa1.a1', '4.fb1.a1', '4.fd1.a1', '4.fh1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.be1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.be1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879105
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fc1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.y1', '32.hk1.b1', '32.hk1.j1', '32.hk1.q1', '32.hk1.r1', '32.hk1.i1', '32.hk1.bb1', '32.hk1.c1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.t1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.by1', '32.hk1.et1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.br1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.bo1', '32.hk1.f1', '32.hk1.bc1', '32.hk1.bd1', '32.hk1.e1', '32.hk1.m1', '32.hk1.v1', '32.hk1.u1', '32.hk1.n1', '32.hk1.be1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.ex1', '32.hk1.cc1', '32.hk1.cd1', '32.hk1.ew1', '32.hk1.eo1', '32.hk1.eh1', '32.hk1.eg1', '32.hk1.ep1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ci1', '32.hk1.cr1', '32.hk1.cq1', '32.hk1.cj1', '32.hk1.bl1', '32.hk1.cy1', '32.hk1.cz1', '32.hk1.bk1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.dq1', '32.hk1.dj1', '32.hk1.di1', '32.hk1.dr1', '32.hk1.dz1', '32.hk1.bu1', '32.hk1.bv1', '32.hk1.dy1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.bt1'], 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '4.ch1.a1', '4.df1.a1', '4.dv1.a1', '4.em1.a1', '4.fh1.a1', '4.fo1.a1'], 'contains': ['16.n1.a1', '16.x1.a1', '16.bd1.a1'], 'core': '8.fc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7436, 3840, 8196, 5576, 7440, 3839, 8189, 5589], 'generators': [81, 22], 'label': '256.30836.8.fc1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fc1.a1', 'normal_contained_in': ['4.ch1.a1', '4.v1.a1', '4.df1.a1', '4.dv1.a1', '4.em1.a1', '4.fh1.a1', '4.fo1.a1'], 'normal_contains': ['16.n1.a1', '16.bd1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fc1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879106
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fd1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '8.fd1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.co1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bo1', '32.hk1.w1', '32.hk1.g1', '32.hk1.h1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.p1', '32.hk1.o1', '32.hk1.be1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bt1', '32.hk1.dp1', '32.hk1.do1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dw1', '32.hk1.dx1', '32.hk1.dh1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.db1', '32.hk1.cl1', '32.hk1.ck1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.bm1', '32.hk1.bn1', '32.hk1.ct1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.f1', '32.hk1.ee1', '32.hk1.eu1', '32.hk1.ev1', '32.hk1.ef1', '32.hk1.cb1', '32.hk1.en1', '32.hk1.em1', '32.hk1.ca1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dq1'], 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '4.ce1.a1', '4.dg1.a1', '4.ea1.a1', '4.es1.a1', '4.ez1.a1', '4.fk1.a1'], 'contains': ['16.o1.a1', '16.p1.a1', '16.u1.a1', '16.dt1.a1'], 'core': '8.fd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2474, 7889, 9104, 1523, 2476, 7886, 9097, 1527], 'generators': [67, 84, 32], 'label': '256.30836.8.fd1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fd1.a1', 'normal_contained_in': ['4.ce1.a1', '4.be1.a1', '4.dg1.a1', '4.ea1.a1', '4.es1.a1', '4.ez1.a1', '4.fk1.a1'], 'normal_contains': ['16.o1.a1', '16.p1.a1', '16.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fd1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879107
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fe1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.y1', '32.hk1.i1', '32.hk1.j1', '32.hk1.z1', '32.hk1.r1', '32.hk1.b1', '32.hk1.co1', '32.hk1.bi1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dk1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.c1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.ei1', '32.hk1.bw1', '32.hk1.g1', '32.hk1.w1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.h1', '32.hk1.cq1', '32.hk1.bk1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.cz1', '32.hk1.cj1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.di1', '32.hk1.dy1', '32.hk1.dq1', '32.hk1.bu1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.bd1', '32.hk1.n1', '32.hk1.f1', '32.hk1.v1', '32.hk1.u1', '32.hk1.e1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.eo1', '32.hk1.cc1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '4.cf1.a1', '4.dg1.a1', '4.eb1.a1', '4.er1.a1', '4.et1.a1', '4.fx1.a1'], 'contains': ['16.o1.a1', '16.q1.a1', '16.ba1.a1', '16.ii1.a1'], 'core': '8.fe1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2745, 1668, 8079, 5708, 2747, 1667, 8073, 5720], 'generators': [67, 80, 128], 'label': '256.30836.8.fe1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fe1.a1', 'normal_contained_in': ['4.cf1.a1', '4.bc1.a1', '4.dg1.a1', '4.eb1.a1', '4.er1.a1', '4.et1.a1', '4.fx1.a1'], 'normal_contains': ['16.o1.a1', '16.ba1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fe1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fe1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879279
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.fz1.b1', '8.gc1.b1'], 'contains': ['32.b1.b1', '32.q1.a1', '32.r1.a1', '32.co1.c1', '32.co1.d1', '32.ei1.b1', '32.ei1.b2', '32.gh1.c1', '32.gh1.d1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9080, -1, 3911, -1, 9084, -1, 3908, -1], 'generators': [3, 140, 32, 128], 'label': '256.30836.16.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bq1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879108
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ff1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.n1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.y1', '32.hk1.i1', '32.hk1.j1', '32.hk1.z1', '32.hk1.r1', '32.hk1.b1', '32.hk1.co1', '32.hk1.bi1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dk1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.c1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.ei1', '32.hk1.bw1', '32.hk1.g1', '32.hk1.w1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.h1', '32.hk1.cq1', '32.hk1.bk1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.cz1', '32.hk1.cj1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.di1', '32.hk1.dy1', '32.hk1.dq1', '32.hk1.bu1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.bd1', '32.hk1.n1', '32.hk1.f1', '32.hk1.v1', '32.hk1.u1', '32.hk1.e1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.eo1', '32.hk1.cc1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '4.cg1.a1', '4.cs1.a1', '4.ec1.a1', '4.eq1.a1', '4.ez1.a1', '4.fx1.a1'], 'contains': ['16.o1.a1', '16.s1.a1', '16.be1.a1'], 'core': '8.ff1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2865, 6673, 7133, 3458, 2866, 6671, 7126, 3465], 'generators': [67, 20], 'label': '256.30836.8.ff1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ff1.a1', 'normal_contained_in': ['4.cg1.a1', '4.bd1.a1', '4.cs1.a1', '4.ec1.a1', '4.eq1.a1', '4.ez1.a1', '4.fx1.a1'], 'normal_contains': ['16.o1.a1', '16.s1.a1', '16.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ff1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ff1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879109
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fg1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.y1', '32.hk1.b1', '32.hk1.j1', '32.hk1.q1', '32.hk1.r1', '32.hk1.i1', '32.hk1.bb1', '32.hk1.c1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.t1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.by1', '32.hk1.et1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.br1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.bo1', '32.hk1.h1', '32.hk1.be1', '32.hk1.bf1', '32.hk1.g1', '32.hk1.o1', '32.hk1.x1', '32.hk1.w1', '32.hk1.p1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.ev1', '32.hk1.ca1', '32.hk1.cb1', '32.hk1.eu1', '32.hk1.em1', '32.hk1.ef1', '32.hk1.ee1', '32.hk1.en1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.ck1', '32.hk1.ct1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.bn1', '32.hk1.da1', '32.hk1.db1', '32.hk1.bm1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.do1', '32.hk1.dh1', '32.hk1.dg1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.bs1', '32.hk1.bt1', '32.hk1.dw1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.bv1'], 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '4.cf1.a1', '4.df1.a1', '4.ec1.a1', '4.es1.a1', '4.ex1.a1', '4.fy1.a1'], 'contains': ['16.o1.a1', '16.t1.a1', '16.x1.a1'], 'core': '8.fg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2208, 9631, 8940, 3015, 2209, 9628, 8932, 3021], 'generators': [81, 18], 'label': '256.30836.8.fg1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fg1.a1', 'normal_contained_in': ['4.cf1.a1', '4.u1.a1', '4.df1.a1', '4.ec1.a1', '4.es1.a1', '4.ex1.a1', '4.fy1.a1'], 'normal_contains': ['16.o1.a1', '16.t1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fg1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879110
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fh1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.r1', '32.hk1.i1', '32.hk1.j1', '32.hk1.q1', '32.hk1.y1', '32.hk1.b1', '32.hk1.c1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.k1', '32.hk1.l1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.br1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.by1', '32.hk1.et1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.bx1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.be1', '32.hk1.h1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.cy1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.eu1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ca1', '32.hk1.ev1'], 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '4.cg1.a1', '4.de1.a1', '4.eb1.a1', '4.ee1.a1', '4.ey1.a1', '4.fy1.a1'], 'contains': ['16.o1.a1', '16.z1.a1', '16.bb1.a1', '16.du1.a1'], 'core': '8.fh1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1461, 6800, 9132, 3950, 1462, 6798, 9124, 3959], 'generators': [21, 86, 32], 'label': '256.30836.8.fh1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fh1.a1', 'normal_contained_in': ['4.cg1.a1', '4.be1.a1', '4.de1.a1', '4.eb1.a1', '4.ee1.a1', '4.ey1.a1', '4.fy1.a1'], 'normal_contains': ['16.o1.a1', '16.z1.a1', '16.bb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fh1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879111
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fi1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.i1', '32.hk1.y1', '32.hk1.q1', '32.hk1.j1', '32.hk1.b1', '32.hk1.r1', '32.hk1.z1', '32.hk1.dc1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.es1', '32.hk1.ek1', '32.hk1.by1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.bz1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cf1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cv1', '32.hk1.bg1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cm1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.dn1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dm1', '32.hk1.bq1', '32.hk1.de1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.c1', '32.hk1.m1', '32.hk1.e1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dw1', '32.hk1.do1', '32.hk1.dh1', '32.hk1.bt1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.bm1', '32.hk1.ck1', '32.hk1.ct1', '32.hk1.db1', '32.hk1.cl1', '32.hk1.bn1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ef1', '32.hk1.cb1', '32.hk1.en1', '32.hk1.ev1', '32.hk1.ca1', '32.hk1.ee1', '32.hk1.eu1', '32.hk1.em1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.p1', '32.hk1.h1', '32.hk1.be1', '32.hk1.w1', '32.hk1.g1', '32.hk1.o1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bi1.a1', '4.ch1.a1', '4.dg1.a1', '4.dy1.a1', '4.en1.a1', '4.ew1.a1', '4.fn1.a1'], 'contains': ['16.p1.a1', '16.q1.a1', '16.bd1.a1'], 'core': '8.fi1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4830, 563, 8234, 3613, 4833, 563, 8227, 3621], 'generators': [71, 80], 'label': '256.30836.8.fi1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fi1.a1', 'normal_contained_in': ['4.ch1.a1', '4.bi1.a1', '4.dg1.a1', '4.dy1.a1', '4.en1.a1', '4.ew1.a1', '4.fn1.a1'], 'normal_contains': ['16.p1.a1', '16.bd1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fi1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fi1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879112
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fj1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.r1', '32.hk1.q1', '32.hk1.j1', '32.hk1.i1', '32.hk1.y1', '32.hk1.z1', '32.hk1.bx1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.de1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.es1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.l1', '32.hk1.s1', '32.hk1.t1', '32.hk1.d1', '32.hk1.c1', '32.hk1.e1', '32.hk1.f1', '32.hk1.v1', '32.hk1.u1', '32.hk1.n1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.bd1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.dr1', '32.hk1.dq1', '32.hk1.bu1', '32.hk1.bv1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.di1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cj1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.cz1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cq1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.ew1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.eg1', '32.hk1.ep1', '32.hk1.eo1', '32.hk1.cc1', '32.hk1.cd1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bi1.a1', '4.bx1.a1', '4.dd1.a1', '4.ea1.a1', '4.ej1.a1', '4.fi1.a1', '4.fq1.a1'], 'contains': ['16.p1.a1', '16.v1.a1', '16.y1.a1'], 'core': '8.fj1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2791, 1198, 5786, 2150, 2792, 1197, 5780, 2155], 'generators': [69, 82], 'label': '256.30836.8.fj1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fj1.a1', 'normal_contained_in': ['4.bx1.a1', '4.bi1.a1', '4.dd1.a1', '4.ea1.a1', '4.ej1.a1', '4.fi1.a1', '4.fq1.a1'], 'normal_contains': ['16.p1.a1', '16.y1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fj1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879113
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fk1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.r1', '32.hk1.i1', '32.hk1.j1', '32.hk1.q1', '32.hk1.y1', '32.hk1.b1', '32.hk1.bb1', '32.hk1.c1', '32.hk1.k1', '32.hk1.t1', '32.hk1.s1', '32.hk1.l1', '32.hk1.d1', '32.hk1.ba1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.dc1', '32.hk1.dl1', '32.hk1.dt1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.ds1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.bj1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.bi1', '32.hk1.cg1', '32.hk1.cp1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.by1', '32.hk1.et1', '32.hk1.bx1', '32.hk1.eq1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.ej1', '32.hk1.er1', '32.hk1.bw1', '32.hk1.f1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.n1', '32.hk1.m1', '32.hk1.v1', '32.hk1.bd1', '32.hk1.e1', '32.hk1.be1', '32.hk1.h1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.dq1', '32.hk1.dj1', '32.hk1.bv1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.bu1', '32.hk1.di1', '32.hk1.dr1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.ci1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.cy1', '32.hk1.cq1', '32.hk1.cj1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ex1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ep1', '32.hk1.eo1', '32.hk1.eh1', '32.hk1.cd1', '32.hk1.ew1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.eu1', '32.hk1.cb1'], 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '4.ch1.a1', '4.db1.a1', '4.ds1.a1', '4.es1.a1', '4.fi1.a1', '4.fr1.a1'], 'contains': ['16.p1.a1', '16.w1.a1', '16.x1.a1', '16.gy1.a1'], 'core': '8.fk1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5972, 2121, 9045, 6498, 5976, 2120, 9037, 6512], 'generators': [81, 70, 128], 'label': '256.30836.8.fk1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fk1.a1', 'normal_contained_in': ['4.ch1.a1', '4.w1.a1', '4.db1.a1', '4.ds1.a1', '4.es1.a1', '4.fi1.a1', '4.fr1.a1'], 'normal_contains': ['16.p1.a1', '16.w1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fk1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fk1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879114
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fl1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.r1', '32.hk1.q1', '32.hk1.j1', '32.hk1.i1', '32.hk1.y1', '32.hk1.z1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.es1', '32.hk1.et1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.f1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.h1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bh1.a1', '4.ci1.a1', '4.cv1.a1', '4.dw1.a1', '4.eo1.a1', '4.ew1.a1', '4.fx1.a1'], 'contains': ['16.q1.a1', '16.r1.a1', '16.s1.a1', '16.cm1.a1'], 'core': '8.fl1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6603, 806, 5089, 4692, 6606, 806, 5084, 4703], 'generators': [68, 80, 136], 'label': '256.30836.8.fl1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fl1.a1', 'normal_contained_in': ['4.ci1.a1', '4.bh1.a1', '4.cv1.a1', '4.dw1.a1', '4.eo1.a1', '4.ew1.a1', '4.fx1.a1'], 'normal_contains': ['16.s1.a1', '16.q1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fl1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fl1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879280
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.br1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.gc1.a1', '8.gd1.a1'], 'contains': ['32.b1.a1', '32.s1.a1', '32.bd1.a1', '32.ej1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2496, -1, 5743, -1, 2498, -1, 5738, -1], 'generators': [83, 4, 128], 'label': '256.30836.16.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.y1.a1', 'old_label': '16.br1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.br1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879115
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.p1.a1', '8.q1.a1', '8.bd1.a1', '8.bq1.a1', '8.fz1.a1', '8.fz1.b1', '8.gf1.a1', '8.gf1.b1', '8.gl1.a1', '8.gl1.b1', '8.gl1.c1', '8.gl1.d1', '8.go1.a1', '8.go1.b1', '8.gu1.a1', '8.gu1.b1', '8.ha1.a1', '8.ha1.b1', '8.hg1.a1', '8.hg1.b1', '8.hg1.c1', '8.hg1.d1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9707, 8126, 2970, 8057, 9712, 8122, 2981, 8075], 'generators': [1, 2, 4, 32, 136, 128], 'label': '256.30836.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.p1.a1', '8.q1.a1', '8.b1.a1', '8.c1.a1', '8.bd1.a1', '8.bq1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879116
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fm1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.c1', '32.hk1.s1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.w1', '32.hk1.g1', '32.hk1.h1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.p1', '32.hk1.o1', '32.hk1.be1', '32.hk1.cq1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.cj1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.do1', '32.hk1.bs1', '32.hk1.bt1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.dh1', '32.hk1.dg1', '32.hk1.dw1', '32.hk1.eo1', '32.hk1.cc1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.cs1', '32.hk1.bm1', '32.hk1.bn1', '32.hk1.ct1', '32.hk1.db1', '32.hk1.cl1', '32.hk1.ck1', '32.hk1.da1', '32.hk1.u1', '32.hk1.e1', '32.hk1.f1', '32.hk1.v1', '32.hk1.bd1', '32.hk1.n1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.em1', '32.hk1.ca1', '32.hk1.cb1', '32.hk1.en1', '32.hk1.ev1', '32.hk1.ef1', '32.hk1.ee1', '32.hk1.eu1', '32.hk1.dq1', '32.hk1.bu1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.di1', '32.hk1.dy1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bi1.a1', '4.ci1.a1', '4.dc1.a1', '4.eb1.a1', '4.eh1.a1', '4.ev1.a1', '4.fs1.a1'], 'contains': ['16.q1.a1', '16.y1.a1', '16.z1.a1'], 'core': '8.fm1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3883, 752, 5496, 5988, 3885, 752, 5492, 6000], 'generators': [69, 80], 'label': '256.30836.8.fm1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fm1.a1', 'normal_contained_in': ['4.ci1.a1', '4.bi1.a1', '4.dc1.a1', '4.eb1.a1', '4.eh1.a1', '4.ev1.a1', '4.fs1.a1'], 'normal_contains': ['16.y1.a1', '16.z1.a1', '16.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fm1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879117
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fn1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.c1', '32.hk1.s1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1'], 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '4.cj1.a1', '4.cx1.a1', '4.dw1.a1', '4.eg1.a1', '4.ff1.a1', '4.fy1.a1'], 'contains': ['16.r1.a1', '16.t1.a1', '16.bb1.a1', '16.fr1.a1'], 'core': '8.fn1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1233, 8911, 7303, 2347, 1234, 8908, 7297, 2352], 'generators': [18, 68, 128], 'label': '256.30836.8.fn1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fn1.a1', 'normal_contained_in': ['4.cj1.a1', '4.ba1.a1', '4.cx1.a1', '4.dw1.a1', '4.eg1.a1', '4.ff1.a1', '4.fy1.a1'], 'normal_contains': ['16.bb1.a1', '16.r1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fn1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879118
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fo1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.r1', '32.hk1.i1', '32.hk1.j1', '32.hk1.q1', '32.hk1.y1', '32.hk1.b1', '32.hk1.c1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.k1', '32.hk1.l1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.br1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.by1', '32.hk1.et1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.bx1', '32.hk1.be1', '32.hk1.h1', '32.hk1.p1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.n1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.cy1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.eu1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.ex1'], 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '4.ci1.a1', '4.cw1.a1', '4.dx1.a1', '4.el1.a1', '4.fh1.a1', '4.fy1.a1'], 'contains': ['16.r1.a1', '16.x1.a1', '16.z1.a1', '16.gz1.a1'], 'core': '8.fo1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4203, 3894, 7949, 7513, 4205, 3893, 7942, 7528], 'generators': [81, 68, 128], 'label': '256.30836.8.fo1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fo1.a1', 'normal_contained_in': ['4.ci1.a1', '4.w1.a1', '4.cw1.a1', '4.dx1.a1', '4.el1.a1', '4.fh1.a1', '4.fy1.a1'], 'normal_contains': ['16.z1.a1', '16.r1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fo1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fo1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879119
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fp1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.co1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bo1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.cq1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.cj1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.eo1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.bd1', '32.hk1.n1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.e1', '32.hk1.f1', '32.hk1.v1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.di1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dq1', '32.hk1.bu1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bf1.a1', '4.cj1.a1', '4.cr1.a1', '4.dx1.a1', '4.ep1.a1', '4.fb1.a1', '4.fx1.a1'], 'contains': ['16.r1.a1', '16.ba1.a1', '16.be1.a1', '16.fs1.a1'], 'core': '8.fp1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [878, 4140, 6641, 6973, 879, 4139, 6635, 6988], 'generators': [19, 68, 128], 'label': '256.30836.8.fp1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fp1.a1', 'normal_contained_in': ['4.cj1.a1', '4.bf1.a1', '4.cr1.a1', '4.dx1.a1', '4.ep1.a1', '4.fb1.a1', '4.fx1.a1'], 'normal_contains': ['16.ba1.a1', '16.be1.a1', '16.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fp1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879120
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fq1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.r1', '32.hk1.q1', '32.hk1.j1', '32.hk1.i1', '32.hk1.y1', '32.hk1.z1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.es1', '32.hk1.et1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.f1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.h1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bh1.a1', '4.by1.a1', '4.cy1.a1', '4.dt1.a1', '4.eq1.a1', '4.fi1.a1', '4.fv1.a1'], 'contains': ['16.s1.a1', '16.v1.a1', '16.w1.a1'], 'core': '8.fq1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8260, 904, 6416, 9497, 8264, 904, 6410, 9517], 'generators': [82, 20], 'label': '256.30836.8.fq1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fq1.a1', 'normal_contained_in': ['4.by1.a1', '4.bh1.a1', '4.cy1.a1', '4.dt1.a1', '4.eq1.a1', '4.fi1.a1', '4.fv1.a1'], 'normal_contains': ['16.s1.a1', '16.w1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fq1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879121
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fr1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.y1', '32.hk1.b1', '32.hk1.j1', '32.hk1.q1', '32.hk1.r1', '32.hk1.i1', '32.hk1.c1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.l1', '32.hk1.s1', '32.hk1.t1', '32.hk1.k1', '32.hk1.by1', '32.hk1.et1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.dc1', '32.hk1.be1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.eu1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.cy1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dq1'], 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '4.ci1.a1', '4.cz1.a1', '4.ec1.a1', '4.ei1.a1', '4.fi1.a1', '4.ft1.a1'], 'contains': ['16.s1.a1', '16.x1.a1', '16.y1.a1'], 'core': '8.fr1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4498, 2836, 6178, 3568, 4501, 2835, 6173, 3576], 'generators': [81, 20], 'label': '256.30836.8.fr1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fr1.a1', 'normal_contained_in': ['4.ci1.a1', '4.v1.a1', '4.cz1.a1', '4.ec1.a1', '4.ei1.a1', '4.fi1.a1', '4.ft1.a1'], 'normal_contains': ['16.y1.a1', '16.s1.a1', '16.x1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fr1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fr1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879159
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.i1.a1', '8.j1.a1', '8.v1.a1', '8.y1.a1', '8.cu1.a1', '8.cv1.a1', '8.hi1.a1', '8.hi1.b1', '8.hi1.c1', '8.hi1.d1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8811, 6318, 5082, 7595, 8815, 6315, 5077, 7612], 'generators': [1, 2, 20, 128], 'label': '256.30836.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.v1.a1', '8.y1.a1', '8.j1.a1', '8.i1.a1', '8.cv1.a1', '8.cu1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879122
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fs1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.bi1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.de1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.c1', '32.hk1.s1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.dc1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.bk1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cz1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.cc1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ew1', '32.hk1.eg1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.e1', '32.hk1.u1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.bd1', '32.hk1.bc1', '32.hk1.m1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.dz1', '32.hk1.dy1', '32.hk1.di1'], 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '4.ck1.a1', '4.da1.a1', '4.dt1.a1', '4.es1.a1', '4.fg1.a1', '4.fm1.a1'], 'contains': ['16.t1.a1', '16.u1.a1', '16.w1.a1'], 'core': '8.fs1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5384, 9390, 7869, 6798, 5387, 9386, 7862, 6812], 'generators': [18, 84], 'label': '256.30836.8.fs1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fs1.a1', 'normal_contained_in': ['4.ck1.a1', '4.ba1.a1', '4.da1.a1', '4.dt1.a1', '4.es1.a1', '4.fg1.a1', '4.fm1.a1'], 'normal_contains': ['16.w1.a1', '16.u1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fs1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fs1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879123
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.ft1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.b1', '32.hk1.r1', '32.hk1.q1', '32.hk1.j1', '32.hk1.i1', '32.hk1.y1', '32.hk1.z1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.eb1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.dn1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.co1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cm1', '32.hk1.cf1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.dd1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.ec1', '32.hk1.es1', '32.hk1.et1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.s1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.e1', '32.hk1.f1', '32.hk1.v1', '32.hk1.u1', '32.hk1.n1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.bd1', '32.hk1.ca1', '32.hk1.cb1', '32.hk1.en1', '32.hk1.em1', '32.hk1.ef1', '32.hk1.ee1', '32.hk1.eu1', '32.hk1.ev1', '32.hk1.bu1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dq1', '32.hk1.dj1', '32.hk1.di1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.bm1', '32.hk1.bn1', '32.hk1.ct1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.ck1', '32.hk1.da1', '32.hk1.db1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cq1', '32.hk1.cj1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.cz1', '32.hk1.bs1', '32.hk1.bt1', '32.hk1.dp1', '32.hk1.do1', '32.hk1.dh1', '32.hk1.dg1', '32.hk1.dw1', '32.hk1.dx1', '32.hk1.cc1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.eo1', '32.hk1.eh1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.ex1', '32.hk1.g1', '32.hk1.h1', '32.hk1.x1', '32.hk1.w1', '32.hk1.p1', '32.hk1.o1', '32.hk1.be1', '32.hk1.bf1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '4.cj1.a1', '4.cu1.a1', '4.ec1.a1', '4.ej1.a1', '4.fg1.a1', '4.fs1.a1'], 'contains': ['16.t1.a1', '16.y1.a1', '16.be1.a1', '16.cn1.a1', '16.ft1.a1', '16.ha1.a1'], 'core': '8.ft1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [378, 9120, 5610, 3143, 378, 9116, 5605, 3150], 'generators': [69, 18, 136, 128], 'label': '256.30836.8.ft1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.ft1.a1', 'normal_contained_in': ['4.cj1.a1', '4.bb1.a1', '4.cu1.a1', '4.ec1.a1', '4.ej1.a1', '4.fg1.a1', '4.fs1.a1'], 'normal_contains': ['16.y1.a1', '16.be1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.ft1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.ft1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879124
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fu1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.i1', '32.hk1.r1', '32.hk1.z1', '32.hk1.j1', '32.hk1.b1', '32.hk1.y1', '32.hk1.q1', '32.hk1.dc1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.dn1', '32.hk1.dv1', '32.hk1.bq1', '32.hk1.de1', '32.hk1.du1', '32.hk1.dm1', '32.hk1.df1', '32.hk1.br1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.k1', '32.hk1.c1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.l1', '32.hk1.cf1', '32.hk1.bh1', '32.hk1.cu1', '32.hk1.cm1', '32.hk1.bg1', '32.hk1.ce1', '32.hk1.cn1', '32.hk1.cv1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.ea1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.es1', '32.hk1.ek1', '32.hk1.ed1', '32.hk1.bz1', '32.hk1.el1', '32.hk1.et1', '32.hk1.by1', '32.hk1.ec1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.bi1', '32.hk1.m1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.f1', '32.hk1.n1', '32.hk1.u1', '32.hk1.bc1', '32.hk1.bs1', '32.hk1.dg1', '32.hk1.dp1', '32.hk1.dx1', '32.hk1.dh1', '32.hk1.bt1', '32.hk1.dw1', '32.hk1.do1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.bu1', '32.hk1.dq1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.dj1', '32.hk1.x1', '32.hk1.bf1', '32.hk1.g1', '32.hk1.o1', '32.hk1.be1', '32.hk1.w1', '32.hk1.p1', '32.hk1.h1', '32.hk1.bl1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.cy1', '32.hk1.ci1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.ef1', '32.hk1.cb1', '32.hk1.eu1', '32.hk1.em1', '32.hk1.ca1', '32.hk1.ee1', '32.hk1.en1', '32.hk1.ev1', '32.hk1.eo1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.eh1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.cc1', '32.hk1.da1', '32.hk1.cs1', '32.hk1.cl1', '32.hk1.bn1', '32.hk1.ct1', '32.hk1.db1', '32.hk1.bm1', '32.hk1.ck1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '4.ck1.a1', '4.df1.a1', '4.dq1.a1', '4.en1.a1', '4.ff1.a1', '4.fp1.a1'], 'contains': ['16.t1.a1', '16.bc1.a1', '16.bd1.a1', '16.hb1.a1'], 'core': '8.fu1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5231, 9444, 7893, 2595, 5234, 9441, 7886, 2601], 'generators': [85, 18, 128], 'label': '256.30836.8.fu1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fu1.a1', 'normal_contained_in': ['4.ck1.a1', '4.bb1.a1', '4.df1.a1', '4.dq1.a1', '4.en1.a1', '4.ff1.a1', '4.fp1.a1'], 'normal_contains': ['16.bc1.a1', '16.bd1.a1', '16.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fu1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879125
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fv1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.co1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bo1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.cq1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.cj1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.eo1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.bd1', '32.hk1.n1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.e1', '32.hk1.f1', '32.hk1.v1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.di1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dq1', '32.hk1.bu1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bg1.a1', '4.ck1.a1', '4.dg1.a1', '4.dz1.a1', '4.em1.a1', '4.fb1.a1', '4.fj1.a1'], 'contains': ['16.u1.a1', '16.ba1.a1', '16.bd1.a1'], 'core': '8.fv1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3585, 4085, 8861, 6107, 3587, 4084, 8853, 6120], 'generators': [19, 84], 'label': '256.30836.8.fv1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fv1.a1', 'normal_contained_in': ['4.ck1.a1', '4.bg1.a1', '4.dg1.a1', '4.dz1.a1', '4.em1.a1', '4.fb1.a1', '4.fj1.a1'], 'normal_contains': ['16.ba1.a1', '16.u1.a1', '16.bd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fv1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fv1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879126
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.k1.a1', '8.r1.a1', '8.w1.a1', '8.cp1.a1', '8.cy1.a1', '8.hh1.a1', '8.hh1.b1', '8.hh1.c1', '8.hh1.d1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8211, 2684, 4870, 9779, 8215, 2684, 4865, 9800], 'generators': [1, 2, 80, 128], 'label': '256.30836.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.r1.a1', '8.w1.a1', '8.d1.a1', '8.k1.a1', '8.cp1.a1', '8.cy1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879127
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fw1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.z1', '32.hk1.y1', '32.hk1.b1', '32.hk1.j1', '32.hk1.q1', '32.hk1.r1', '32.hk1.i1', '32.hk1.c1', '32.hk1.bb1', '32.hk1.ba1', '32.hk1.d1', '32.hk1.l1', '32.hk1.s1', '32.hk1.t1', '32.hk1.k1', '32.hk1.by1', '32.hk1.et1', '32.hk1.es1', '32.hk1.bz1', '32.hk1.ed1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.ec1', '32.hk1.bw1', '32.hk1.er1', '32.hk1.eq1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.bg1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.bh1', '32.hk1.cf1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.ce1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cw1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.cg1', '32.hk1.bq1', '32.hk1.dv1', '32.hk1.du1', '32.hk1.br1', '32.hk1.df1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.de1', '32.hk1.bo1', '32.hk1.dt1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.dc1', '32.hk1.be1', '32.hk1.h1', '32.hk1.g1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.o1', '32.hk1.p1', '32.hk1.w1', '32.hk1.bc1', '32.hk1.f1', '32.hk1.e1', '32.hk1.bd1', '32.hk1.v1', '32.hk1.m1', '32.hk1.n1', '32.hk1.u1', '32.hk1.eu1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.em1', '32.hk1.ew1', '32.hk1.cd1', '32.hk1.cc1', '32.hk1.ex1', '32.hk1.ep1', '32.hk1.eg1', '32.hk1.eh1', '32.hk1.eo1', '32.hk1.da1', '32.hk1.bn1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.cs1', '32.hk1.cy1', '32.hk1.bl1', '32.hk1.bk1', '32.hk1.cz1', '32.hk1.cr1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.cq1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.do1', '32.hk1.dy1', '32.hk1.bv1', '32.hk1.bu1', '32.hk1.dz1', '32.hk1.dr1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.dq1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bi1.a1', '4.by1.a1', '4.de1.a1', '4.dz1.a1', '4.ek1.a1', '4.fh1.a1', '4.fp1.a1'], 'contains': ['16.v1.a1', '16.z1.a1', '16.bd1.a1'], 'core': '8.fw1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5421, 3452, 7790, 8437, 5424, 3451, 7782, 8455], 'generators': [21, 82], 'label': '256.30836.8.fw1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fw1.a1', 'normal_contained_in': ['4.by1.a1', '4.bi1.a1', '4.de1.a1', '4.dz1.a1', '4.ek1.a1', '4.fh1.a1', '4.fp1.a1'], 'normal_contains': ['16.z1.a1', '16.bd1.a1', '16.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fw1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fw1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879128
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fx1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.i1', '32.hk1.y1', '32.hk1.q1', '32.hk1.j1', '32.hk1.b1', '32.hk1.r1', '32.hk1.z1', '32.hk1.dc1', '32.hk1.bo1', '32.hk1.dk1', '32.hk1.ds1', '32.hk1.bp1', '32.hk1.dd1', '32.hk1.dt1', '32.hk1.dl1', '32.hk1.es1', '32.hk1.ek1', '32.hk1.by1', '32.hk1.ec1', '32.hk1.el1', '32.hk1.et1', '32.hk1.ed1', '32.hk1.bz1', '32.hk1.co1', '32.hk1.cw1', '32.hk1.cg1', '32.hk1.bi1', '32.hk1.cx1', '32.hk1.cp1', '32.hk1.bj1', '32.hk1.ch1', '32.hk1.cf1', '32.hk1.bh1', '32.hk1.cn1', '32.hk1.cv1', '32.hk1.bg1', '32.hk1.ce1', '32.hk1.cu1', '32.hk1.cm1', '32.hk1.bx1', '32.hk1.eb1', '32.hk1.er1', '32.hk1.ej1', '32.hk1.ea1', '32.hk1.bw1', '32.hk1.ei1', '32.hk1.eq1', '32.hk1.dn1', '32.hk1.dv1', '32.hk1.df1', '32.hk1.br1', '32.hk1.du1', '32.hk1.dm1', '32.hk1.bq1', '32.hk1.de1', '32.hk1.bb1', '32.hk1.t1', '32.hk1.d1', '32.hk1.l1', '32.hk1.s1', '32.hk1.ba1', '32.hk1.k1', '32.hk1.c1', '32.hk1.dg1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.bt1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.dp1', '32.hk1.e1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.n1', '32.hk1.f1', '32.hk1.v1', '32.hk1.bd1', '32.hk1.cs1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.db1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.cl1', '32.hk1.ew1', '32.hk1.eo1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ep1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.cd1', '32.hk1.cb1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.ee1', '32.hk1.ca1', '32.hk1.em1', '32.hk1.eu1', '32.hk1.cj1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.bk1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.cq1', '32.hk1.bf1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.w1', '32.hk1.be1', '32.hk1.o1', '32.hk1.g1', '32.hk1.dr1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.bv1', '32.hk1.dy1', '32.hk1.dq1', '32.hk1.bu1', '32.hk1.di1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bf1.a1', '4.ck1.a1', '4.db1.a1', '4.dn1.a1', '4.er1.a1', '4.fc1.a1', '4.fv1.a1'], 'contains': ['16.w1.a1', '16.ba1.a1', '16.bc1.a1', '16.ij1.a1'], 'core': '8.fx1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7391, 2375, 7921, 9552, 7395, 2374, 7914, 9573], 'generators': [85, 70, 128], 'label': '256.30836.8.fx1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fx1.a1', 'normal_contained_in': ['4.ck1.a1', '4.bf1.a1', '4.db1.a1', '4.dn1.a1', '4.er1.a1', '4.fc1.a1', '4.fv1.a1'], 'normal_contains': ['16.bc1.a1', '16.w1.a1', '16.ba1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fx1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fx1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879160
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.bf1.d1', '16.dv1.b1', '16.dw1.b1', '16.dx1.a1', '16.dy1.b1', '16.ed1.a1', '16.ee1.b1', '16.en1.f1', '16.en1.h1', '16.en1.n1', '16.en1.p1', '16.jf1.f1', '16.jf1.h1', '16.jf1.n1', '16.jf1.p1', '16.jg1.g1', '16.jg1.h1', '16.jg1.o1', '16.jg1.p1'], 'core': '16.bf1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [9894, -1, 3053, -1, 9898, -1, 3047, -1], 'generators': [33, 34, 4, 128, 136], 'label': '256.30836.8.gl1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.gl1.d1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gl1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879129
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '8.fy1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': ['32.hk1.a1', '32.hk1.q1', '32.hk1.r1', '32.hk1.b1', '32.hk1.j1', '32.hk1.z1', '32.hk1.y1', '32.hk1.i1', '32.hk1.co1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cp1', '32.hk1.cx1', '32.hk1.ch1', '32.hk1.cg1', '32.hk1.cw1', '32.hk1.dn1', '32.hk1.br1', '32.hk1.bq1', '32.hk1.dm1', '32.hk1.du1', '32.hk1.de1', '32.hk1.df1', '32.hk1.dv1', '32.hk1.bx1', '32.hk1.ej1', '32.hk1.ei1', '32.hk1.bw1', '32.hk1.ea1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eb1', '32.hk1.cf1', '32.hk1.cv1', '32.hk1.cu1', '32.hk1.ce1', '32.hk1.bg1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.bh1', '32.hk1.bb1', '32.hk1.l1', '32.hk1.k1', '32.hk1.ba1', '32.hk1.s1', '32.hk1.c1', '32.hk1.d1', '32.hk1.t1', '32.hk1.es1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.et1', '32.hk1.el1', '32.hk1.bz1', '32.hk1.by1', '32.hk1.ek1', '32.hk1.dc1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dd1', '32.hk1.bp1', '32.hk1.dl1', '32.hk1.dk1', '32.hk1.bo1', '32.hk1.cq1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.cr1', '32.hk1.cz1', '32.hk1.cj1', '32.hk1.ci1', '32.hk1.cy1', '32.hk1.g1', '32.hk1.w1', '32.hk1.x1', '32.hk1.h1', '32.hk1.p1', '32.hk1.bf1', '32.hk1.be1', '32.hk1.o1', '32.hk1.cd1', '32.hk1.ep1', '32.hk1.eo1', '32.hk1.cc1', '32.hk1.eg1', '32.hk1.ew1', '32.hk1.ex1', '32.hk1.eh1', '32.hk1.dp1', '32.hk1.bt1', '32.hk1.bs1', '32.hk1.do1', '32.hk1.dw1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.dx1', '32.hk1.bd1', '32.hk1.n1', '32.hk1.m1', '32.hk1.bc1', '32.hk1.u1', '32.hk1.e1', '32.hk1.f1', '32.hk1.v1', '32.hk1.cl1', '32.hk1.db1', '32.hk1.da1', '32.hk1.ck1', '32.hk1.bm1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.bn1', '32.hk1.di1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.dj1', '32.hk1.bv1', '32.hk1.dr1', '32.hk1.dq1', '32.hk1.bu1', '32.hk1.eu1', '32.hk1.ee1', '32.hk1.ef1', '32.hk1.ev1', '32.hk1.en1', '32.hk1.cb1', '32.hk1.ca1', '32.hk1.em1'], 'conjugacy_class_count': 1, 'contained_in': ['4.bg1.a1', '4.cj1.a1', '4.dd1.a1', '4.eb1.a1', '4.ed1.a1', '4.fc1.a1', '4.ft1.a1'], 'contains': ['16.y1.a1', '16.ba1.a1', '16.bb1.a1', '16.fu1.a1'], 'core': '8.fy1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1020, 2955, 7109, 3513, 1021, 2954, 7103, 3521], 'generators': [69, 86, 128], 'label': '256.30836.8.fy1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.fy1.a1', 'normal_contained_in': ['4.cj1.a1', '4.bg1.a1', '4.dd1.a1', '4.eb1.a1', '4.ed1.a1', '4.fc1.a1', '4.ft1.a1'], 'normal_contains': ['16.y1.a1', '16.ba1.a1', '16.bb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.fy1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.fy1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879130
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.fz1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.bh1.a1', '16.bi1.a1', '16.bj1.a1', '16.bm1.a1', '16.bn1.a1', '16.bq1.a1', '16.bx1.a1', '16.en1.a1', '16.en1.b1', '16.en1.e1', '16.en1.f1', '16.en1.i1', '16.en1.j1', '16.en1.m1', '16.en1.n1', '16.hc1.a1', '16.hc1.a2', '16.hc1.c1', '16.hc1.c2', '16.hc1.e1', '16.hc1.e2', '16.hc1.g1', '16.hc1.g2', '16.jd1.a1', '16.jd1.b1', '16.jd1.e1', '16.jd1.f1', '16.jd1.i1', '16.jd1.j1', '16.jd1.m1', '16.jd1.n1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9840, -1, 1826, -1, 9845, -1, 1825, -1], 'generators': [1, 2, 4, 128, 32], 'label': '256.30836.8.fz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.fz1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.fz1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879131
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.fz1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.bh1.a1', '16.bi1.b1', '16.bj1.a1', '16.bm1.b1', '16.bn1.a1', '16.bq1.b1', '16.bx1.a1', '16.en1.c1', '16.en1.d1', '16.en1.g1', '16.en1.h1', '16.en1.k1', '16.en1.l1', '16.en1.o1', '16.en1.p1', '16.hc1.b1', '16.hc1.b2', '16.hc1.d1', '16.hc1.d2', '16.hc1.f1', '16.hc1.f2', '16.hc1.h1', '16.hc1.h2', '16.jd1.c1', '16.jd1.d1', '16.jd1.g1', '16.jd1.h1', '16.jd1.k1', '16.jd1.l1', '16.jd1.o1', '16.jd1.p1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9840, -1, 2885, -1, 9845, -1, 2880, -1], 'generators': [1, 2, 140, 128, 32], 'label': '256.30836.8.fz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.fz1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.fz1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879132
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.ga1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.bi1.a1', '16.bk1.a1', '16.bl1.a1', '16.bt1.a1', '16.bv1.a1', '16.by1.a1', '16.bz1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9286, -1, 4207, -1, 9291, -1, 4203, -1], 'generators': [2, 4, 16], 'label': '256.30836.8.ga1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.ga1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ga1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879133
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.ga1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.bi1.b1', '16.bk1.a1', '16.bl1.a1', '16.bt1.b1', '16.bv1.b1', '16.by1.a1', '16.bz1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9286, -1, 4239, -1, 9291, -1, 4235, -1], 'generators': [2, 140, 16], 'label': '256.30836.8.ga1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.ga1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ga1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879134
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1'], 'contains': ['16.bm1.a1', '16.bo1.a1', '16.bp1.a1', '16.bs1.a1', '16.bu1.a1', '16.ca1.a1', '16.cb1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7155, -1, 4309, -1, 7159, -1, 4306, -1], 'generators': [1, 4, 64], 'label': '256.30836.8.gb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bk1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bk1.a1', 'old_label': '8.gb1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879135
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1'], 'contains': ['16.bm1.b1', '16.bo1.a1', '16.bp1.a1', '16.bs1.b1', '16.bu1.b1', '16.ca1.a1', '16.cb1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7155, -1, 4342, -1, 7159, -1, 4337, -1], 'generators': [1, 140, 64], 'label': '256.30836.8.gb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bk1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bk1.a1', 'old_label': '8.gb1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gb1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879136
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.cl1.a1'], 'contains': ['16.bq1.a1', '16.br1.a1', '16.bw1.a1', '16.cc1.a1', '16.cd1.a1', '16.ce1.a1', '16.cf1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5287, -1, 4490, -1, 5289, -1, 4486, -1], 'generators': [3, 4, 80], 'label': '256.30836.8.gc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.cl1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cl1.a1', 'old_label': '8.gc1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879137
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.g1.a1', '8.s1.a1', '8.u1.a1', '8.cq1.a1', '8.cs1.a1', '8.gg1.a1', '8.gg1.b1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6076, 7064, 9063, 3909, 6079, 7062, 9055, 3917], 'generators': [1, 2, 64, 32], 'label': '256.30836.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.u1.a1', '8.s1.a1', '8.g1.a1', '8.e1.a1', '8.cq1.a1', '8.cs1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879138
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.cl1.a1'], 'contains': ['16.bq1.b1', '16.br1.b1', '16.bw1.b1', '16.cc1.a1', '16.cd1.a1', '16.ce1.a1', '16.cf1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [5287, -1, 4519, -1, 5289, -1, 4515, -1], 'generators': [3, 140, 80], 'label': '256.30836.8.gc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.cl1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cl1.a1', 'old_label': '8.gc1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gc1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879139
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.cu1.a1'], 'contains': ['16.br1.a1', '16.bu1.a1', '16.bv1.a1', '16.cg1.a1', '16.ch1.a1', '16.cl1.a1', '16.cn1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [418, -1, 4660, -1, 419, -1, 4655, -1], 'generators': [65, 18, 4], 'label': '256.30836.8.gd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.cu1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cu1.a1', 'old_label': '8.gd1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879140
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.cu1.a1'], 'contains': ['16.br1.b1', '16.bu1.b1', '16.bv1.b1', '16.cg1.a1', '16.ch1.a1', '16.cl1.a1', '16.cn1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [418, -1, 4675, -1, 419, -1, 4671, -1], 'generators': [65, 18, 140], 'label': '256.30836.8.gd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.cu1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cu1.a1', 'old_label': '8.gd1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gd1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879141
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.ge1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.cv1.a1'], 'contains': ['16.bs1.a1', '16.bt1.a1', '16.bw1.a1', '16.ci1.a1', '16.cj1.a1', '16.ck1.a1', '16.cm1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7918, -1, 4264, -1, 7922, -1, 4261, -1], 'generators': [4, 16, 64], 'label': '256.30836.8.ge1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.cv1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cv1.a1', 'old_label': '8.ge1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ge1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879142
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.ge1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.cv1.a1'], 'contains': ['16.bs1.b1', '16.bt1.b1', '16.bw1.b1', '16.ci1.a1', '16.cj1.a1', '16.ck1.a1', '16.cm1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7918, -1, 4283, -1, 7922, -1, 4280, -1], 'generators': [140, 16, 64], 'label': '256.30836.8.ge1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.cv1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cv1.a1', 'old_label': '8.ge1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ge1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879144
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.co1.b1', '16.cp1.b1', '16.cq1.b1', '16.cx1.a1', '16.cy1.a1', '16.db1.a1', '16.de1.a1', '16.en1.i1', '16.en1.j1', '16.en1.k1', '16.en1.l1', '16.en1.m1', '16.en1.n1', '16.en1.o1', '16.en1.p1', '16.ik1.e1', '16.ik1.e2', '16.ik1.f1', '16.ik1.f2', '16.ik1.g1', '16.ik1.g2', '16.ik1.h1', '16.ik1.h2', '16.je1.d1', '16.je1.d2', '16.je1.e1', '16.je1.e2', '16.je1.g1', '16.je1.g2', '16.je1.h1', '16.je1.h2'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9787, -1, 2108, -1, 9792, -1, 2052, -1], 'generators': [1, 34, 4, 128, 168], 'label': '256.30836.8.gf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.gf1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gf1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879145
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gg1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.co1.a1', '16.cs1.a1', '16.ct1.a1', '16.cz1.a1', '16.da1.a1', '16.dj1.a1', '16.dk1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6031, -1, 9698, -1, 6033, -1, 9689, -1], 'generators': [1, 2, 64], 'label': '256.30836.8.gg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.gg1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879146
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gg1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.co1.b1', '16.cs1.b1', '16.ct1.b1', '16.cz1.a1', '16.da1.a1', '16.dj1.a1', '16.dk1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6031, -1, 9666, -1, 6033, -1, 9657, -1], 'generators': [1, 34, 64], 'label': '256.30836.8.gg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.gg1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gg1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879147
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1'], 'contains': ['16.cp1.a1', '16.cu1.a1', '16.cv1.a1', '16.dc1.a1', '16.dd1.a1', '16.df1.a1', '16.dg1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [698, -1, 9829, -1, 699, -1, 9820, -1], 'generators': [17, 2, 4], 'label': '256.30836.8.gh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.gh1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879148
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '8.h1.a1', '8.t1.a1', '8.z1.a1', '8.cr1.a1', '8.ct1.a1', '8.gp1.a1', '8.gp1.b1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1429, 9967, 7372, 9589, 1429, 9963, 7366, 9610], 'generators': [1, 2, 16, 128], 'label': '256.30836.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.t1.a1', '8.z1.a1', '8.f1.a1', '8.h1.a1', '8.cr1.a1', '8.ct1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879149
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1'], 'contains': ['16.cp1.b1', '16.cu1.b1', '16.cv1.b1', '16.dc1.a1', '16.dd1.a1', '16.df1.a1', '16.dg1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [698, -1, 9796, -1, 699, -1, 9788, -1], 'generators': [17, 34, 4], 'label': '256.30836.8.gh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '8.gh1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gh1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879150
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1'], 'contains': ['16.cq1.a1', '16.cr1.a1', '16.cw1.a1', '16.dh1.a1', '16.di1.a1', '16.dl1.a1', '16.dm1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2161, -1, 9936, -1, 2162, -1, 9927, -1], 'generators': [81, 2, 84], 'label': '256.30836.8.gi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '8.gi1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879151
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1'], 'contains': ['16.cq1.b1', '16.cr1.b1', '16.cw1.b1', '16.dh1.a1', '16.di1.a1', '16.dl1.a1', '16.dm1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2161, -1, 9906, -1, 2162, -1, 9897, -1], 'generators': [81, 34, 84], 'label': '256.30836.8.gi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '8.gi1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gi1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879152
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1'], 'contains': ['16.cr1.a1', '16.cs1.a1', '16.cu1.a1', '16.dn1.a1', '16.do1.a1', '16.dp1.a1', '16.dq1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [279, -1, 9880, -1, 279, -1, 9871, -1], 'generators': [17, 2, 64], 'label': '256.30836.8.gj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '8.gj1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879153
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1'], 'contains': ['16.cr1.b1', '16.cs1.b1', '16.cu1.b1', '16.dn1.a1', '16.do1.a1', '16.dp1.a1', '16.dq1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [279, -1, 9857, -1, 279, -1, 9848, -1], 'generators': [17, 34, 64], 'label': '256.30836.8.gj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '8.gj1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gj1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879154
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gk1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1'], 'contains': ['16.ct1.a1', '16.cv1.a1', '16.cw1.a1', '16.dr1.a1', '16.ds1.a1', '16.dt1.a1', '16.du1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [758, -1, 9995, -1, 758, -1, 9987, -1], 'generators': [65, 2, 84], 'label': '256.30836.8.gk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '8.gk1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879155
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gk1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1'], 'contains': ['16.ct1.b1', '16.cv1.b1', '16.cw1.b1', '16.dr1.a1', '16.ds1.a1', '16.dt1.a1', '16.du1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [758, -1, 9965, -1, 758, -1, 9957, -1], 'generators': [65, 34, 84], 'label': '256.30836.8.gk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '8.gk1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gk1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879156
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.bf1.a1', '16.dv1.a1', '16.dw1.a1', '16.dx1.a1', '16.dy1.a1', '16.ed1.a1', '16.ee1.a1', '16.en1.a1', '16.en1.c1', '16.en1.i1', '16.en1.k1', '16.jf1.a1', '16.jf1.c1', '16.jf1.i1', '16.jf1.k1', '16.jg1.a1', '16.jg1.b1', '16.jg1.i1', '16.jg1.j1'], 'core': '16.bf1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9894, -1, 3070, -1, 9898, -1, 3064, -1], 'generators': [1, 2, 4, 128, 136], 'label': '256.30836.8.gl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.gl1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879157
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.bf1.b1', '16.dv1.a1', '16.dw1.b1', '16.dx1.b1', '16.dy1.a1', '16.ed1.b1', '16.ee1.b1', '16.en1.b1', '16.en1.d1', '16.en1.j1', '16.en1.l1', '16.jf1.b1', '16.jf1.d1', '16.jf1.j1', '16.jf1.l1', '16.jg1.c1', '16.jg1.d1', '16.jg1.k1', '16.jg1.l1'], 'core': '16.bf1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9894, -1, 2351, -1, 9898, -1, 2349, -1], 'generators': [1, 34, 4, 128, 136], 'label': '256.30836.8.gl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.gl1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gl1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879158
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.bf1.c1', '16.dv1.b1', '16.dw1.a1', '16.dx1.b1', '16.dy1.b1', '16.ed1.b1', '16.ee1.a1', '16.en1.e1', '16.en1.g1', '16.en1.m1', '16.en1.o1', '16.jf1.e1', '16.jf1.g1', '16.jf1.m1', '16.jf1.o1', '16.jg1.e1', '16.jg1.f1', '16.jg1.m1', '16.jg1.n1'], 'core': '16.bf1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9894, -1, 2557, -1, 9898, -1, 2555, -1], 'generators': [33, 2, 4, 128, 136], 'label': '256.30836.8.gl1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.gl1.c1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gl1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879300
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cx1.a1', '8.gc1.a1', '8.gc1.b1'], 'contains': ['32.q1.a1', '32.bb1.a1', '32.bd1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4978, -1, 5576, -1, 4980, -1, 5571, -1], 'generators': [3, 84], 'label': '256.30836.16.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cx1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cl1.a1', 'old_label': '16.cd1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879169
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.go1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.eo1.a1', '16.ep1.a1', '16.eq1.a1', '16.et1.a1', '16.eu1.a1', '16.fb1.a1', '16.fe1.a1', '16.hc1.a1', '16.hc1.a2', '16.hc1.b1', '16.hc1.b2', '16.hc1.e1', '16.hc1.e2', '16.hc1.f1', '16.hc1.f2', '16.ik1.a1', '16.ik1.a2', '16.ik1.b1', '16.ik1.b2', '16.ik1.e1', '16.ik1.e2', '16.ik1.f1', '16.ik1.f2', '16.jf1.a1', '16.jf1.b1', '16.jf1.e1', '16.jf1.f1', '16.jf1.i1', '16.jf1.j1', '16.jf1.m1', '16.jf1.n1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9760, -1, 1736, -1, 9765, -1, 1734, -1], 'generators': [1, 2, 4, 32, 136], 'label': '256.30836.8.go1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.go1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.go1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879170
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.l1.a1', '8.n1.a1', '8.x1.a1', '8.bb1.a1', '8.cw1.a1', '8.cz1.a1', '8.gv1.a1', '8.gv1.b1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7777, 8181, 6751, 9138, 7782, 8179, 6745, 9158], 'generators': [1, 2, 68, 128], 'label': '256.30836.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.x1.a1', '8.bb1.a1', '8.n1.a1', '8.l1.a1', '8.cz1.a1', '8.cw1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879171
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.go1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.eo1.b1', '16.ep1.a1', '16.eq1.a1', '16.et1.b1', '16.eu1.b1', '16.fb1.a1', '16.fe1.a1', '16.hc1.c1', '16.hc1.c2', '16.hc1.d1', '16.hc1.d2', '16.hc1.g1', '16.hc1.g2', '16.hc1.h1', '16.hc1.h2', '16.ik1.c1', '16.ik1.c2', '16.ik1.d1', '16.ik1.d2', '16.ik1.g1', '16.ik1.g2', '16.ik1.h1', '16.ik1.h2', '16.jf1.c1', '16.jf1.d1', '16.jf1.g1', '16.jf1.h1', '16.jf1.k1', '16.jf1.l1', '16.jf1.o1', '16.jf1.p1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9760, -1, 2543, -1, 9765, -1, 2541, -1], 'generators': [129, 2, 4, 32, 136], 'label': '256.30836.8.go1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.go1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.go1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879172
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.eo1.a1', '16.er1.a1', '16.es1.a1', '16.ew1.a1', '16.ez1.a1', '16.fj1.a1', '16.fk1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [109, -1, 7585, -1, 109, -1, 7578, -1], 'generators': [1, 2, 16], 'label': '256.30836.8.gp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.gp1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gp1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879173
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gp1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.eo1.b1', '16.er1.a1', '16.es1.a1', '16.ew1.b1', '16.ez1.b1', '16.fj1.a1', '16.fk1.a1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [109, -1, 7617, -1, 109, -1, 7610, -1], 'generators': [129, 2, 16], 'label': '256.30836.8.gp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.gp1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gp1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879174
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bj1.a1'], 'contains': ['16.et1.a1', '16.ev1.a1', '16.fa1.a1', '16.fc1.a1', '16.fd1.a1', '16.fh1.a1', '16.fi1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [229, -1, 4549, -1, 229, -1, 4545, -1], 'generators': [1, 82, 4], 'label': '256.30836.8.gq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bj1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '8.gq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879175
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gq1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bj1.a1'], 'contains': ['16.et1.b1', '16.ev1.b1', '16.fa1.b1', '16.fc1.a1', '16.fd1.a1', '16.fh1.a1', '16.fi1.a1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [229, -1, 4578, -1, 229, -1, 4574, -1], 'generators': [129, 82, 4], 'label': '256.30836.8.gq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bj1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '8.gq1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gq1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879176
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gr1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bs1.a1'], 'contains': ['16.eu1.a1', '16.ex1.a1', '16.ey1.a1', '16.ff1.a1', '16.fg1.a1', '16.fl1.a1', '16.fm1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [170, -1, 5151, -1, 170, -1, 5146, -1], 'generators': [1, 66, 68], 'label': '256.30836.8.gr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bs1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bs1.a1', 'old_label': '8.gr1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gr1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879177
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gr1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bs1.a1'], 'contains': ['16.eu1.b1', '16.ex1.b1', '16.ey1.b1', '16.ff1.a1', '16.fg1.a1', '16.fl1.a1', '16.fm1.a1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [170, -1, 5182, -1, 170, -1, 5178, -1], 'generators': [129, 66, 68], 'label': '256.30836.8.gr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bs1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bs1.a1', 'old_label': '8.gr1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gr1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879178
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gs1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bw1.a1'], 'contains': ['16.ev1.a1', '16.ew1.a1', '16.ex1.a1', '16.fn1.a1', '16.fo1.a1', '16.fp1.a1', '16.fq1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [56, -1, 9404, -1, 56, -1, 9396, -1], 'generators': [1, 66, 16], 'label': '256.30836.8.gs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bw1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '8.gs1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879179
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gs1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bw1.a1'], 'contains': ['16.ev1.b1', '16.ew1.b1', '16.ex1.b1', '16.fn1.a1', '16.fo1.a1', '16.fp1.a1', '16.fq1.a1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [56, -1, 9427, -1, 56, -1, 9419, -1], 'generators': [129, 66, 16], 'label': '256.30836.8.gs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bw1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '8.gs1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gs1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879180
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gt1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.cj1.a1'], 'contains': ['16.ey1.a1', '16.ez1.a1', '16.fa1.a1', '16.fr1.a1', '16.fs1.a1', '16.ft1.a1', '16.fu1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [15, -1, 5303, -1, 15, -1, 5299, -1], 'generators': [1, 18, 68], 'label': '256.30836.8.gt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.cj1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cj1.a1', 'old_label': '8.gt1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gt1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879181
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.m1.a1', '8.o1.a1', '8.ba1.a1', '8.bc1.a1', '8.cx1.a1', '8.da1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6128, 6255, 7052, 9247, 6131, 6253, 7046, 9267], 'generators': [1, 2, 84], 'label': '256.30836.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.ba1.a1', '8.bc1.a1', '8.o1.a1', '8.m1.a1', '8.da1.a1', '8.cx1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879182
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gt1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.cj1.a1'], 'contains': ['16.ey1.b1', '16.ez1.b1', '16.fa1.b1', '16.fr1.a1', '16.fs1.a1', '16.ft1.a1', '16.fu1.a1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [15, -1, 5322, -1, 15, -1, 5318, -1], 'generators': [129, 18, 68], 'label': '256.30836.8.gt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.cj1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cj1.a1', 'old_label': '8.gt1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gt1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879183
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.fv1.a1', '16.fw1.a1', '16.fx1.a1', '16.ge1.a1', '16.gf1.a1', '16.gi1.a1', '16.gl1.a1', '16.hc1.a1', '16.hc1.a2', '16.hc1.b1', '16.hc1.b2', '16.hc1.c1', '16.hc1.c2', '16.hc1.d1', '16.hc1.d2', '16.je1.a1', '16.je1.a2', '16.je1.b1', '16.je1.b2', '16.je1.d1', '16.je1.d2', '16.je1.g1', '16.je1.g2', '16.jg1.a1', '16.jg1.b1', '16.jg1.c1', '16.jg1.d1', '16.jg1.e1', '16.jg1.f1', '16.jg1.g1', '16.jg1.h1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9813, -1, 1941, -1, 9819, -1, 1939, -1], 'generators': [1, 2, 4, 32, 8], 'label': '256.30836.8.gu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.gu1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gu1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879184
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gu1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.fv1.b1', '16.fw1.b1', '16.fx1.b1', '16.ge1.a1', '16.gf1.a1', '16.gi1.a1', '16.gl1.a1', '16.hc1.e1', '16.hc1.e2', '16.hc1.f1', '16.hc1.f2', '16.hc1.g1', '16.hc1.g2', '16.hc1.h1', '16.hc1.h2', '16.je1.c1', '16.je1.c2', '16.je1.e1', '16.je1.e2', '16.je1.f1', '16.je1.f2', '16.je1.h1', '16.je1.h2', '16.jg1.i1', '16.jg1.j1', '16.jg1.k1', '16.jg1.l1', '16.jg1.m1', '16.jg1.n1', '16.jg1.o1', '16.jg1.p1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9813, -1, 1990, -1, 9819, -1, 1988, -1], 'generators': [1, 130, 4, 32, 8], 'label': '256.30836.8.gu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.gu1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gu1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879185
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gv1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1'], 'contains': ['16.fv1.a1', '16.gb1.a1', '16.gc1.a1', '16.gg1.a1', '16.gh1.a1', '16.gq1.a1', '16.gr1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8492, -1, 7190, -1, 8496, -1, 7184, -1], 'generators': [1, 2, 68], 'label': '256.30836.8.gv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '8.gv1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gv1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879186
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gv1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1'], 'contains': ['16.fv1.b1', '16.gb1.b1', '16.gc1.b1', '16.gg1.a1', '16.gh1.a1', '16.gq1.a1', '16.gr1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8492, -1, 7222, -1, 8496, -1, 7215, -1], 'generators': [1, 130, 68], 'label': '256.30836.8.gv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '8.gv1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gv1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879187
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gw1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.fw1.a1', '16.fy1.a1', '16.gd1.a1', '16.gj1.a1', '16.gk1.a1', '16.gm1.a1', '16.gn1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2421, -1, 5875, -1, 2422, -1, 5870, -1], 'generators': [81, 2, 4], 'label': '256.30836.8.gw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.gw1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879188
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gw1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1'], 'contains': ['16.fw1.b1', '16.fy1.b1', '16.gd1.b1', '16.gj1.a1', '16.gk1.a1', '16.gm1.a1', '16.gn1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2421, -1, 5904, -1, 2422, -1, 5899, -1], 'generators': [81, 130, 4], 'label': '256.30836.8.gw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '8.gw1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gw1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879189
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gx1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1'], 'contains': ['16.fx1.a1', '16.fz1.a1', '16.ga1.a1', '16.go1.a1', '16.gp1.a1', '16.gs1.a1', '16.gt1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3449, -1, 4726, -1, 3450, -1, 4721, -1], 'generators': [5, 2, 16], 'label': '256.30836.8.gx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '8.gx1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gx1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879190
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gx1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1'], 'contains': ['16.fx1.b1', '16.fz1.b1', '16.ga1.b1', '16.go1.a1', '16.gp1.a1', '16.gs1.a1', '16.gt1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3449, -1, 4758, -1, 3450, -1, 4753, -1], 'generators': [5, 130, 16], 'label': '256.30836.8.gx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '8.gx1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gx1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879191
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gy1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1'], 'contains': ['16.fy1.a1', '16.ga1.a1', '16.gb1.a1', '16.gu1.a1', '16.gv1.a1', '16.gy1.a1', '16.gz1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [819, -1, 9730, -1, 819, -1, 9722, -1], 'generators': [81, 2, 68], 'label': '256.30836.8.gy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.w1.a1', 'old_label': '8.gy1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gy1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879192
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '16.a1.a1', 'complements': ['128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.j1.a1', '4.l1.a1', '4.p1.a1', '4.r1.a1', '4.bl1.a1', '4.bn1.a1', '4.br1.a1', '4.bu1.a1', '4.cn1.a1', '4.cp1.a1', '4.dj1.a1', '4.dl1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7420, 7885, 5683, 6950, 7423, 7924, 5679, 6965], 'generators': [1, 2, 4, 16], 'label': '256.30836.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.bl1.a1', '4.bn1.a1', '4.br1.a1', '4.bu1.a1', '4.j1.a1', '4.l1.a1', '4.p1.a1', '4.r1.a1', '4.cn1.a1', '4.cp1.a1', '4.dj1.a1', '4.dl1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879193
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.h1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.h1.a1', '2.i1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.o1.a1', '8.be1.a1', '8.bp1.a1', '8.br1.a1', '8.cb1.a1', '8.gw1.a1', '8.gw1.b1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3822, 7369, 6223, 7686, 3824, 7367, 6218, 7703], 'generators': [81, 2, 4, 128], 'label': '256.30836.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.a1', '2.i1.a1', '2.h1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.a1', '8.o1.a1', '8.be1.a1', '8.bp1.a1', '8.br1.a1', '8.cb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879194
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gy1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1'], 'contains': ['16.fy1.b1', '16.ga1.b1', '16.gb1.b1', '16.gu1.a1', '16.gv1.a1', '16.gy1.a1', '16.gz1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [819, -1, 9764, -1, 819, -1, 9756, -1], 'generators': [81, 130, 68], 'label': '256.30836.8.gy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.w1.a1', 'old_label': '8.gy1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gy1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879195
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gz1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1'], 'contains': ['16.fz1.a1', '16.gc1.a1', '16.gd1.a1', '16.gw1.a1', '16.gx1.a1', '16.ha1.a1', '16.hb1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2053, -1, 5831, -1, 2054, -1, 5826, -1], 'generators': [69, 2, 16], 'label': '256.30836.8.gz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '8.gz1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gz1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879196
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.gz1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1'], 'contains': ['16.fz1.b1', '16.gc1.b1', '16.gd1.b1', '16.gw1.a1', '16.gx1.a1', '16.ha1.a1', '16.hb1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2053, -1, 5850, -1, 2054, -1, 5845, -1], 'generators': [69, 130, 16], 'label': '256.30836.8.gz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '8.gz1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.gz1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879197
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.ha1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.hd1.a1', '16.he1.a1', '16.hf1.a1', '16.hi1.a1', '16.hj1.a1', '16.hm1.a1', '16.hp1.a1', '16.ik1.a1', '16.ik1.a2', '16.ik1.c1', '16.ik1.c2', '16.ik1.e1', '16.ik1.e2', '16.ik1.g1', '16.ik1.g2', '16.jd1.a1', '16.jd1.c1', '16.jd1.e1', '16.jd1.g1', '16.jd1.i1', '16.jd1.k1', '16.jd1.m1', '16.jd1.o1', '16.jg1.a1', '16.jg1.c1', '16.jg1.e1', '16.jg1.g1', '16.jg1.i1', '16.jg1.k1', '16.jg1.m1', '16.jg1.o1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9867, -1, 2906, -1, 9872, -1, 2929, -1], 'generators': [1, 2, 4, 160, 8], 'label': '256.30836.8.ha1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.ha1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ha1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879263
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bg1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.hg1.b1', '8.hh1.b1', '8.hi1.b1'], 'contains': ['32.j1.a1', '32.k1.b1', '32.l1.b1', '32.gb1.b1', '32.gk1.b1', '32.gk1.h1', '32.gt1.b1', '32.gt1.c1'], 'core': '16.bg1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9399, 7181, 4175, 7804, 9404, 7179, 4171, 7821], 'generators': [129, 2, 136, 160], 'label': '256.30836.16.bg1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.bg1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.k1.b1', '32.j1.a1', '32.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.bg1.b1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879198
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.ha1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.hd1.a1', '16.he1.a1', '16.hf1.b1', '16.hi1.b1', '16.hj1.a1', '16.hm1.a1', '16.hp1.b1', '16.ik1.b1', '16.ik1.b2', '16.ik1.d1', '16.ik1.d2', '16.ik1.f1', '16.ik1.f2', '16.ik1.h1', '16.ik1.h2', '16.jd1.b1', '16.jd1.d1', '16.jd1.f1', '16.jd1.h1', '16.jd1.j1', '16.jd1.l1', '16.jd1.n1', '16.jd1.p1', '16.jg1.b1', '16.jg1.d1', '16.jg1.f1', '16.jg1.h1', '16.jg1.j1', '16.jg1.l1', '16.jg1.n1', '16.jg1.p1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9867, -1, 1840, -1, 9872, -1, 1838, -1], 'generators': [129, 2, 4, 160, 8], 'label': '256.30836.8.ha1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.ha1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ha1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879199
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1'], 'contains': ['16.hf1.a1', '16.hg1.a1', '16.hh1.a1', '16.hu1.a1', '16.hv1.a1', '16.ia1.a1', '16.ib1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9435, -1, 4821, -1, 9440, -1, 4817, -1], 'generators': [17, 2, 20], 'label': '256.30836.8.hb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '8.hb1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879200
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hb1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1'], 'contains': ['16.hf1.b1', '16.hg1.a1', '16.hh1.a1', '16.hu1.b1', '16.hv1.b1', '16.ia1.a1', '16.ib1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9435, -1, 4789, -1, 9440, -1, 4785, -1], 'generators': [145, 2, 20], 'label': '256.30836.8.hb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '8.hb1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hb1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879201
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bm1.a1'], 'contains': ['16.hi1.a1', '16.hk1.a1', '16.hl1.a1', '16.hn1.a1', '16.ho1.a1', '16.ht1.a1', '16.hw1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8797, -1, 9376, -1, 8801, -1, 9368, -1], 'generators': [1, 66, 4], 'label': '256.30836.8.hc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bm1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bm1.a1', 'old_label': '8.hc1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879202
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bm1.a1'], 'contains': ['16.hi1.b1', '16.hk1.a1', '16.hl1.a1', '16.hn1.a1', '16.ho1.a1', '16.ht1.b1', '16.hw1.b1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8797, -1, 9344, -1, 8801, -1, 9336, -1], 'generators': [129, 66, 4], 'label': '256.30836.8.hc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bm1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bm1.a1', 'old_label': '8.hc1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hc1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879203
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.dh1.a1'], 'contains': ['16.hp1.a1', '16.hq1.a1', '16.hr1.a1', '16.hs1.a1', '16.hx1.a1', '16.hy1.a1', '16.hz1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7275, -1, 6697, -1, 7278, -1, 6691, -1], 'generators': [5, 6, 80], 'label': '256.30836.8.hd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.dh1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.dh1.a1', 'old_label': '8.hd1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879204
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.h1.a1', '2.j1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.l1.a1', '8.bf1.a1', '8.bh1.a1', '8.bs1.a1', '8.bu1.a1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8367, 7127, 7165, 3629, 8371, 7124, 7159, 3638], 'generators': [2, 4, 64], 'label': '256.30836.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.b1.a1', '2.h1.a1', '2.j1.a1'], 'normal_contains': ['8.b1.a1', '8.e1.a1', '8.l1.a1', '8.bh1.a1', '8.bf1.a1', '8.bu1.a1', '8.bs1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879205
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.dh1.a1'], 'contains': ['16.hp1.b1', '16.hq1.a1', '16.hr1.a1', '16.hs1.b1', '16.hx1.b1', '16.hy1.a1', '16.hz1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7275, -1, 6727, -1, 7278, -1, 6721, -1], 'generators': [133, 6, 80], 'label': '256.30836.8.hd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.dh1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.dh1.a1', 'old_label': '8.hd1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hd1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879206
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.he1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ef1.a1'], 'contains': ['16.hs1.a1', '16.ht1.a1', '16.hu1.a1', '16.ic1.a1', '16.id1.a1', '16.ie1.a1', '16.if1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1687, -1, 9633, -1, 1688, -1, 9625, -1], 'generators': [17, 66, 20], 'label': '256.30836.8.he1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.ef1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ef1.a1', 'old_label': '8.he1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.he1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879207
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.he1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ef1.a1'], 'contains': ['16.hs1.b1', '16.ht1.b1', '16.hu1.b1', '16.ic1.a1', '16.id1.a1', '16.ie1.a1', '16.if1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1687, -1, 9600, -1, 1688, -1, 9591, -1], 'generators': [145, 66, 20], 'label': '256.30836.8.he1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.ef1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ef1.a1', 'old_label': '8.he1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.he1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879208
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.er1.a1'], 'contains': ['16.hv1.a1', '16.hw1.a1', '16.hx1.a1', '16.ig1.a1', '16.ih1.a1', '16.ii1.a1', '16.ij1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9335, -1, 6975, -1, 9340, -1, 6969, -1], 'generators': [5, 70, 80], 'label': '256.30836.8.hf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.er1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.er1.a1', 'old_label': '8.hf1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879209
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.er1.a1'], 'contains': ['16.hv1.b1', '16.hw1.b1', '16.hx1.b1', '16.ig1.a1', '16.ih1.a1', '16.ii1.a1', '16.ij1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9335, -1, 6956, -1, 9340, -1, 6950, -1], 'generators': [133, 70, 80], 'label': '256.30836.8.hf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.er1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.er1.a1', 'old_label': '8.hf1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hf1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879210
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hg1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.bg1.a1', '16.il1.a1', '16.im1.a1', '16.ir1.a1', '16.is1.a1', '16.ix1.a1', '16.iy1.a1', '16.jd1.a1', '16.jd1.b1', '16.jd1.c1', '16.jd1.d1', '16.je1.a1', '16.je1.a2', '16.je1.e1', '16.je1.e2', '16.jf1.a1', '16.jf1.b1', '16.jf1.g1', '16.jf1.h1'], 'core': '16.bg1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9920, -1, 3004, -1, 9925, -1, 2987, -1], 'generators': [1, 2, 4, 160, 136], 'label': '256.30836.8.hg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.hg1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879211
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hg1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.bg1.b1', '16.il1.a1', '16.im1.a1', '16.ir1.b1', '16.is1.b1', '16.ix1.b1', '16.iy1.b1', '16.jd1.e1', '16.jd1.f1', '16.jd1.g1', '16.jd1.h1', '16.je1.b1', '16.je1.b2', '16.je1.h1', '16.je1.h2', '16.jf1.c1', '16.jf1.d1', '16.jf1.e1', '16.jf1.f1'], 'core': '16.bg1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9920, -1, 2142, -1, 9925, -1, 2144, -1], 'generators': [129, 2, 4, 160, 136], 'label': '256.30836.8.hg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.hg1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hg1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879212
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '8.hg1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '64.267', 'aut_weyl_index': 512, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.bg1.c1', '16.il1.b1', '16.im1.b1', '16.ir1.a1', '16.is1.a1', '16.ix1.b1', '16.iy1.b1', '16.jd1.i1', '16.jd1.j1', '16.jd1.k1', '16.jd1.l1', '16.je1.c1', '16.je1.c2', '16.je1.d1', '16.je1.d2', '16.jf1.i1', '16.jf1.j1', '16.jf1.o1', '16.jf1.p1'], 'core': '16.bg1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9920, -1, 2128, -1, 9925, -1, 2130, -1], 'generators': [1, 130, 4, 160, 136], 'label': '256.30836.8.hg1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.hg1.c1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.hg1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879301
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ce1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.db1.a1', '8.gc1.a1', '8.gc1.b1'], 'contains': ['32.r1.a1', '32.s1.a1', '32.bb1.a1', '32.cq1.a1', '32.cq1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4937, -1, 5635, -1, 4940, -1, 5630, -1], 'generators': [83, 84, 32], 'label': '256.30836.16.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.db1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cl1.a1', 'old_label': '16.ce1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879223
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.a1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1', '8.n1.a1', '8.o1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.c1.b1', '32.h1.a1', '32.h1.b1', '32.j1.a1', '32.j1.b1', '32.m1.a1', '32.bw1.a1', '32.cr1.a1', '32.em1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6119, 6158, 6914, 6160, 6122, 6156, 6908, 6174], 'generators': [2, 136, 32, 128], 'label': '256.30836.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.g1.a1', '8.f1.a1', '8.j1.a1', '8.h1.a1', '8.e1.a1', '8.i1.a1', '8.n1.a1', '8.o1.a1', '8.l1.a1', '8.m1.a1', '8.k1.a1'], 'normal_contains': ['32.a1.a1', '32.j1.a1', '32.j1.b1', '32.h1.a1', '32.h1.b1', '32.c1.a1', '32.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879224
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.b1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.p1.a1', '8.q1.a1', '8.r1.a1', '8.s1.a1', '8.t1.a1', '8.u1.a1', '8.v1.a1', '8.w1.a1', '8.x1.a1', '8.y1.a1', '8.z1.a1', '8.ba1.a1', '8.bb1.a1', '8.bc1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '32.d1.b1', '32.g1.a1', '32.g1.b1', '32.k1.a1', '32.k1.b1', '32.n1.a1', '32.be1.a1', '32.dj1.a1', '32.en1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7582, 7009, 6582, 7357, 7585, 7007, 6576, 7373], 'generators': [1, 136, 32, 128], 'label': '256.30836.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.p1.a1', '8.q1.a1', '8.r1.a1', '8.u1.a1', '8.t1.a1', '8.v1.a1', '8.s1.a1', '8.x1.a1', '8.y1.a1', '8.ba1.a1', '8.bb1.a1', '8.z1.a1', '8.bc1.a1', '8.w1.a1'], 'normal_contains': ['32.a1.a1', '32.k1.b1', '32.k1.a1', '32.g1.b1', '32.g1.a1', '32.d1.a1', '32.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879225
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.c1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.p1.a1', '8.bd1.a1', '8.be1.a1', '8.bf1.a1', '8.bg1.a1', '8.bh1.a1', '8.bi1.a1', '8.bj1.a1', '8.bk1.a1', '8.bl1.a1', '8.bm1.a1', '8.bn1.a1', '8.bo1.a1', '8.bp1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '32.bf1.a1', '32.bx1.a1', '32.cs1.a1', '32.dk1.a1', '32.eo1.a1', '32.fp1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7286, 3127, 6079, 2018, 7290, 3125, 6073, 2023], 'generators': [4, 136, 32, 128], 'label': '256.30836.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.p1.a1', '8.b1.a1', '8.bd1.a1', '8.be1.a1', '8.bl1.a1', '8.bg1.a1', '8.bm1.a1', '8.bi1.a1', '8.bj1.a1', '8.bh1.a1', '8.bf1.a1', '8.bk1.a1', '8.bp1.a1', '8.bn1.a1', '8.bo1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.b1', '32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879226
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.k1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.i1.a1', '2.k1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '8.n1.a1', '8.bi1.a1', '8.bl1.a1', '8.bv1.a1', '8.bx1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3924, 8087, 7345, 1139, 3926, 8084, 7339, 1141], 'generators': [65, 2, 4], 'label': '256.30836.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.b1.a1', '2.i1.a1', '2.k1.a1'], 'normal_contains': ['8.b1.a1', '8.g1.a1', '8.n1.a1', '8.bl1.a1', '8.bi1.a1', '8.bx1.a1', '8.bv1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879227
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.d1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.q1.a1', '8.bq1.a1', '8.br1.a1', '8.bs1.a1', '8.bt1.a1', '8.bu1.a1', '8.bv1.a1', '8.bw1.a1', '8.bx1.a1', '8.by1.a1', '8.bz1.a1', '8.ca1.a1', '8.cb1.a1', '8.cc1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '32.e1.b1', '32.o1.a1', '32.bg1.a1', '32.ct1.a1', '32.dl1.a1', '32.ep1.a1', '32.fq1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6744, 4875, 6554, 7124, 6747, 4873, 6548, 7139], 'generators': [6, 136, 32, 128], 'label': '256.30836.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.q1.a1', '8.b1.a1', '8.bq1.a1', '8.br1.a1', '8.bx1.a1', '8.bt1.a1', '8.bw1.a1', '8.bv1.a1', '8.bu1.a1', '8.bs1.a1', '8.cc1.a1', '8.bz1.a1', '8.ca1.a1', '8.by1.a1', '8.cb1.a1'], 'normal_contains': ['32.a1.a1', '32.e1.a1', '32.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879228
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.e1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.p1.a1', '8.bq1.a1', '8.cd1.a1', '8.ce1.a1', '8.cf1.a1', '8.cg1.a1', '8.ch1.a1', '8.ci1.a1', '8.cj1.a1', '8.ck1.a1', '8.cl1.a1', '8.cm1.a1', '8.cn1.a1', '8.co1.a1'], 'contains': ['32.a1.a1', '32.i1.a1', '32.i1.b1', '32.p1.a1', '32.bh1.a1', '32.by1.a1', '32.cu1.a1', '32.dm1.a1', '32.fr1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6770, 4476, 6540, 3129, 6774, 4475, 6534, 3105], 'generators': [5, 136, 32, 128], 'label': '256.30836.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.p1.a1', '8.c1.a1', '8.bq1.a1', '8.cd1.a1', '8.ck1.a1', '8.cf1.a1', '8.cl1.a1', '8.ch1.a1', '8.ci1.a1', '8.cg1.a1', '8.ce1.a1', '8.cj1.a1', '8.cm1.a1', '8.cn1.a1', '8.co1.a1'], 'normal_contains': ['32.a1.a1', '32.i1.b1', '32.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879229
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.f1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.bd1.a1', '8.bq1.a1', '8.cp1.a1', '8.cq1.a1', '8.cr1.a1', '8.cs1.a1', '8.ct1.a1', '8.cu1.a1', '8.cv1.a1', '8.cw1.a1', '8.cx1.a1', '8.cy1.a1', '8.cz1.a1', '8.da1.a1'], 'contains': ['32.a1.a1', '32.l1.a1', '32.l1.b1', '32.q1.a1', '32.bi1.a1', '32.bz1.a1', '32.cv1.a1', '32.dn1.a1', '32.eq1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6797, 3615, 6568, 7451, 6800, 3614, 6562, 7468], 'generators': [3, 136, 32, 128], 'label': '256.30836.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.a1.a1', '8.bd1.a1', '8.bq1.a1', '8.cp1.a1', '8.cq1.a1', '8.cr1.a1', '8.cv1.a1', '8.cs1.a1', '8.ct1.a1', '8.cu1.a1', '8.cz1.a1', '8.da1.a1', '8.cx1.a1', '8.cw1.a1', '8.cy1.a1'], 'normal_contains': ['32.a1.a1', '32.l1.b1', '32.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879230
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.g1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.q1.a1', '8.bd1.a1', '8.db1.a1', '8.dc1.a1', '8.dd1.a1', '8.de1.a1', '8.df1.a1', '8.dg1.a1', '8.dh1.a1', '8.di1.a1', '8.dj1.a1', '8.dk1.a1', '8.dl1.a1', '8.dm1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '32.f1.b1', '32.r1.a1', '32.bj1.a1', '32.cw1.a1', '32.do1.a1', '32.er1.a1', '32.fs1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7608, 3219, 6093, 5955, 7612, 3218, 6087, 5968], 'generators': [7, 136, 32, 128], 'label': '256.30836.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.q1.a1', '8.c1.a1', '8.bd1.a1', '8.db1.a1', '8.dh1.a1', '8.dd1.a1', '8.df1.a1', '8.dg1.a1', '8.de1.a1', '8.dc1.a1', '8.dk1.a1', '8.dl1.a1', '8.dj1.a1', '8.dm1.a1', '8.di1.a1'], 'normal_contains': ['32.a1.a1', '32.f1.b1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879240
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.p1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.be1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.v1.a1', '8.bm1.a1', '8.bw1.a1', '8.cl1.a1', '8.cv1.a1', '8.dd1.a1', '8.ds1.a1', '8.dy1.a1', '8.ej1.a1', '8.eq1.a1', '8.fd1.a1', '8.fi1.a1', '8.fj1.a1', '8.fk1.a1'], 'contains': ['32.a1.a1', '32.bq1.a1', '32.dr1.a1', '32.fv1.a1'], 'core': '16.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4649, 3447, 7632, 2629, 4651, 3446, 7625, 2606], 'generators': [23, 32, 128], 'label': '256.30836.16.p1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.p1.a1', 'normal_contained_in': ['8.v1.a1', '8.j1.a1', '8.bm1.a1', '8.bw1.a1', '8.cl1.a1', '8.cv1.a1', '8.dd1.a1', '8.ds1.a1', '8.fd1.a1', '8.eq1.a1', '8.ej1.a1', '8.dy1.a1', '8.fj1.a1', '8.fk1.a1', '8.fi1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.p1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879231
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.h1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.dp1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.r1.a1', '8.be1.a1', '8.br1.a1', '8.cd1.a1', '8.cp1.a1', '8.db1.a1', '8.dn1.a1', '8.do1.a1', '8.dp1.a1', '8.dq1.a1', '8.dr1.a1', '8.ds1.a1', '8.dt1.a1', '8.du1.a1'], 'contains': ['32.a1.a1', '32.s1.a1', '32.bk1.a1', '32.ca1.a1', '32.cx1.a1', '32.dp1.a1', '32.es1.a1', '32.ft1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2672, 6126, 7585, 3781, 2674, 6124, 7578, 3715], 'generators': [83, 136, 32, 128], 'label': '256.30836.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.r1.a1', '8.d1.a1', '8.be1.a1', '8.br1.a1', '8.cd1.a1', '8.cp1.a1', '8.db1.a1', '8.do1.a1', '8.ds1.a1', '8.dq1.a1', '8.dp1.a1', '8.dn1.a1', '8.dr1.a1', '8.du1.a1', '8.dt1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879232
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.i1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.bz1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.s1.a1', '8.bf1.a1', '8.bs1.a1', '8.ce1.a1', '8.cq1.a1', '8.dc1.a1', '8.dn1.a1', '8.dv1.a1', '8.dw1.a1', '8.dx1.a1', '8.dy1.a1', '8.dz1.a1', '8.ea1.a1', '8.eb1.a1'], 'contains': ['32.a1.a1', '32.t1.a1', '32.bl1.a1', '32.cb1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6158, 5954, 7796, 5101, 6161, 5951, 7789, 5112], 'generators': [64, 136, 32], 'label': '256.30836.16.i1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.i1.a1', 'normal_contained_in': ['8.s1.a1', '8.e1.a1', '8.bf1.a1', '8.bs1.a1', '8.ce1.a1', '8.cq1.a1', '8.dc1.a1', '8.dn1.a1', '8.dv1.a1', '8.dy1.a1', '8.dw1.a1', '8.dx1.a1', '8.eb1.a1', '8.dz1.a1', '8.ea1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879233
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.j1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.x1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.t1.a1', '8.bg1.a1', '8.bt1.a1', '8.cf1.a1', '8.cr1.a1', '8.dd1.a1', '8.do1.a1', '8.dv1.a1', '8.ec1.a1', '8.ed1.a1', '8.ee1.a1', '8.ef1.a1', '8.eg1.a1', '8.eh1.a1'], 'contains': ['32.a1.a1', '32.u1.a1', '32.cy1.a1', '32.dq1.a1'], 'core': '16.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4553, 3569, 6894, 3362, 4556, 3568, 6888, 3370], 'generators': [16, 136, 128], 'label': '256.30836.16.j1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.j1.a1', 'normal_contained_in': ['8.t1.a1', '8.f1.a1', '8.bg1.a1', '8.bt1.a1', '8.cf1.a1', '8.cr1.a1', '8.dd1.a1', '8.do1.a1', '8.ed1.a1', '8.ec1.a1', '8.dv1.a1', '8.eg1.a1', '8.ef1.a1', '8.ee1.a1', '8.eh1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.j1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879234
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.k1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.bw1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.u1.a1', '8.bh1.a1', '8.bu1.a1', '8.cg1.a1', '8.cs1.a1', '8.de1.a1', '8.dp1.a1', '8.ec1.a1', '8.ei1.a1', '8.ej1.a1', '8.ek1.a1', '8.el1.a1', '8.em1.a1', '8.en1.a1'], 'contains': ['32.a1.a1', '32.bm1.a1', '32.cz1.a1', '32.et1.a1'], 'core': '16.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4050, 3019, 7704, 1850, 4052, 3018, 7698, 1854], 'generators': [66, 32, 128], 'label': '256.30836.16.k1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.k1.a1', 'normal_contained_in': ['8.u1.a1', '8.e1.a1', '8.bh1.a1', '8.bu1.a1', '8.cg1.a1', '8.cs1.a1', '8.de1.a1', '8.dp1.a1', '8.ec1.a1', '8.ej1.a1', '8.ei1.a1', '8.en1.a1', '8.el1.a1', '8.em1.a1', '8.ek1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.k1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879235
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.l1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.ca1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.s1.a1', '8.bi1.a1', '8.bv1.a1', '8.ch1.a1', '8.cs1.a1', '8.df1.a1', '8.dq1.a1', '8.ed1.a1', '8.eo1.a1', '8.ep1.a1', '8.eq1.a1', '8.er1.a1', '8.es1.a1', '8.et1.a1'], 'contains': ['32.a1.a1', '32.v1.a1', '32.bn1.a1', '32.cc1.a1'], 'core': '16.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5299, 3079, 7462, 3880, 5301, 3079, 7455, 3889], 'generators': [65, 136, 32], 'label': '256.30836.16.l1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.l1.a1', 'normal_contained_in': ['8.s1.a1', '8.g1.a1', '8.bi1.a1', '8.bv1.a1', '8.ch1.a1', '8.cs1.a1', '8.df1.a1', '8.dq1.a1', '8.ed1.a1', '8.eq1.a1', '8.eo1.a1', '8.ep1.a1', '8.es1.a1', '8.er1.a1', '8.et1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.l1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879236
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.m1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.t1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.t1.a1', '8.bj1.a1', '8.bw1.a1', '8.ci1.a1', '8.ct1.a1', '8.dg1.a1', '8.dp1.a1', '8.dw1.a1', '8.eo1.a1', '8.eu1.a1', '8.ev1.a1', '8.ew1.a1', '8.ex1.a1', '8.ey1.a1'], 'contains': ['32.a1.a1', '32.bo1.a1', '32.da1.a1', '32.eu1.a1'], 'core': '16.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3241, 5763, 7823, 7499, 3242, 5824, 7816, 7516], 'generators': [17, 32, 128], 'label': '256.30836.16.m1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.m1.a1', 'normal_contained_in': ['8.t1.a1', '8.h1.a1', '8.bj1.a1', '8.bw1.a1', '8.ci1.a1', '8.ct1.a1', '8.dg1.a1', '8.dp1.a1', '8.eu1.a1', '8.eo1.a1', '8.dw1.a1', '8.ew1.a1', '8.ev1.a1', '8.ex1.a1', '8.ey1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.m1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879237
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.h1.a1', '2.k1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '8.j1.a1', '8.bj1.a1', '8.bm1.a1', '8.bw1.a1', '8.cc1.a1', '8.gh1.a1', '8.gh1.b1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2670, 6931, 8939, 8617, 2672, 6929, 8931, 8636], 'generators': [17, 2, 4, 32], 'label': '256.30836.4.l1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.c1.a1', '2.h1.a1', '2.k1.a1'], 'normal_contains': ['8.b1.a1', '8.j1.a1', '8.h1.a1', '8.bm1.a1', '8.bj1.a1', '8.bw1.a1', '8.cc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879238
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.n1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.bd1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.v1.a1', '8.bk1.a1', '8.bt1.a1', '8.cj1.a1', '8.cu1.a1', '8.dg1.a1', '8.dr1.a1', '8.dx1.a1', '8.ei1.a1', '8.ep1.a1', '8.ez1.a1', '8.fa1.a1', '8.fb1.a1', '8.fc1.a1'], 'contains': ['32.a1.a1', '32.w1.a1', '32.ev1.a1', '32.fu1.a1'], 'core': '16.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7325, 4523, 6304, 4977, 7328, 4521, 6299, 4987], 'generators': [22, 136, 128], 'label': '256.30836.16.n1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.n1.a1', 'normal_contained_in': ['8.v1.a1', '8.i1.a1', '8.bk1.a1', '8.bt1.a1', '8.cj1.a1', '8.cu1.a1', '8.dg1.a1', '8.dr1.a1', '8.ez1.a1', '8.ep1.a1', '8.ei1.a1', '8.dx1.a1', '8.fa1.a1', '8.fc1.a1', '8.fb1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.n1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879239
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.o1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.ce1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.u1.a1', '8.bl1.a1', '8.bx1.a1', '8.ck1.a1', '8.cq1.a1', '8.dh1.a1', '8.do1.a1', '8.eu1.a1', '8.ez1.a1', '8.fd1.a1', '8.fe1.a1', '8.ff1.a1', '8.fg1.a1', '8.fh1.a1'], 'contains': ['32.a1.a1', '32.bp1.a1', '32.db1.a1', '32.ew1.a1'], 'core': '16.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3677, 7135, 7922, 3176, 3678, 7132, 7915, 3153], 'generators': [67, 32, 128], 'label': '256.30836.16.o1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.o1.a1', 'normal_contained_in': ['8.u1.a1', '8.g1.a1', '8.bl1.a1', '8.bx1.a1', '8.ck1.a1', '8.cq1.a1', '8.dh1.a1', '8.do1.a1', '8.fd1.a1', '8.eu1.a1', '8.ez1.a1', '8.fh1.a1', '8.ff1.a1', '8.fe1.a1', '8.fg1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.o1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879262
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bg1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.hg1.a1', '8.hh1.a1', '8.hi1.a1'], 'contains': ['32.j1.a1', '32.k1.a1', '32.l1.a1', '32.gb1.a1', '32.gk1.a1', '32.gk1.e1', '32.gt1.a1', '32.gt1.d1'], 'core': '16.bg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9399, 7181, 4258, 7739, 9404, 7179, 4255, 7756], 'generators': [1, 2, 136, 160], 'label': '256.30836.16.bg1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.bg1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.k1.a1', '32.j1.a1', '32.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.bg1.a1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879241
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.q1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.dv1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.w1.a1', '8.bn1.a1', '8.by1.a1', '8.cm1.a1', '8.cp1.a1', '8.di1.a1', '8.dv1.a1', '8.ek1.a1', '8.eo1.a1', '8.fa1.a1', '8.fe1.a1', '8.fi1.a1', '8.fl1.a1', '8.fm1.a1'], 'contains': ['32.a1.a1', '32.x1.a1', '32.ex1.a1', '32.fw1.a1'], 'core': '16.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6296, 686, 6170, 6003, 6299, 686, 6165, 6016], 'generators': [80, 136, 128], 'label': '256.30836.16.q1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.q1.a1', 'normal_contained_in': ['8.w1.a1', '8.k1.a1', '8.bn1.a1', '8.by1.a1', '8.cm1.a1', '8.cp1.a1', '8.di1.a1', '8.fe1.a1', '8.dv1.a1', '8.fi1.a1', '8.eo1.a1', '8.ek1.a1', '8.fa1.a1', '8.fm1.a1', '8.fl1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.q1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879242
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.r1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.x1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.x1.a1', '8.bf1.a1', '8.bu1.a1', '8.ch1.a1', '8.cw1.a1', '8.dh1.a1', '8.ds1.a1', '8.ee1.a1', '8.ev1.a1', '8.fb1.a1', '8.fl1.a1', '8.fn1.a1', '8.fo1.a1', '8.fp1.a1'], 'contains': ['32.a1.a1', '32.y1.a1', '32.dc1.a1', '32.ds1.a1'], 'core': '16.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4737, 4826, 6934, 5039, 4739, 4824, 6928, 5049], 'generators': [68, 136, 128], 'label': '256.30836.16.r1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.r1.a1', 'normal_contained_in': ['8.x1.a1', '8.l1.a1', '8.bf1.a1', '8.bu1.a1', '8.ch1.a1', '8.cw1.a1', '8.dh1.a1', '8.ds1.a1', '8.ee1.a1', '8.ev1.a1', '8.fb1.a1', '8.fo1.a1', '8.fl1.a1', '8.fp1.a1', '8.fn1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.r1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.r1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879243
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.s1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.y1.a1', '8.bg1.a1', '8.bz1.a1', '8.ci1.a1', '8.cv1.a1', '8.dj1.a1', '8.dt1.a1', '8.dz1.a1', '8.el1.a1', '8.er1.a1', '8.ff1.a1', '8.fl1.a1', '8.fq1.a1', '8.fr1.a1'], 'contains': ['32.a1.a1', '32.z1.a1', '32.ey1.a1', '32.fx1.a1'], 'core': '16.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6398, 3265, 6795, 4372, 6401, 3264, 6789, 4382], 'generators': [20, 136, 128], 'label': '256.30836.16.s1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.s1.a1', 'normal_contained_in': ['8.y1.a1', '8.i1.a1', '8.bg1.a1', '8.bz1.a1', '8.ci1.a1', '8.cv1.a1', '8.dj1.a1', '8.dt1.a1', '8.ff1.a1', '8.er1.a1', '8.el1.a1', '8.dz1.a1', '8.fr1.a1', '8.fq1.a1', '8.fl1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.s1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879244
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.t1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.z1.a1', '8.bk1.a1', '8.bz1.a1', '8.cl1.a1', '8.ct1.a1', '8.dk1.a1', '8.dq1.a1', '8.ea1.a1', '8.ek1.a1', '8.fg1.a1', '8.fn1.a1', '8.fs1.a1', '8.ft1.a1', '8.fu1.a1'], 'contains': ['32.a1.a1', '32.ba1.a1', '32.dd1.a1', '32.dt1.a1'], 'core': '16.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3851, 9222, 7220, 3942, 3853, 9219, 7214, 3951], 'generators': [18, 136, 128], 'label': '256.30836.16.t1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.t1.a1', 'normal_contained_in': ['8.z1.a1', '8.f1.a1', '8.bk1.a1', '8.bz1.a1', '8.cl1.a1', '8.ct1.a1', '8.dk1.a1', '8.dq1.a1', '8.fg1.a1', '8.ek1.a1', '8.ea1.a1', '8.ft1.a1', '8.fu1.a1', '8.fs1.a1', '8.fn1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.t1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879245
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.u1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.fd1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.ba1.a1', '8.bn1.a1', '8.ca1.a1', '8.cn1.a1', '8.cx1.a1', '8.db1.a1', '8.dz1.a1', '8.ee1.a1', '8.ei1.a1', '8.es1.a1', '8.ew1.a1', '8.fd1.a1', '8.fs1.a1', '8.fv1.a1'], 'contains': ['32.a1.a1', '32.bb1.a1', '32.br1.a1', '32.cd1.a1'], 'core': '16.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5109, 4705, 7355, 5369, 5112, 4703, 7349, 5380], 'generators': [84, 136, 32], 'label': '256.30836.16.u1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.u1.a1', 'normal_contained_in': ['8.ba1.a1', '8.m1.a1', '8.bn1.a1', '8.ca1.a1', '8.cn1.a1', '8.cx1.a1', '8.db1.a1', '8.fd1.a1', '8.ee1.a1', '8.es1.a1', '8.ew1.a1', '8.ei1.a1', '8.dz1.a1', '8.fs1.a1', '8.fv1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.u1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879246
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.v1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.ec1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.r1.a1', '8.bo1.a1', '8.ca1.a1', '8.co1.a1', '8.cy1.a1', '8.dl1.a1', '8.ea1.a1', '8.ec1.a1', '8.et1.a1', '8.eu1.a1', '8.fb1.a1', '8.fj1.a1', '8.fq1.a1', '8.fw1.a1'], 'contains': ['32.a1.a1', '32.ce1.a1', '32.de1.a1', '32.fy1.a1'], 'core': '16.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5430, 2774, 6330, 7562, 5433, 2772, 6325, 7578], 'generators': [82, 32, 128], 'label': '256.30836.16.v1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.v1.a1', 'normal_contained_in': ['8.r1.a1', '8.k1.a1', '8.bo1.a1', '8.ca1.a1', '8.co1.a1', '8.cy1.a1', '8.dl1.a1', '8.eu1.a1', '8.ec1.a1', '8.fj1.a1', '8.et1.a1', '8.ea1.a1', '8.fb1.a1', '8.fw1.a1', '8.fq1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.v1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879247
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.w1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.bb1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.bb1.a1', '8.bh1.a1', '8.bs1.a1', '8.ck1.a1', '8.cz1.a1', '8.df1.a1', '8.du1.a1', '8.ef1.a1', '8.ex1.a1', '8.fa1.a1', '8.fk1.a1', '8.fq1.a1', '8.fs1.a1', '8.fx1.a1'], 'contains': ['32.a1.a1', '32.cf1.a1', '32.du1.a1', '32.ez1.a1'], 'core': '16.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6976, 3327, 7565, 7404, 6979, 3325, 7558, 7420], 'generators': [70, 32, 128], 'label': '256.30836.16.w1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.w1.a1', 'normal_contained_in': ['8.bb1.a1', '8.l1.a1', '8.bh1.a1', '8.bs1.a1', '8.ck1.a1', '8.cz1.a1', '8.df1.a1', '8.du1.a1', '8.ef1.a1', '8.fk1.a1', '8.ex1.a1', '8.fa1.a1', '8.fx1.a1', '8.fq1.a1', '8.fs1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.w1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879248
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.m1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.j1.a1', '2.k1.a1'], 'contains': ['8.b1.a1', '8.k1.a1', '8.m1.a1', '8.bn1.a1', '8.bo1.a1', '8.by1.a1', '8.ca1.a1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8269, 457, 5290, 6608, 8273, 457, 5286, 6622], 'generators': [2, 4, 80], 'label': '256.30836.4.m1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.a1.a1', '2.k1.a1', '2.j1.a1'], 'normal_contains': ['8.b1.a1', '8.m1.a1', '8.k1.a1', '8.bn1.a1', '8.bo1.a1', '8.ca1.a1', '8.by1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879249
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.x1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.dw1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.w1.a1', '8.bp1.a1', '8.cb1.a1', '8.cn1.a1', '8.cy1.a1', '8.dm1.a1', '8.dw1.a1', '8.ed1.a1', '8.em1.a1', '8.fc1.a1', '8.fg1.a1', '8.fk1.a1', '8.fo1.a1', '8.fr1.a1'], 'contains': ['32.a1.a1', '32.bs1.a1', '32.dv1.a1', '32.fz1.a1'], 'core': '16.x1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5349, 3509, 7605, 6208, 5352, 3507, 7599, 6222], 'generators': [81, 32, 128], 'label': '256.30836.16.x1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.x1.a1', 'normal_contained_in': ['8.w1.a1', '8.d1.a1', '8.bp1.a1', '8.cb1.a1', '8.cn1.a1', '8.cy1.a1', '8.dm1.a1', '8.fg1.a1', '8.ed1.a1', '8.fk1.a1', '8.dw1.a1', '8.em1.a1', '8.fc1.a1', '8.fr1.a1', '8.fo1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.x1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879250
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.y1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.x1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.x1.a1', '8.bi1.a1', '8.bx1.a1', '8.ce1.a1', '8.cz1.a1', '8.de1.a1', '8.dr1.a1', '8.eg1.a1', '8.ew1.a1', '8.fj1.a1', '8.fm1.a1', '8.fr1.a1', '8.ft1.a1', '8.fy1.a1'], 'contains': ['32.a1.a1', '32.bc1.a1', '32.df1.a1', '32.dw1.a1'], 'core': '16.y1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3190, 4075, 6504, 3238, 3191, 4075, 6498, 3215], 'generators': [69, 136, 128], 'label': '256.30836.16.y1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.y1.a1', 'normal_contained_in': ['8.x1.a1', '8.n1.a1', '8.bi1.a1', '8.bx1.a1', '8.ce1.a1', '8.cz1.a1', '8.de1.a1', '8.dr1.a1', '8.eg1.a1', '8.fj1.a1', '8.ew1.a1', '8.fm1.a1', '8.fr1.a1', '8.fy1.a1', '8.ft1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.y1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879251
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.z1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.j1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.y1.a1', '8.bj1.a1', '8.cc1.a1', '8.cf1.a1', '8.cu1.a1', '8.dk1.a1', '8.du1.a1', '8.eb1.a1', '8.en1.a1', '8.es1.a1', '8.fh1.a1', '8.fm1.a1', '8.fo1.a1', '8.fw1.a1'], 'contains': ['32.a1.a1', '32.bt1.a1', '32.dx1.a1', '32.ga1.a1'], 'core': '16.z1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4787, 4583, 7408, 7065, 4790, 4582, 7402, 7070], 'generators': [21, 32, 128], 'label': '256.30836.16.z1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.z1.a1', 'normal_contained_in': ['8.y1.a1', '8.j1.a1', '8.bj1.a1', '8.cc1.a1', '8.cf1.a1', '8.cu1.a1', '8.dk1.a1', '8.du1.a1', '8.fh1.a1', '8.es1.a1', '8.en1.a1', '8.eb1.a1', '8.fm1.a1', '8.fw1.a1', '8.fo1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.z1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879252
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.ba1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.z1.a1', '8.bm1.a1', '8.cc1.a1', '8.cj1.a1', '8.cr1.a1', '8.dj1.a1', '8.dn1.a1', '8.em1.a1', '8.et1.a1', '8.fe1.a1', '8.fp1.a1', '8.fv1.a1', '8.fx1.a1', '8.fy1.a1'], 'contains': ['32.a1.a1', '32.bu1.a1', '32.dg1.a1', '32.fa1.a1'], 'core': '16.ba1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4000, 3661, 7435, 6270, 4001, 3660, 7428, 6284], 'generators': [19, 32, 128], 'label': '256.30836.16.ba1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.ba1.a1', 'normal_contained_in': ['8.z1.a1', '8.h1.a1', '8.bm1.a1', '8.cc1.a1', '8.cj1.a1', '8.cr1.a1', '8.dj1.a1', '8.dn1.a1', '8.fe1.a1', '8.et1.a1', '8.em1.a1', '8.fy1.a1', '8.fx1.a1', '8.fv1.a1', '8.fp1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.ba1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879253
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.bb1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.eq1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.bc1.a1', '8.bo1.a1', '8.by1.a1', '8.cd1.a1', '8.da1.a1', '8.dm1.a1', '8.dx1.a1', '8.ef1.a1', '8.el1.a1', '8.eq1.a1', '8.ey1.a1', '8.fh1.a1', '8.fn1.a1', '8.fy1.a1'], 'contains': ['32.a1.a1', '32.bv1.a1', '32.dh1.a1', '32.fb1.a1'], 'core': '16.bb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4466, 3173, 7731, 3586, 4468, 3171, 7724, 3594], 'generators': [86, 32, 128], 'label': '256.30836.16.bb1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.bb1.a1', 'normal_contained_in': ['8.bc1.a1', '8.m1.a1', '8.bo1.a1', '8.by1.a1', '8.cd1.a1', '8.da1.a1', '8.dm1.a1', '8.fh1.a1', '8.ef1.a1', '8.eq1.a1', '8.ey1.a1', '8.el1.a1', '8.dx1.a1', '8.fy1.a1', '8.fn1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.bb1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879254
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.bc1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.ez1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.ba1.a1', '8.bp1.a1', '8.br1.a1', '8.cm1.a1', '8.da1.a1', '8.dl1.a1', '8.eb1.a1', '8.eg1.a1', '8.ej1.a1', '8.er1.a1', '8.ev1.a1', '8.ez1.a1', '8.fu1.a1', '8.fx1.a1'], 'contains': ['32.a1.a1', '32.cg1.a1', '32.dy1.a1', '32.fc1.a1'], 'core': '16.bc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6209, 3387, 7022, 6089, 6212, 3386, 7016, 6110], 'generators': [85, 32, 128], 'label': '256.30836.16.bc1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.bc1.a1', 'normal_contained_in': ['8.ba1.a1', '8.o1.a1', '8.bp1.a1', '8.br1.a1', '8.cm1.a1', '8.da1.a1', '8.dl1.a1', '8.ez1.a1', '8.eg1.a1', '8.ej1.a1', '8.er1.a1', '8.ev1.a1', '8.eb1.a1', '8.fx1.a1', '8.fu1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.bc1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879255
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.bd1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.bb1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.bb1.a1', '8.bl1.a1', '8.bv1.a1', '8.cg1.a1', '8.cw1.a1', '8.dc1.a1', '8.dt1.a1', '8.eh1.a1', '8.ey1.a1', '8.fc1.a1', '8.fi1.a1', '8.fu1.a1', '8.fv1.a1', '8.fw1.a1'], 'contains': ['32.a1.a1', '32.ch1.a1', '32.dz1.a1', '32.fd1.a1'], 'core': '16.bd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5248, 4766, 7896, 4915, 5250, 4764, 7889, 4924], 'generators': [71, 32, 128], 'label': '256.30836.16.bd1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.bd1.a1', 'normal_contained_in': ['8.bb1.a1', '8.n1.a1', '8.bl1.a1', '8.bv1.a1', '8.cg1.a1', '8.cw1.a1', '8.dc1.a1', '8.dt1.a1', '8.eh1.a1', '8.fi1.a1', '8.ey1.a1', '8.fc1.a1', '8.fw1.a1', '8.fu1.a1', '8.fv1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.bd1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879256
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '16.be1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '8.ep1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.bc1.a1', '8.be1.a1', '8.cb1.a1', '8.co1.a1', '8.cx1.a1', '8.di1.a1', '8.dy1.a1', '8.eh1.a1', '8.en1.a1', '8.ep1.a1', '8.ex1.a1', '8.ff1.a1', '8.fp1.a1', '8.ft1.a1'], 'contains': ['32.a1.a1', '32.bd1.a1', '32.di1.a1', '32.ea1.a1'], 'core': '16.be1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3625, 4644, 6848, 5772, 3627, 4642, 6842, 5785], 'generators': [87, 136, 128], 'label': '256.30836.16.be1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.be1.a1', 'normal_contained_in': ['8.bc1.a1', '8.o1.a1', '8.be1.a1', '8.cb1.a1', '8.co1.a1', '8.cx1.a1', '8.di1.a1', '8.ff1.a1', '8.eh1.a1', '8.dy1.a1', '8.ep1.a1', '8.ex1.a1', '8.en1.a1', '8.ft1.a1', '8.fp1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.be1.a1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.be1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879257
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bf1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.gl1.a1', '8.gm1.a1', '8.gn1.a1'], 'contains': ['32.d1.a1', '32.e1.a1', '32.f1.a1', '32.cm1.a1', '32.gx1.a1', '32.gx1.c1', '32.hf1.a1'], 'core': '16.bf1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9373, 7212, 4286, 7674, 9377, 7210, 4282, 7691], 'generators': [1, 6, 136, 128], 'label': '256.30836.16.bf1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.bf1.a1', 'normal_contained_in': ['8.q1.a1'], 'normal_contains': ['32.d1.a1', '32.e1.a1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.bf1.a1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879258
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bf1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.gl1.b1', '8.gm1.b1', '8.gn1.b1'], 'contains': ['32.d1.a1', '32.e1.b1', '32.f1.b1', '32.cm1.b1', '32.gx1.b1', '32.gx1.d1', '32.hf1.b1'], 'core': '16.bf1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9373, 7212, 4189, 7642, 9377, 7210, 4185, 7659], 'generators': [1, 38, 136, 128], 'label': '256.30836.16.bf1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.bf1.b1', 'normal_contained_in': ['8.q1.a1'], 'normal_contains': ['32.d1.a1', '32.e1.b1', '32.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.bf1.b1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879259
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.n1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.l1.a1', '2.m1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.m1.a1', '8.cd1.a1', '8.cn1.a1', '8.db1.a1', '8.dm1.a1', '8.gi1.a1', '8.gi1.b1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3361, 4913, 9024, 2827, 3363, 4911, 9016, 2833], 'generators': [81, 2, 84, 32], 'label': '256.30836.4.n1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.a1.a1', '2.m1.a1', '2.l1.a1'], 'normal_contains': ['8.c1.a1', '8.d1.a1', '8.m1.a1', '8.cd1.a1', '8.cn1.a1', '8.db1.a1', '8.dm1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879260
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bf1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.gl1.c1', '8.gm1.c1', '8.gn1.c1'], 'contains': ['32.d1.b1', '32.e1.a1', '32.f1.b1', '32.cm1.c1', '32.gx1.e1', '32.gx1.g1', '32.hf1.c1'], 'core': '16.bf1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9373, 7212, 4230, 7610, 9377, 7210, 4227, 7626], 'generators': [33, 6, 136, 128], 'label': '256.30836.16.bf1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.bf1.c1', 'normal_contained_in': ['8.q1.a1'], 'normal_contains': ['32.d1.b1', '32.e1.a1', '32.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.bf1.c1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.bf1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879261
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bf1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.gl1.d1', '8.gm1.d1', '8.gn1.d1'], 'contains': ['32.d1.b1', '32.e1.b1', '32.f1.a1', '32.cm1.d1', '32.gx1.f1', '32.gx1.h1', '32.hf1.d1'], 'core': '16.bf1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9373, 7212, 4272, 7707, 9377, 7210, 4269, 7724], 'generators': [33, 38, 136, 128], 'label': '256.30836.16.bf1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.bf1.d1', 'normal_contained_in': ['8.q1.a1'], 'normal_contains': ['32.d1.b1', '32.e1.b1', '32.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.bf1.d1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.bf1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879264
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bg1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.hg1.c1', '8.hh1.c1', '8.hi1.c1'], 'contains': ['32.j1.b1', '32.k1.a1', '32.l1.b1', '32.gb1.c1', '32.gk1.c1', '32.gk1.d1', '32.gt1.e1', '32.gt1.h1'], 'core': '16.bg1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9399, 7181, 4161, 7772, 9404, 7179, 4158, 7789], 'generators': [1, 130, 136, 160], 'label': '256.30836.16.bg1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.bg1.c1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.k1.a1', '32.j1.b1', '32.l1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.bg1.c1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.bg1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879265
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bg1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.hg1.d1', '8.hh1.d1', '8.hi1.d1'], 'contains': ['32.j1.b1', '32.k1.b1', '32.l1.a1', '32.gb1.d1', '32.gk1.f1', '32.gk1.g1', '32.gt1.f1', '32.gt1.g1'], 'core': '16.bg1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9399, 7181, 4328, 7837, 9404, 7179, 4324, 7854], 'generators': [129, 130, 136, 160], 'label': '256.30836.16.bg1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.bg1.d1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.k1.b1', '32.j1.b1', '32.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.bg1.d1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.bg1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879266
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.fz1.a1', '8.fz1.b1'], 'contains': ['32.m1.a1', '32.n1.a1', '32.q1.a1', '32.ci1.a1', '32.ci1.b1', '32.ci1.c1', '32.ci1.d1', '32.eb1.a1', '32.eb1.b1', '32.eb1.c1', '32.eb1.d1', '32.gb1.a1', '32.gb1.b1', '32.gb1.c1', '32.gb1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9054, -1, 3633, -1, 9058, -1, 3630, -1], 'generators': [1, 2, 32, 128], 'label': '256.30836.16.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.bh1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879267
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.fz1.a1', '8.ga1.a1'], 'contains': ['32.b1.a1', '32.m1.a1', '32.o1.a1', '32.cj1.a1', '32.cj1.b1', '32.cj1.e1', '32.cj1.f1', '32.ec1.a1', '32.ec1.c1', '32.gc1.a1', '32.gc1.c1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9186, -1, 3897, -1, 9191, -1, 3894, -1], 'generators': [2, 4, 32, 128], 'label': '256.30836.16.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.bi1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879268
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.fz1.b1', '8.ga1.b1'], 'contains': ['32.b1.b1', '32.m1.a1', '32.o1.a1', '32.cj1.c1', '32.cj1.d1', '32.cj1.g1', '32.cj1.h1', '32.ec1.b1', '32.ec1.d1', '32.gc1.b1', '32.gc1.d1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9186, -1, 4106, -1, 9191, -1, 4102, -1], 'generators': [2, 140, 32, 128], 'label': '256.30836.16.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.bi1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879269
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.fz1.a1', '8.fz1.b1'], 'contains': ['32.m1.a1', '32.p1.a1', '32.r1.a1', '32.ck1.a1', '32.ck1.b1', '32.ck1.c1', '32.ck1.d1', '32.ed1.a1', '32.ed1.a2', '32.ed1.b1', '32.ed1.b2', '32.gd1.a1', '32.gd1.b1', '32.gd1.c1', '32.gd1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9213, -1, 3310, -1, 9218, -1, 3304, -1], 'generators': [5, 2, 32, 128], 'label': '256.30836.16.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.bj1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879270
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.o1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.l1.a1', '2.n1.a1'], 'contains': ['8.c1.a1', '8.e1.a1', '8.n1.a1', '8.ce1.a1', '8.cg1.a1', '8.dc1.a1', '8.de1.a1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4966, 4688, 7326, 803, 4968, 4687, 7320, 805], 'generators': [5, 2, 64], 'label': '256.30836.4.o1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.b1.a1', '2.l1.a1', '2.n1.a1'], 'normal_contains': ['8.c1.a1', '8.e1.a1', '8.n1.a1', '8.cg1.a1', '8.ce1.a1', '8.de1.a1', '8.dc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879271
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.ga1.a1', '8.ga1.b1'], 'contains': ['32.m1.a1', '32.u1.a1', '32.ba1.a1', '32.ee1.a1', '32.ee1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5600, -1, 4981, -1, 5602, -1, 4977, -1], 'generators': [2, 16, 128], 'label': '256.30836.16.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.bk1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879272
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.ga1.a1', '8.ga1.b1'], 'contains': ['32.m1.a1', '32.w1.a1', '32.z1.a1', '32.ge1.a1', '32.ge1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8021, -1, 4862, -1, 8026, -1, 4858, -1], 'generators': [2, 20, 128], 'label': '256.30836.16.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.bl1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879273
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.fz1.a1', '8.gb1.a1'], 'contains': ['32.b1.a1', '32.n1.a1', '32.p1.a1', '32.cl1.a1', '32.cl1.c1', '32.ef1.a1', '32.ef1.c1', '32.gf1.a1', '32.gf1.b1', '32.gf1.e1', '32.gf1.f1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9160, -1, 3647, -1, 9164, -1, 3644, -1], 'generators': [1, 4, 32, 128], 'label': '256.30836.16.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.bm1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879274
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.fz1.b1', '8.gb1.b1'], 'contains': ['32.b1.b1', '32.n1.a1', '32.p1.a1', '32.cl1.b1', '32.cl1.d1', '32.ef1.b1', '32.ef1.d1', '32.gf1.c1', '32.gf1.d1', '32.gf1.g1', '32.gf1.h1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9160, -1, 4036, -1, 9164, -1, 4033, -1], 'generators': [1, 140, 32, 128], 'label': '256.30836.16.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.bm1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bm1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879275
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.fz1.a1', '8.fz1.b1'], 'contains': ['32.n1.a1', '32.o1.a1', '32.r1.a1', '32.cm1.a1', '32.cm1.b1', '32.cm1.c1', '32.cm1.d1', '32.eg1.a1', '32.eg1.a2', '32.eg1.b1', '32.eg1.b2', '32.gg1.a1', '32.gg1.a2', '32.gg1.b1', '32.gg1.b2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9239, -1, 3212, -1, 9244, -1, 3206, -1], 'generators': [1, 6, 32, 128], 'label': '256.30836.16.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.bn1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879276
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bo1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.gb1.a1', '8.gb1.b1'], 'contains': ['32.n1.a1', '32.t1.a1', '32.v1.a1', '32.cn1.a1', '32.cn1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7100, -1, 5699, -1, 7104, -1, 5693, -1], 'generators': [1, 64, 32], 'label': '256.30836.16.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bk1.a1', 'old_label': '16.bo1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879277
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.gb1.a1', '8.gb1.b1'], 'contains': ['32.n1.a1', '32.y1.a1', '32.bc1.a1', '32.eh1.a1', '32.eh1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4890, -1, 5376, -1, 4892, -1, 5371, -1], 'generators': [1, 68, 128], 'label': '256.30836.16.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bk1.a1', 'old_label': '16.bp1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879278
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.fz1.a1', '8.gc1.a1'], 'contains': ['32.b1.a1', '32.q1.a1', '32.r1.a1', '32.co1.a1', '32.co1.b1', '32.ei1.a1', '32.ei1.a2', '32.gh1.a1', '32.gh1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9080, -1, 3143, -1, 9084, -1, 3137, -1], 'generators': [3, 4, 32, 128], 'label': '256.30836.16.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.bq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879281
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.p1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.m1.a1', '2.n1.a1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.j1.a1', '8.cf1.a1', '8.cl1.a1', '8.dd1.a1', '8.dk1.a1', '8.gx1.a1', '8.gx1.b1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4149, 9207, 5585, 3231, 4152, 9203, 5581, 3239], 'generators': [5, 2, 16, 128], 'label': '256.30836.4.p1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.c1.a1', '2.m1.a1', '2.n1.a1'], 'normal_contains': ['8.c1.a1', '8.f1.a1', '8.j1.a1', '8.cf1.a1', '8.cl1.a1', '8.dd1.a1', '8.dk1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879282
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.br1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.gc1.b1', '8.gd1.b1'], 'contains': ['32.b1.b1', '32.s1.a1', '32.bd1.a1', '32.ej1.b1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2496, -1, 5799, -1, 2498, -1, 5794, -1], 'generators': [83, 140, 128], 'label': '256.30836.16.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.y1.a1', 'old_label': '16.br1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.br1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879283
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1', '8.gb1.a1', '8.ge1.a1'], 'contains': ['32.b1.a1', '32.t1.a1', '32.y1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6933, -1, 5005, -1, 6936, -1, 5000, -1], 'generators': [4, 64], 'label': '256.30836.16.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.r1.a1', 'old_label': '16.bs1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879284
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bf1.a1', '8.gb1.b1', '8.ge1.b1'], 'contains': ['32.b1.b1', '32.t1.a1', '32.y1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6933, -1, 5039, -1, 6936, -1, 5035, -1], 'generators': [140, 64], 'label': '256.30836.16.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.r1.a1', 'old_label': '16.bs1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bs1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879285
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bt1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.ga1.a1', '8.ge1.a1'], 'contains': ['32.b1.a1', '32.u1.a1', '32.z1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7218, -1, 4885, -1, 7221, -1, 4881, -1], 'generators': [4, 16], 'label': '256.30836.16.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.j1.a1', 'old_label': '16.bt1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879286
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bt1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bg1.a1', '8.ga1.b1', '8.ge1.b1'], 'contains': ['32.b1.b1', '32.u1.a1', '32.z1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7218, -1, 4942, -1, 7221, -1, 4938, -1], 'generators': [140, 16], 'label': '256.30836.16.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.j1.a1', 'old_label': '16.bt1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bt1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879287
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bi1.a1', '8.gb1.a1', '8.gd1.a1'], 'contains': ['32.b1.a1', '32.v1.a1', '32.bc1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3955, -1, 5656, -1, 3957, -1, 5652, -1], 'generators': [65, 4], 'label': '256.30836.16.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bi1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.p1.a1', 'old_label': '16.bu1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879288
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bi1.a1', '8.gb1.b1', '8.gd1.b1'], 'contains': ['32.b1.b1', '32.v1.a1', '32.bc1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3955, -1, 5675, -1, 3957, -1, 5671, -1], 'generators': [65, 140], 'label': '256.30836.16.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bi1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.p1.a1', 'old_label': '16.bu1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bu1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879289
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bk1.a1', '8.ga1.a1', '8.gd1.a1'], 'contains': ['32.b1.a1', '32.w1.a1', '32.ba1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7020, -1, 5595, -1, 7023, -1, 5590, -1], 'generators': [18, 4], 'label': '256.30836.16.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bk1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '16.bv1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879290
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bk1.a1', '8.ga1.b1', '8.gd1.b1'], 'contains': ['32.b1.b1', '32.w1.a1', '32.ba1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7020, -1, 5614, -1, 7023, -1, 5609, -1], 'generators': [18, 140], 'label': '256.30836.16.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bk1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '16.bv1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bv1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879291
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bn1.a1', '8.gc1.a1', '8.ge1.a1'], 'contains': ['32.b1.a1', '32.x1.a1', '32.bb1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6865, -1, 5287, -1, 6869, -1, 5283, -1], 'generators': [4, 80], 'label': '256.30836.16.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bn1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.x1.a1', 'old_label': '16.bw1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879292
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.q1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.m1.a1', '2.o1.a1'], 'contains': ['8.c1.a1', '8.g1.a1', '8.l1.a1', '8.ch1.a1', '8.ck1.a1', '8.df1.a1', '8.dh1.a1'], 'core': '4.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7675, 7815, 7283, 2755, 7679, 7813, 7276, 2761], 'generators': [65, 2, 68], 'label': '256.30836.4.q1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.q1.a1', 'normal_contained_in': ['2.b1.a1', '2.m1.a1', '2.o1.a1'], 'normal_contains': ['8.c1.a1', '8.g1.a1', '8.l1.a1', '8.ck1.a1', '8.ch1.a1', '8.dh1.a1', '8.df1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879293
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bn1.a1', '8.gc1.b1', '8.ge1.b1'], 'contains': ['32.b1.b1', '32.x1.a1', '32.bb1.a1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6865, -1, 5306, -1, 6869, -1, 5302, -1], 'generators': [140, 80], 'label': '256.30836.16.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bn1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.x1.a1', 'old_label': '16.bw1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879294
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bq1.a1', '8.fz1.a1', '8.fz1.b1'], 'contains': ['32.o1.a1', '32.p1.a1', '32.q1.a1', '32.cp1.a1', '32.cp1.a2', '32.cp1.b1', '32.cp1.b2', '32.ek1.a1', '32.ek1.a2', '32.ek1.a3', '32.ek1.a4', '32.gi1.a1', '32.gi1.b1', '32.gi1.c1', '32.gi1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9133, -1, 2751, -1, 9138, -1, 2748, -1], 'generators': [5, 6, 32, 128], 'label': '256.30836.16.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.bx1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879295
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.by1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bt1.a1', '8.ga1.a1', '8.ga1.b1'], 'contains': ['32.o1.a1', '32.u1.a1', '32.w1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7640, -1, 4904, -1, 7644, -1, 4900, -1], 'generators': [6, 16], 'label': '256.30836.16.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bt1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.by1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.by1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879296
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.bz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bz1.a1', '8.ga1.a1', '8.ga1.b1'], 'contains': ['32.o1.a1', '32.z1.a1', '32.ba1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7057, -1, 4923, -1, 7060, -1, 4919, -1], 'generators': [18, 20], 'label': '256.30836.16.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bz1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.bz1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879297
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ca1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ce1.a1', '8.gb1.a1', '8.gb1.b1'], 'contains': ['32.p1.a1', '32.t1.a1', '32.bc1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5716, -1, 5107, -1, 5719, -1, 5102, -1], 'generators': [5, 64], 'label': '256.30836.16.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ce1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bk1.a1', 'old_label': '16.ca1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879298
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ch1.a1', '8.gb1.a1', '8.gb1.b1'], 'contains': ['32.p1.a1', '32.v1.a1', '32.y1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5931, -1, 5088, -1, 5934, -1, 5083, -1], 'generators': [65, 68], 'label': '256.30836.16.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ch1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bk1.a1', 'old_label': '16.cb1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879299
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cp1.a1', '8.gc1.a1', '8.gc1.b1'], 'contains': ['32.q1.a1', '32.s1.a1', '32.x1.a1', '32.gj1.a1', '32.gj1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5479, -1, 5554, -1, 5481, -1, 5550, -1], 'generators': [3, 80, 128], 'label': '256.30836.16.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cl1.a1', 'old_label': '16.cc1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879303
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.j1.a1', '128.j1.b1', '128.l1.a1', '128.l1.b1', '128.k1.a1', '128.k1.b1', '128.n1.a1', '128.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '4.t1.a1', '4.u1.a1', '4.x1.a1', '4.bc1.a1', '4.bv1.a1', '4.bw1.a1', '4.bz1.a1', '4.cf1.a1', '4.et1.a1', '4.eu1.a1', '4.ex1.a1', '4.fa1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2728, 3748, 8052, 6185, 2802, 3746, 8061, 6066], 'generators': [1, 2, 16, 64], 'label': '256.30836.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '4.bw1.a1', '4.bv1.a1', '4.cf1.a1', '4.bz1.a1', '4.u1.a1', '4.t1.a1', '4.bc1.a1', '4.x1.a1', '4.et1.a1', '4.eu1.a1', '4.ex1.a1', '4.fa1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879304
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.r1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.l1.a1', '2.o1.a1'], 'contains': ['8.c1.a1', '8.h1.a1', '8.i1.a1', '8.ci1.a1', '8.cj1.a1', '8.dg1.a1', '8.dj1.a1', '8.hb1.a1', '8.hb1.b1'], 'core': '4.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8675, 4626, 5399, 7167, 8679, 4625, 5394, 7183], 'generators': [17, 2, 20, 128], 'label': '256.30836.4.r1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.r1.a1', 'normal_contained_in': ['2.c1.a1', '2.l1.a1', '2.o1.a1'], 'normal_contains': ['8.c1.a1', '8.h1.a1', '8.i1.a1', '8.ci1.a1', '8.cj1.a1', '8.dg1.a1', '8.dj1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879305
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dq1.a1', '8.gd1.a1', '8.gd1.b1'], 'contains': ['32.s1.a1', '32.v1.a1', '32.ba1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2538, -1, 5778, -1, 2539, -1, 5773, -1], 'generators': [65, 18], 'label': '256.30836.16.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cu1.a1', 'old_label': '16.cg1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879306
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ch1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dr1.a1', '8.gd1.a1', '8.gd1.b1'], 'contains': ['32.s1.a1', '32.w1.a1', '32.bc1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2641, -1, 5722, -1, 2642, -1, 5716, -1], 'generators': [69, 22], 'label': '256.30836.16.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dr1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cu1.a1', 'old_label': '16.ch1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879307
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ci1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.dv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dv1.a1', '8.ge1.a1', '8.ge1.b1'], 'contains': ['32.t1.a1', '32.u1.a1', '32.x1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6474, -1, 5056, -1, 6477, -1, 5051, -1], 'generators': [16, 64], 'label': '256.30836.16.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dv1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cv1.a1', 'old_label': '16.ci1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879308
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dz1.a1', '8.ge1.a1', '8.ge1.b1'], 'contains': ['32.t1.a1', '32.z1.a1', '32.bb1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6502, -1, 5071, -1, 6505, -1, 5066, -1], 'generators': [20, 64], 'label': '256.30836.16.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dz1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cv1.a1', 'old_label': '16.cj1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879309
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ck1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ee1.a1', '8.ge1.a1', '8.ge1.b1'], 'contains': ['32.u1.a1', '32.y1.a1', '32.bb1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5390, -1, 5022, -1, 5393, -1, 5017, -1], 'generators': [68, 16], 'label': '256.30836.16.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ee1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cv1.a1', 'old_label': '16.ck1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879310
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.ep1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ep1.a1', '8.gd1.a1', '8.gd1.b1'], 'contains': ['32.v1.a1', '32.w1.a1', '32.bd1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4427, -1, 5761, -1, 4429, -1, 5756, -1], 'generators': [65, 22], 'label': '256.30836.16.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ep1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cu1.a1', 'old_label': '16.cl1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879311
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fl1.a1', '8.ge1.a1', '8.ge1.b1'], 'contains': ['32.x1.a1', '32.y1.a1', '32.z1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6898, -1, 4960, -1, 6902, -1, 4956, -1], 'generators': [68, 80], 'label': '256.30836.16.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fl1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cv1.a1', 'old_label': '16.cm1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879312
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ft1.a1', '8.gd1.a1', '8.gd1.b1'], 'contains': ['32.ba1.a1', '32.bc1.a1', '32.bd1.a1', '32.el1.a1', '32.el1.a2'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2357, -1, 5869, -1, 2358, -1, 5864, -1], 'generators': [69, 18, 128], 'label': '256.30836.16.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ft1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cu1.a1', 'old_label': '16.cn1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879313
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.co1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.gf1.a1', '8.gg1.a1'], 'contains': ['32.c1.a1', '32.be1.a1', '32.bi1.a1', '32.ci1.a1', '32.ci1.b1', '32.fe1.a1', '32.fe1.b1', '32.gk1.a1', '32.gk1.b1', '32.gk1.c1', '32.gk1.f1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8654, -1, 4315, -1, 8658, -1, 4310, -1], 'generators': [1, 2, 168, 128], 'label': '256.30836.16.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.co1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.co1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879314
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.co1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.gf1.b1', '8.gg1.b1'], 'contains': ['32.c1.b1', '32.be1.a1', '32.bi1.a1', '32.ci1.c1', '32.ci1.d1', '32.fe1.c1', '32.fe1.d1', '32.gk1.d1', '32.gk1.e1', '32.gk1.g1', '32.gk1.h1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8654, -1, 4300, -1, 8658, -1, 4296, -1], 'generators': [1, 34, 168, 128], 'label': '256.30836.16.co1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.co1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.co1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879315
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.s1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.n1.a1', '2.o1.a1'], 'contains': ['8.c1.a1', '8.k1.a1', '8.o1.a1', '8.cm1.a1', '8.co1.a1', '8.di1.a1', '8.dl1.a1'], 'core': '4.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8404, 501, 5187, 9202, 8408, 501, 5182, 9222], 'generators': [5, 2, 80], 'label': '256.30836.4.s1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.s1.a1', 'normal_contained_in': ['2.a1.a1', '2.o1.a1', '2.n1.a1'], 'normal_contains': ['8.c1.a1', '8.o1.a1', '8.k1.a1', '8.cm1.a1', '8.co1.a1', '8.dl1.a1', '8.di1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879316
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.gf1.a1', '8.gh1.a1'], 'contains': ['32.c1.a1', '32.bf1.a1', '32.bg1.a1', '32.cj1.a1', '32.cj1.b1', '32.cj1.c1', '32.cj1.d1', '32.ff1.a1', '32.ff1.a2', '32.gl1.a1', '32.gl1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8681, -1, 4022, -1, 8685, -1, 4019, -1], 'generators': [2, 4, 168, 128], 'label': '256.30836.16.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.cp1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879317
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.gf1.b1', '8.gh1.b1'], 'contains': ['32.c1.b1', '32.bf1.a1', '32.bg1.a1', '32.cj1.e1', '32.cj1.f1', '32.cj1.g1', '32.cj1.h1', '32.ff1.b1', '32.ff1.b2', '32.gl1.c1', '32.gl1.d1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8681, -1, 3995, -1, 8685, -1, 3991, -1], 'generators': [34, 4, 168, 128], 'label': '256.30836.16.cp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.cp1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cp1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879318
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.gf1.a1', '8.gi1.a1'], 'contains': ['32.c1.a1', '32.bh1.a1', '32.bj1.a1', '32.ck1.a1', '32.ck1.b1', '32.fg1.a1', '32.fg1.b1', '32.gm1.a1', '32.gm1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8734, -1, 3786, -1, 8738, -1, 3783, -1], 'generators': [5, 2, 168, 128], 'label': '256.30836.16.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879319
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.gf1.b1', '8.gi1.b1'], 'contains': ['32.c1.b1', '32.bh1.a1', '32.bj1.a1', '32.ck1.c1', '32.ck1.d1', '32.fg1.c1', '32.fg1.d1', '32.gm1.c1', '32.gm1.d1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8734, -1, 3282, -1, 8738, -1, 3276, -1], 'generators': [5, 34, 168, 128], 'label': '256.30836.16.cq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.cq1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cq1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879320
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.gi1.a1', '8.gj1.a1'], 'contains': ['32.c1.a1', '32.bk1.a1', '32.bs1.a1', '32.gn1.a1', '32.gn1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2752, -1, 9160, -1, 2754, -1, 9152, -1], 'generators': [81, 2, 128], 'label': '256.30836.16.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.l1.a1', 'old_label': '16.cr1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879321
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.gi1.b1', '8.gj1.b1'], 'contains': ['32.c1.b1', '32.bk1.a1', '32.bs1.a1', '32.gn1.c1', '32.gn1.d1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2752, -1, 9136, -1, 2754, -1, 9128, -1], 'generators': [81, 34, 128], 'label': '256.30836.16.cr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.l1.a1', 'old_label': '16.cr1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cr1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879322
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.gg1.a1', '8.gj1.a1'], 'contains': ['32.c1.a1', '32.bl1.a1', '32.bm1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4395, -1, 8844, -1, 4397, -1, 8836, -1], 'generators': [2, 64], 'label': '256.30836.16.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.cs1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879323
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.gg1.b1', '8.gj1.b1'], 'contains': ['32.c1.b1', '32.bl1.a1', '32.bm1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4395, -1, 8825, -1, 4397, -1, 8817, -1], 'generators': [34, 64], 'label': '256.30836.16.cs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.cs1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cs1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879324
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ct1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.gg1.a1', '8.gk1.a1'], 'contains': ['32.c1.a1', '32.bn1.a1', '32.bp1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3522, -1, 8883, -1, 3523, -1, 8875, -1], 'generators': [65, 2], 'label': '256.30836.16.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.ct1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879325
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ct1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.gg1.b1', '8.gk1.b1'], 'contains': ['32.c1.b1', '32.bn1.a1', '32.bp1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3522, -1, 8863, -1, 3523, -1, 8855, -1], 'generators': [65, 34], 'label': '256.30836.16.ct1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.ct1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ct1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879326
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.t1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.m1.a1', 'complements': ['64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dm1.a1', '64.dm1.e2', '64.dm1.e1', '64.dm1.a2', '64.dm1.c1', '64.dm1.g2', '64.dm1.g1', '64.dm1.c2', '64.dm1.b1', '64.dm1.f2', '64.dm1.f1', '64.dm1.b2', '64.dm1.d1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.f1', '64.dn1.h2', '64.dn1.e1', '64.dn1.e2', '64.dn1.h1', '64.do1.a1', '64.do1.b2', '64.do1.d2', '64.do1.c1', '64.do1.d1', '64.do1.c2', '64.do1.a2', '64.do1.b1', '64.do1.e2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.h2', '64.do1.g1', '64.do1.e1', '64.do1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.h1.a1', '2.l1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.h1.a1', '8.dn1.a1', '8.dp1.a1', '8.dw1.a1', '8.em1.a1', '8.gj1.a1', '8.gj1.b1'], 'core': '4.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [999, 5045, 9188, 6544, 1000, 5044, 9180, 6558], 'generators': [17, 2, 64, 32], 'label': '256.30836.4.t1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.t1.a1', 'normal_contained_in': ['2.d1.a1', '2.h1.a1', '2.l1.a1'], 'normal_contains': ['8.d1.a1', '8.h1.a1', '8.e1.a1', '8.dp1.a1', '8.dn1.a1', '8.dw1.a1', '8.em1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.t1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879327
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.gh1.a1', '8.gj1.a1'], 'contains': ['32.c1.a1', '32.bo1.a1', '32.bu1.a1', '32.fh1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2197, -1, 9061, -1, 2199, -1, 9054, -1], 'generators': [17, 2, 128], 'label': '256.30836.16.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.cu1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879328
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.gh1.b1', '8.gj1.b1'], 'contains': ['32.c1.b1', '32.bo1.a1', '32.bu1.a1', '32.fh1.b1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2197, -1, 9008, -1, 2199, -1, 9001, -1], 'generators': [17, 34, 128], 'label': '256.30836.16.cu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.cu1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cu1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879329
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.gh1.a1', '8.gk1.a1'], 'contains': ['32.c1.a1', '32.bq1.a1', '32.bt1.a1', '32.go1.a1', '32.go1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2991, -1, 9035, -1, 2992, -1, 9027, -1], 'generators': [21, 2, 128], 'label': '256.30836.16.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.a1', 'old_label': '16.cv1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879330
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.gh1.b1', '8.gk1.b1'], 'contains': ['32.c1.b1', '32.bq1.a1', '32.bt1.a1', '32.go1.c1', '32.go1.d1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2991, -1, 8963, -1, 2992, -1, 8955, -1], 'generators': [21, 34, 128], 'label': '256.30836.16.cv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.a1', 'old_label': '16.cv1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cv1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879331
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.gi1.a1', '8.gk1.a1'], 'contains': ['32.c1.a1', '32.br1.a1', '32.bv1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3116, -1, 9427, -1, 3117, -1, 9419, -1], 'generators': [2, 84], 'label': '256.30836.16.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '16.cw1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879332
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '8.gi1.b1', '8.gk1.b1'], 'contains': ['32.c1.b1', '32.br1.a1', '32.bv1.a1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3116, -1, 9268, -1, 3117, -1, 9260, -1], 'generators': [34, 84], 'label': '256.30836.16.cw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '16.cw1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cw1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879333
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.gf1.a1', '8.gf1.b1'], 'contains': ['32.be1.a1', '32.bf1.a1', '32.bh1.a1', '32.cl1.a1', '32.cl1.b1', '32.cl1.c1', '32.cl1.d1', '32.fi1.a1', '32.fi1.b1', '32.fi1.c1', '32.fi1.d1', '32.gp1.a1', '32.gp1.a2', '32.gp1.b1', '32.gp1.b2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8920, -1, 2327, -1, 8925, -1, 2325, -1], 'generators': [1, 4, 168, 128], 'label': '256.30836.16.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cx1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879361
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.gl1.c1', '8.gl1.d1'], 'contains': ['32.d1.b1', '32.bw1.a1', '32.bz1.a1', '32.ci1.b1', '32.ci1.d1', '32.gt1.c1', '32.gt1.d1', '32.gt1.g1', '32.gt1.h1', '32.hb1.b1', '32.hb1.d1'], 'core': '32.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9586, -1, 4133, -1, 9590, -1, 4130, -1], 'generators': [33, 2, 136, 128], 'label': '256.30836.16.dv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.dv1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dv1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879334
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.gf1.a1', '8.gf1.b1'], 'contains': ['32.be1.a1', '32.bg1.a1', '32.bj1.a1', '32.cm1.a1', '32.cm1.b1', '32.cm1.c1', '32.cm1.d1', '32.fj1.a1', '32.fj1.a2', '32.fj1.b1', '32.fj1.b2', '32.gq1.a1', '32.gq1.a2', '32.gq1.b1', '32.gq1.b2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8946, -1, 2622, -1, 8951, -1, 2618, -1], 'generators': [1, 6, 168, 128], 'label': '256.30836.16.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.cy1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879335
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.cz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.gg1.a1', '8.gg1.b1'], 'contains': ['32.be1.a1', '32.bl1.a1', '32.bn1.a1', '32.cn1.a1', '32.cn1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6348, -1, 8568, -1, 6350, -1, 8560, -1], 'generators': [1, 64, 168], 'label': '256.30836.16.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.cz1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879336
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.da1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '8.gg1.a1', '8.gg1.b1'], 'contains': ['32.be1.a1', '32.bm1.a1', '32.bp1.a1', '32.fk1.a1', '32.fk1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4174, -1, 8647, -1, 4177, -1, 8640, -1], 'generators': [1, 66, 128], 'label': '256.30836.16.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.da1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.da1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879337
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.u1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.d1', '64.dl1.o1', '64.dl1.p1', '64.dl1.c1', '64.dl1.g1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.b2', '64.dm1.h1', '64.dm1.h2', '64.dm1.b1', '64.dm1.d2', '64.dm1.f1', '64.dm1.f2', '64.dm1.d1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.f1', '64.dn1.e2', '64.dn1.e1', '64.dn1.f2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.h2', '64.do1.a1', '64.do1.c2', '64.do1.a2', '64.do1.c1', '64.do1.d1', '64.do1.b2', '64.do1.d2', '64.do1.b1', '64.do1.g2', '64.do1.e1', '64.do1.g1', '64.do1.e2', '64.do1.f2', '64.do1.h1', '64.do1.f1', '64.do1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.i1.a1', '2.m1.a1'], 'contains': ['8.d1.a1', '8.f1.a1', '8.g1.a1', '8.do1.a1', '8.dq1.a1', '8.ed1.a1', '8.fg1.a1'], 'core': '4.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1211, 9905, 8912, 1555, 1212, 9901, 8904, 1559], 'generators': [65, 2, 16], 'label': '256.30836.4.u1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.u1.a1', 'normal_contained_in': ['2.d1.a1', '2.i1.a1', '2.m1.a1'], 'normal_contains': ['8.d1.a1', '8.g1.a1', '8.f1.a1', '8.do1.a1', '8.dq1.a1', '8.fg1.a1', '8.ed1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.u1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879338
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.db1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.gf1.a1', '8.gf1.b1'], 'contains': ['32.bf1.a1', '32.bi1.a1', '32.bj1.a1', '32.co1.a1', '32.co1.b1', '32.co1.c1', '32.co1.d1', '32.fl1.a1', '32.fl1.a2', '32.fl1.a3', '32.fl1.a4', '32.gr1.a1', '32.gr1.a2', '32.gr1.b1', '32.gr1.b2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8974, -1, 2229, -1, 8978, -1, 2227, -1], 'generators': [3, 4, 168, 128], 'label': '256.30836.16.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.db1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.db1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879339
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bj1.a1', '8.gh1.a1', '8.gh1.b1'], 'contains': ['32.bf1.a1', '32.bo1.a1', '32.bt1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2857, -1, 8940, -1, 2858, -1, 8932, -1], 'generators': [17, 4], 'label': '256.30836.16.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bj1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.dc1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879340
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bm1.a1', '8.gh1.a1', '8.gh1.b1'], 'contains': ['32.bf1.a1', '32.bq1.a1', '32.bu1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2894, -1, 8921, -1, 2895, -1, 8913, -1], 'generators': [19, 4], 'label': '256.30836.16.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bm1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.dd1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879341
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.de1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bq1.a1', '8.gf1.a1', '8.gf1.b1'], 'contains': ['32.bg1.a1', '32.bh1.a1', '32.bi1.a1', '32.cp1.a1', '32.cp1.a2', '32.cp1.b1', '32.cp1.b2', '32.fm1.a1', '32.fm1.a2', '32.fm1.b1', '32.fm1.b2', '32.gs1.a1', '32.gs1.a2', '32.gs1.b1', '32.gs1.b2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8708, -1, 2389, -1, 8712, -1, 2388, -1], 'generators': [5, 6, 168, 128], 'label': '256.30836.16.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.de1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.de1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879342
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.df1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bw1.a1', '8.gh1.a1', '8.gh1.b1'], 'contains': ['32.bg1.a1', '32.bo1.a1', '32.bq1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2821, -1, 8985, -1, 2822, -1, 8978, -1], 'generators': [17, 6], 'label': '256.30836.16.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bw1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.df1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.df1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879343
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cc1.a1', '8.gh1.a1', '8.gh1.b1'], 'contains': ['32.bg1.a1', '32.bt1.a1', '32.bu1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3285, -1, 8902, -1, 3286, -1, 8894, -1], 'generators': [21, 6], 'label': '256.30836.16.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.l1.a1', 'old_label': '16.dg1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879344
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cd1.a1', '8.gi1.a1', '8.gi1.b1'], 'contains': ['32.bh1.a1', '32.bk1.a1', '32.bv1.a1', '32.fn1.a1', '32.fn1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2708, -1, 9086, -1, 2710, -1, 9079, -1], 'generators': [5, 86, 128], 'label': '256.30836.16.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.dh1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879345
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.di1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cn1.a1', '8.gi1.a1', '8.gi1.b1'], 'contains': ['32.bh1.a1', '32.br1.a1', '32.bs1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4094, -1, 9230, -1, 4096, -1, 9222, -1], 'generators': [81, 84], 'label': '256.30836.16.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cn1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.di1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.di1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879346
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cq1.a1', '8.gg1.a1', '8.gg1.b1'], 'contains': ['32.bi1.a1', '32.bl1.a1', '32.bp1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5643, -1, 8705, -1, 5646, -1, 8698, -1], 'generators': [3, 64], 'label': '256.30836.16.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.dj1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879347
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cs1.a1', '8.gg1.a1', '8.gg1.b1'], 'contains': ['32.bi1.a1', '32.bm1.a1', '32.bn1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5556, -1, 8670, -1, 5558, -1, 8663, -1], 'generators': [65, 66], 'label': '256.30836.16.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cs1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.dk1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879362
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.gl1.a1', '8.gl1.c1'], 'contains': ['32.e1.a1', '32.bw1.a1', '32.bx1.a1', '32.cj1.a1', '32.cj1.c1', '32.cj1.e1', '32.cj1.g1', '32.gu1.a1', '32.gu1.c1', '32.hc1.a1', '32.hc1.c1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9639, -1, 3952, -1, 9644, -1, 3949, -1], 'generators': [2, 4, 136, 128], 'label': '256.30836.16.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.dw1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879348
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.v1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.do1.a1', '64.do1.c2', '64.do1.a2', '64.do1.c1', '64.do1.d1', '64.do1.b2', '64.do1.d2', '64.do1.b1', '64.do1.e1', '64.do1.g2', '64.do1.e2', '64.do1.g1', '64.do1.h1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2', '64.dn1.e1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2', '64.dn1.g1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.i1.a1', '2.l1.a1'], 'contains': ['8.d1.a1', '8.i1.a1', '8.n1.a1', '8.dr1.a1', '8.dt1.a1', '8.fc1.a1', '8.fr1.a1'], 'core': '4.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3719, 4982, 6875, 2559, 3721, 4980, 6869, 2565], 'generators': [81, 2, 20], 'label': '256.30836.4.v1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.v1.a1', 'normal_contained_in': ['2.e1.a1', '2.i1.a1', '2.l1.a1'], 'normal_contains': ['8.d1.a1', '8.i1.a1', '8.n1.a1', '8.dr1.a1', '8.dt1.a1', '8.fc1.a1', '8.fr1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.v1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879349
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.db1.a1', '8.gi1.a1', '8.gi1.b1'], 'contains': ['32.bj1.a1', '32.bk1.a1', '32.br1.a1', '32.cq1.a1', '32.cq1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3451, -1, 8490, -1, 3453, -1, 8482, -1], 'generators': [83, 84, 168], 'label': '256.30836.16.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.db1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.dl1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879350
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dm1.a1', '8.gi1.a1', '8.gi1.b1'], 'contains': ['32.bj1.a1', '32.bs1.a1', '32.bv1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4509, -1, 9249, -1, 4512, -1, 9241, -1], 'generators': [81, 86], 'label': '256.30836.16.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dm1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.n1.a1', 'old_label': '16.dm1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879351
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dn1.a1', '8.gj1.a1', '8.gj1.b1'], 'contains': ['32.bk1.a1', '32.bl1.a1', '32.bu1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2242, -1, 9181, -1, 2243, -1, 9173, -1], 'generators': [19, 64], 'label': '256.30836.16.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dn1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '16.dn1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879352
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.do1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dp1.a1', '8.gj1.a1', '8.gj1.b1'], 'contains': ['32.bk1.a1', '32.bm1.a1', '32.bo1.a1', '32.fo1.a1', '32.fo1.a2'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2110, -1, 9111, -1, 2111, -1, 9104, -1], 'generators': [17, 66, 128], 'label': '256.30836.16.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '16.do1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.do1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879353
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.dw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dw1.a1', '8.gj1.a1', '8.gj1.b1'], 'contains': ['32.bl1.a1', '32.bo1.a1', '32.bs1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2788, -1, 9213, -1, 2790, -1, 9205, -1], 'generators': [17, 64], 'label': '256.30836.16.dp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dw1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '16.dp1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879354
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.em1.a1', '8.gj1.a1', '8.gj1.b1'], 'contains': ['32.bm1.a1', '32.bs1.a1', '32.bu1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2275, -1, 9199, -1, 2276, -1, 9190, -1], 'generators': [81, 66], 'label': '256.30836.16.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.em1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.t1.a1', 'old_label': '16.dq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879355
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.eq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.eq1.a1', '8.gk1.a1', '8.gk1.b1'], 'contains': ['32.bn1.a1', '32.bq1.a1', '32.bv1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2925, -1, 9300, -1, 2927, -1, 9292, -1], 'generators': [65, 86], 'label': '256.30836.16.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.eq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '16.dr1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879356
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ds1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.es1.a1', '8.gk1.a1', '8.gk1.b1'], 'contains': ['32.bn1.a1', '32.br1.a1', '32.bt1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3150, -1, 9285, -1, 3151, -1, 9277, -1], 'generators': [65, 84], 'label': '256.30836.16.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.es1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '16.ds1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879357
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dt1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.fd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fd1.a1', '8.gk1.a1', '8.gk1.b1'], 'contains': ['32.bp1.a1', '32.bq1.a1', '32.br1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2952, -1, 9314, -1, 2953, -1, 9306, -1], 'generators': [67, 84], 'label': '256.30836.16.dt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '16.dt1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879358
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.du1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fh1.a1', '8.gk1.a1', '8.gk1.b1'], 'contains': ['32.bp1.a1', '32.bt1.a1', '32.bv1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2571, -1, 9329, -1, 2572, -1, 9321, -1], 'generators': [21, 86], 'label': '256.30836.16.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fh1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.be1.a1', 'old_label': '16.du1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.du1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879359
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.w1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.o1', '64.dl1.d1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.c1', '64.dl1.p1', '64.dn1.a1', '64.dn1.b2', '64.dn1.d1', '64.dn1.c2', '64.dn1.c1', '64.dn1.d2', '64.dn1.b1', '64.dn1.a2', '64.dn1.e2', '64.dn1.f1', '64.dn1.h2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.f2', '64.dn1.e1', '64.do1.a1', '64.do1.c2', '64.do1.d2', '64.do1.b1', '64.do1.d1', '64.do1.b2', '64.do1.a2', '64.do1.c1', '64.do1.e1', '64.do1.g2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.f2', '64.do1.e2', '64.do1.g1', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.h1', '64.dm1.b2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dm1.d2', '64.dm1.b1', '64.dm1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.a1', '2.m1.a1'], 'contains': ['8.d1.a1', '8.j1.a1', '8.l1.a1', '8.ds1.a1', '8.du1.a1', '8.fk1.a1', '8.fo1.a1', '8.gy1.a1', '8.gy1.b1'], 'core': '4.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2099, 6838, 9103, 7789, 2100, 6836, 9096, 7806], 'generators': [81, 2, 68, 128], 'label': '256.30836.4.w1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.w1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.a1', '2.m1.a1'], 'normal_contains': ['8.d1.a1', '8.j1.a1', '8.l1.a1', '8.ds1.a1', '8.du1.a1', '8.fk1.a1', '8.fo1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.w1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879360
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.gl1.a1', '8.gl1.b1'], 'contains': ['32.d1.a1', '32.bw1.a1', '32.bz1.a1', '32.ci1.a1', '32.ci1.c1', '32.gt1.a1', '32.gt1.b1', '32.gt1.e1', '32.gt1.f1', '32.hb1.a1', '32.hb1.c1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9586, -1, 4147, -1, 9590, -1, 4144, -1], 'generators': [1, 2, 136, 128], 'label': '256.30836.16.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.dv1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879363
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.gl1.b1', '8.gl1.d1'], 'contains': ['32.e1.b1', '32.bw1.a1', '32.bx1.a1', '32.cj1.b1', '32.cj1.d1', '32.cj1.f1', '32.cj1.h1', '32.gu1.b1', '32.gu1.d1', '32.hc1.b1', '32.hc1.d1'], 'core': '32.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9639, -1, 3938, -1, 9644, -1, 3935, -1], 'generators': [34, 4, 136, 128], 'label': '256.30836.16.dw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.dw1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dw1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879364
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.gl1.a1', '8.gl1.d1'], 'contains': ['32.f1.a1', '32.bw1.a1', '32.by1.a1', '32.ck1.a1', '32.ck1.c1', '32.gv1.a1', '32.gv1.c1', '32.hd1.a1', '32.hd1.c1', '32.hd1.e1', '32.hd1.g1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9666, -1, 3967, -1, 9670, -1, 3963, -1], 'generators': [5, 2, 136, 128], 'label': '256.30836.16.dx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.dx1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dx1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879365
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.gl1.b1', '8.gl1.c1'], 'contains': ['32.f1.b1', '32.bw1.a1', '32.by1.a1', '32.ck1.b1', '32.ck1.d1', '32.gv1.b1', '32.gv1.d1', '32.hd1.b1', '32.hd1.d1', '32.hd1.f1', '32.hd1.h1'], 'core': '32.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9666, -1, 3324, -1, 9670, -1, 3317, -1], 'generators': [37, 2, 136, 128], 'label': '256.30836.16.dx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.dx1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dx1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879366
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.gl1.a1', '8.gl1.b1'], 'contains': ['32.d1.a1', '32.bx1.a1', '32.by1.a1', '32.cl1.a1', '32.cl1.b1', '32.gw1.a1', '32.gw1.b1', '32.he1.a1', '32.he1.b1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9692, -1, 3605, -1, 9697, -1, 3602, -1], 'generators': [1, 4, 136, 128], 'label': '256.30836.16.dy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.dy1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dy1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879367
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.gl1.c1', '8.gl1.d1'], 'contains': ['32.d1.b1', '32.bx1.a1', '32.by1.a1', '32.cl1.c1', '32.cl1.d1', '32.gw1.c1', '32.gw1.d1', '32.he1.c1', '32.he1.d1'], 'core': '32.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9692, -1, 3619, -1, 9697, -1, 3616, -1], 'generators': [33, 4, 136, 128], 'label': '256.30836.16.dy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.dy1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dy1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879368
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.gm1.a1', '8.gm1.b1'], 'contains': ['32.d1.a1', '32.ca1.a1', '32.ce1.a1', '32.gy1.a1', '32.gy1.b1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5846, -1, 5190, -1, 5849, -1, 5185, -1], 'generators': [1, 82, 128], 'label': '256.30836.16.dz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.dz1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dz1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879369
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.dz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.gm1.c1', '8.gm1.d1'], 'contains': ['32.d1.b1', '32.ca1.a1', '32.ce1.a1', '32.gy1.c1', '32.gy1.d1'], 'core': '32.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5846, -1, 5147, -1, 5849, -1, 5143, -1], 'generators': [33, 82, 128], 'label': '256.30836.16.dz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.dz1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.dz1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879370
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.x1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.j1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.d1', '64.dl1.o1', '64.dl1.k1', '64.dl1.h1', '64.dl1.g1', '64.dl1.l1', '64.dl1.p1', '64.dl1.c1', '64.dn1.a1', '64.dn1.b2', '64.dn1.d1', '64.dn1.c2', '64.dn1.c1', '64.dn1.d2', '64.dn1.b1', '64.dn1.a2', '64.dn1.f1', '64.dn1.e2', '64.dn1.g1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.e1', '64.dn1.f2', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.b2', '64.dm1.h1', '64.dm1.f2', '64.dm1.d1', '64.dm1.d2', '64.dm1.f1', '64.dm1.h2', '64.dm1.b1', '64.do1.a1', '64.do1.c2', '64.do1.d2', '64.do1.b1', '64.do1.d1', '64.do1.b2', '64.do1.a2', '64.do1.c1', '64.do1.g2', '64.do1.e1', '64.do1.f1', '64.do1.h2', '64.do1.f2', '64.do1.h1', '64.do1.g1', '64.do1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.j1.a1', '2.n1.a1'], 'contains': ['8.e1.a1', '8.f1.a1', '8.k1.a1', '8.dv1.a1', '8.ea1.a1', '8.ec1.a1', '8.ek1.a1'], 'core': '4.x1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4509, 3042, 6064, 3830, 4512, 3041, 6059, 3838], 'generators': [2, 16, 64], 'label': '256.30836.4.x1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.x1.a1', 'normal_contained_in': ['2.d1.a1', '2.j1.a1', '2.n1.a1'], 'normal_contains': ['8.f1.a1', '8.e1.a1', '8.k1.a1', '8.ec1.a1', '8.dv1.a1', '8.ek1.a1', '8.ea1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.x1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879371
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ea1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.gn1.a1', '8.gn1.b1'], 'contains': ['32.d1.a1', '32.cb1.a1', '32.cc1.a1', '32.cn1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8072, -1, 8156, -1, 8077, -1, 8148, -1], 'generators': [1, 64, 136], 'label': '256.30836.16.ea1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.ea1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ea1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879372
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ea1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.s1.a1', '8.gn1.c1', '8.gn1.d1'], 'contains': ['32.d1.b1', '32.cb1.a1', '32.cc1.a1', '32.cn1.b1'], 'core': '32.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8072, -1, 8182, -1, 8077, -1, 8175, -1], 'generators': [33, 64, 136], 'label': '256.30836.16.ea1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.ea1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ea1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879373
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '8.gm1.a1', '8.gm1.b1'], 'contains': ['32.d1.a1', '32.cd1.a1', '32.cg1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7713, -1, 5268, -1, 7717, -1, 5264, -1], 'generators': [1, 84], 'label': '256.30836.16.eb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ba1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.eb1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879374
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ba1.a1', '8.gm1.c1', '8.gm1.d1'], 'contains': ['32.d1.b1', '32.cd1.a1', '32.cg1.a1'], 'core': '32.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7713, -1, 5249, -1, 7717, -1, 5245, -1], 'generators': [33, 84], 'label': '256.30836.16.eb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ba1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.eb1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eb1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879375
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ec1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.gn1.a1', '8.gn1.b1'], 'contains': ['32.d1.a1', '32.cf1.a1', '32.ch1.a1', '32.hg1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8211, -1, 7968, -1, 8215, -1, 7961, -1], 'generators': [1, 70, 128], 'label': '256.30836.16.ec1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.ec1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ec1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879376
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ec1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.gn1.c1', '8.gn1.d1'], 'contains': ['32.d1.b1', '32.cf1.a1', '32.ch1.a1', '32.hg1.b1'], 'core': '32.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8211, -1, 8110, -1, 8215, -1, 8102, -1], 'generators': [33, 70, 128], 'label': '256.30836.16.ec1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.ec1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ec1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879377
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ed1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.gl1.a1', '8.gl1.d1'], 'contains': ['32.f1.a1', '32.bx1.a1', '32.bz1.a1', '32.co1.a1', '32.co1.c1', '32.gz1.a1', '32.gz1.c1', '32.hh1.a1', '32.hh1.a2'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9719, -1, 3883, -1, 9723, -1, 3880, -1], 'generators': [3, 4, 136, 128], 'label': '256.30836.16.ed1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.ed1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ed1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879378
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ed1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.gl1.b1', '8.gl1.c1'], 'contains': ['32.f1.b1', '32.bx1.a1', '32.bz1.a1', '32.co1.b1', '32.co1.d1', '32.gz1.b1', '32.gz1.d1', '32.hh1.b1', '32.hh1.b2'], 'core': '32.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9719, -1, 3184, -1, 9723, -1, 3179, -1], 'generators': [35, 4, 136, 128], 'label': '256.30836.16.ed1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.ed1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ed1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879379
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ee1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bq1.a1', '8.gl1.a1', '8.gl1.c1'], 'contains': ['32.e1.a1', '32.by1.a1', '32.bz1.a1', '32.cp1.a1', '32.cp1.a2', '32.ha1.a1', '32.ha1.b1', '32.hi1.a1', '32.hi1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9612, -1, 3352, -1, 9617, -1, 3345, -1], 'generators': [5, 6, 136, 128], 'label': '256.30836.16.ee1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.ee1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ee1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879380
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ee1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bq1.a1', '8.gl1.b1', '8.gl1.d1'], 'contains': ['32.e1.b1', '32.by1.a1', '32.bz1.a1', '32.cp1.b1', '32.cp1.b2', '32.ha1.c1', '32.ha1.d1', '32.hi1.c1', '32.hi1.d1'], 'core': '32.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9612, -1, 3240, -1, 9617, -1, 3234, -1], 'generators': [5, 38, 136, 128], 'label': '256.30836.16.ee1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.ee1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ee1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879381
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.y1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.d1', '64.dl1.o1', '64.dl1.p1', '64.dl1.c1', '64.dl1.g1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.f1', '64.dn1.e2', '64.dn1.e1', '64.dn1.f2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.h2', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.b2', '64.dm1.h1', '64.dm1.h2', '64.dm1.b1', '64.dm1.d2', '64.dm1.f1', '64.dm1.f2', '64.dm1.d1', '64.do1.a1', '64.do1.c2', '64.do1.a2', '64.do1.c1', '64.do1.d1', '64.do1.b2', '64.do1.d2', '64.do1.b1', '64.do1.g2', '64.do1.e1', '64.do1.g1', '64.do1.e2', '64.do1.f2', '64.do1.h1', '64.do1.f1', '64.do1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.j1.a1', '2.l1.a1'], 'contains': ['8.e1.a1', '8.i1.a1', '8.m1.a1', '8.dx1.a1', '8.dz1.a1', '8.ei1.a1', '8.el1.a1'], 'core': '4.y1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6434, 4393, 8437, 1948, 6437, 4391, 8430, 1952], 'generators': [2, 20, 64], 'label': '256.30836.4.y1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.y1.a1', 'normal_contained_in': ['2.f1.a1', '2.j1.a1', '2.l1.a1'], 'normal_contains': ['8.e1.a1', '8.i1.a1', '8.m1.a1', '8.ei1.a1', '8.el1.a1', '8.dx1.a1', '8.dz1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.y1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.y1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879382
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ef1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.br1.a1', '8.gm1.a1', '8.gm1.c1'], 'contains': ['32.e1.a1', '32.ca1.a1', '32.cg1.a1', '32.hj1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6612, -1, 5512, -1, 6616, -1, 5507, -1], 'generators': [85, 6, 128], 'label': '256.30836.16.ef1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.br1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.ef1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ef1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879383
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ef1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.br1.a1', '8.gm1.b1', '8.gm1.d1'], 'contains': ['32.e1.b1', '32.ca1.a1', '32.cg1.a1', '32.hj1.b1'], 'core': '32.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6612, -1, 5401, -1, 6616, -1, 5396, -1], 'generators': [85, 38, 128], 'label': '256.30836.16.ef1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.br1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.ef1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ef1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879384
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bs1.a1', '8.gn1.a1', '8.gn1.c1'], 'contains': ['32.e1.a1', '32.cb1.a1', '32.cf1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8292, -1, 8086, -1, 8296, -1, 8079, -1], 'generators': [6, 64], 'label': '256.30836.16.eg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bs1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.eg1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879385
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bs1.a1', '8.gn1.b1', '8.gn1.d1'], 'contains': ['32.e1.b1', '32.cb1.a1', '32.cf1.a1'], 'core': '32.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8292, -1, 7945, -1, 8296, -1, 7938, -1], 'generators': [38, 64], 'label': '256.30836.16.eg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bs1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.eg1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eg1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879386
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bv1.a1', '8.gn1.a1', '8.gn1.c1'], 'contains': ['32.e1.a1', '32.cc1.a1', '32.ch1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7255, -1, 8133, -1, 7258, -1, 8125, -1], 'generators': [65, 6], 'label': '256.30836.16.eh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bv1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.eh1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eh1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879387
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bv1.a1', '8.gn1.b1', '8.gn1.d1'], 'contains': ['32.e1.b1', '32.cc1.a1', '32.ch1.a1'], 'core': '32.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7255, -1, 8010, -1, 7258, -1, 8003, -1], 'generators': [65, 38], 'label': '256.30836.16.eh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bv1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.eh1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eh1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879388
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ei1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ca1.a1', '8.gm1.a1', '8.gm1.c1'], 'contains': ['32.e1.a1', '32.cd1.a1', '32.ce1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7144, -1, 5211, -1, 7148, -1, 5206, -1], 'generators': [82, 84], 'label': '256.30836.16.ei1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ca1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.ei1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ei1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879389
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ei1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ca1.a1', '8.gm1.b1', '8.gm1.d1'], 'contains': ['32.e1.b1', '32.cd1.a1', '32.ce1.a1'], 'core': '32.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7144, -1, 5168, -1, 7148, -1, 5164, -1], 'generators': [114, 84], 'label': '256.30836.16.ei1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ca1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.ei1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ei1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879390
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ej1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.db1.a1', '8.gm1.a1', '8.gm1.d1'], 'contains': ['32.f1.a1', '32.ca1.a1', '32.cd1.a1', '32.cq1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5758, -1, 5351, -1, 5760, -1, 5346, -1], 'generators': [83, 84, 136], 'label': '256.30836.16.ej1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.db1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.ej1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ej1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879391
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ej1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.db1.a1', '8.gm1.b1', '8.gm1.c1'], 'contains': ['32.f1.b1', '32.ca1.a1', '32.cd1.a1', '32.cq1.b1'], 'core': '32.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5758, -1, 5327, -1, 5760, -1, 5323, -1], 'generators': [115, 84, 136], 'label': '256.30836.16.ej1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.db1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.ej1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ej1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879404
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.gf1.a1', '8.gl1.c1'], 'contains': ['32.ci1.b1', '32.cj1.a1', '32.ck1.b1', '32.cl1.c1', '32.cm1.c1', '32.co1.b1', '32.cp1.a2', '32.hk1.q1', '32.hk1.r1', '32.hk1.y1', '32.hk1.z1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.cu1', '32.hk1.cv1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 1965, -1, 9564, -1, 1963, -1], 'generators': [33, 2, 4, 128], 'label': '256.30836.16.en1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.e1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879455
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.do1.a1', '8.gs1.a1', '8.gs1.b1'], 'contains': ['32.cx1.a1', '32.cy1.a1', '32.db1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1343, -1, 8284, -1, 1343, -1, 8276, -1], 'generators': [67, 16], 'label': '256.30836.16.fn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.do1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '16.fn1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879392
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.z1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.o1', '64.dl1.d1', '64.dl1.c1', '64.dl1.p1', '64.dl1.l1', '64.dl1.g1', '64.dl1.h1', '64.dl1.k1', '64.do1.a1', '64.do1.c2', '64.do1.a2', '64.do1.c1', '64.do1.d1', '64.do1.b2', '64.do1.d2', '64.do1.b1', '64.do1.e1', '64.do1.g2', '64.do1.e2', '64.do1.g1', '64.do1.h1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2', '64.dn1.e1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2', '64.dn1.g1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.h1', '64.dm1.b2', '64.dm1.b1', '64.dm1.h2', '64.dm1.f1', '64.dm1.d2', '64.dm1.d1', '64.dm1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.a1', '2.n1.a1'], 'contains': ['8.e1.a1', '8.j1.a1', '8.o1.a1', '8.dy1.a1', '8.eb1.a1', '8.ej1.a1', '8.en1.a1'], 'core': '4.z1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3975, 6122, 8571, 4833, 3977, 6120, 8563, 4843], 'generators': [21, 2, 64], 'label': '256.30836.4.z1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.z1.a1', 'normal_contained_in': ['2.f1.a1', '2.h1.a1', '2.n1.a1'], 'normal_contains': ['8.j1.a1', '8.e1.a1', '8.o1.a1', '8.ej1.a1', '8.dy1.a1', '8.en1.a1', '8.eb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.z1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879393
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ek1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dc1.a1', '8.gn1.a1', '8.gn1.d1'], 'contains': ['32.f1.a1', '32.cb1.a1', '32.ch1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8168, -1, 8067, -1, 8171, -1, 8060, -1], 'generators': [7, 64], 'label': '256.30836.16.ek1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.ek1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ek1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879394
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ek1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dc1.a1', '8.gn1.b1', '8.gn1.c1'], 'contains': ['32.f1.b1', '32.cb1.a1', '32.ch1.a1'], 'core': '32.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8168, -1, 8048, -1, 8171, -1, 8041, -1], 'generators': [39, 64], 'label': '256.30836.16.ek1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.ek1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ek1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879395
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.el1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.df1.a1', '8.gn1.a1', '8.gn1.d1'], 'contains': ['32.f1.a1', '32.cc1.a1', '32.cf1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8255, -1, 8029, -1, 8259, -1, 8022, -1], 'generators': [65, 70], 'label': '256.30836.16.el1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.df1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.el1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.el1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879396
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.el1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.df1.a1', '8.gn1.b1', '8.gn1.c1'], 'contains': ['32.f1.b1', '32.cc1.a1', '32.cf1.a1'], 'core': '32.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8255, -1, 7991, -1, 8259, -1, 7984, -1], 'generators': [97, 70], 'label': '256.30836.16.el1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.df1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '16.el1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.el1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879397
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.em1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dl1.a1', '8.gm1.a1', '8.gm1.d1'], 'contains': ['32.f1.a1', '32.ce1.a1', '32.cg1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7802, -1, 5230, -1, 7805, -1, 5226, -1], 'generators': [85, 82], 'label': '256.30836.16.em1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dl1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.em1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.em1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879398
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.em1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dl1.a1', '8.gm1.b1', '8.gm1.c1'], 'contains': ['32.f1.b1', '32.ce1.a1', '32.cg1.a1'], 'core': '32.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7802, -1, 5126, -1, 7805, -1, 5122, -1], 'generators': [117, 82], 'label': '256.30836.16.em1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dl1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '16.em1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.em1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879399
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.gf1.a1', '8.gl1.a1'], 'contains': ['32.ci1.a1', '32.cj1.a1', '32.ck1.a1', '32.cl1.a1', '32.cm1.a1', '32.co1.a1', '32.cp1.a1', '32.hk1.a1', '32.hk1.b1', '32.hk1.i1', '32.hk1.j1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.ce1', '32.hk1.cf1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 2062, -1, 9564, -1, 2061, -1], 'generators': [1, 2, 4, 128], 'label': '256.30836.16.en1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879400
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.gf1.a1', '8.gl1.b1'], 'contains': ['32.ci1.a1', '32.cj1.b1', '32.ck1.b1', '32.cl1.a1', '32.cm1.b1', '32.co1.b1', '32.cp1.b1', '32.hk1.c1', '32.hk1.d1', '32.hk1.k1', '32.hk1.l1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.cg1', '32.hk1.ch1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 1715, -1, 9564, -1, 1714, -1], 'generators': [1, 170, 4, 128], 'label': '256.30836.16.en1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879401
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.gf1.a1', '8.gl1.a1'], 'contains': ['32.ci1.a1', '32.cj1.c1', '32.ck1.a1', '32.cl1.b1', '32.cm1.a1', '32.co1.c1', '32.cp1.a2', '32.hk1.e1', '32.hk1.f1', '32.hk1.m1', '32.hk1.n1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.ci1', '32.hk1.cj1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 3101, -1, 9564, -1, 3095, -1], 'generators': [1, 2, 140, 128], 'label': '256.30836.16.en1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879402
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.gf1.a1', '8.gl1.b1'], 'contains': ['32.ci1.a1', '32.cj1.d1', '32.ck1.b1', '32.cl1.b1', '32.cm1.b1', '32.co1.d1', '32.cp1.b2', '32.hk1.g1', '32.hk1.h1', '32.hk1.o1', '32.hk1.p1', '32.hk1.bm1', '32.hk1.bn1', '32.hk1.ck1', '32.hk1.cl1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 2417, -1, 9564, -1, 2416, -1], 'generators': [1, 170, 140, 128], 'label': '256.30836.16.en1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879403
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ba1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.d1', '64.dl1.o1', '64.dl1.k1', '64.dl1.h1', '64.dl1.g1', '64.dl1.l1', '64.dl1.p1', '64.dl1.c1', '64.dn1.a1', '64.dn1.b2', '64.dn1.d1', '64.dn1.c2', '64.dn1.c1', '64.dn1.d2', '64.dn1.b1', '64.dn1.a2', '64.dn1.f1', '64.dn1.e2', '64.dn1.g1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.e1', '64.dn1.f2', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.b2', '64.dm1.h1', '64.dm1.f2', '64.dm1.d1', '64.dm1.d2', '64.dm1.f1', '64.dm1.h2', '64.dm1.b1', '64.do1.a1', '64.do1.c2', '64.do1.d2', '64.do1.b1', '64.do1.d1', '64.do1.b2', '64.do1.a2', '64.do1.c1', '64.do1.g2', '64.do1.e1', '64.do1.f1', '64.do1.h2', '64.do1.f2', '64.do1.h1', '64.do1.g1', '64.do1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.j1.a1', '2.m1.a1'], 'contains': ['8.f1.a1', '8.l1.a1', '8.m1.a1', '8.ee1.a1', '8.ef1.a1', '8.fn1.a1', '8.fs1.a1'], 'core': '4.ba1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3296, 9136, 7449, 3683, 3298, 9133, 7442, 3691], 'generators': [2, 68, 16], 'label': '256.30836.4.ba1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ba1.a1', 'normal_contained_in': ['2.g1.a1', '2.j1.a1', '2.m1.a1'], 'normal_contains': ['8.f1.a1', '8.l1.a1', '8.m1.a1', '8.ef1.a1', '8.ee1.a1', '8.fs1.a1', '8.fn1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ba1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879405
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.gf1.a1', '8.gl1.d1'], 'contains': ['32.ci1.b1', '32.cj1.b1', '32.ck1.a1', '32.cl1.c1', '32.cm1.d1', '32.co1.a1', '32.cp1.b2', '32.hk1.s1', '32.hk1.t1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.cw1', '32.hk1.cx1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 2049, -1, 9564, -1, 2047, -1], 'generators': [33, 170, 4, 128], 'label': '256.30836.16.en1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.f1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879406
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.gf1.a1', '8.gl1.c1'], 'contains': ['32.ci1.b1', '32.cj1.c1', '32.ck1.b1', '32.cl1.d1', '32.cm1.c1', '32.co1.d1', '32.cp1.a1', '32.hk1.u1', '32.hk1.v1', '32.hk1.bc1', '32.hk1.bd1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.cy1', '32.hk1.cz1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 2472, -1, 9564, -1, 2471, -1], 'generators': [33, 2, 140, 128], 'label': '256.30836.16.en1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.g1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879407
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.gf1.a1', '8.gl1.d1'], 'contains': ['32.ci1.b1', '32.cj1.d1', '32.ck1.a1', '32.cl1.d1', '32.cm1.d1', '32.co1.c1', '32.cp1.b1', '32.hk1.w1', '32.hk1.x1', '32.hk1.be1', '32.hk1.bf1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.da1', '32.hk1.db1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 3087, -1, 9564, -1, 3081, -1], 'generators': [33, 170, 140, 128], 'label': '256.30836.16.en1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.h1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879408
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.gf1.b1', '8.gl1.a1'], 'contains': ['32.ci1.c1', '32.cj1.e1', '32.ck1.c1', '32.cl1.a1', '32.cm1.a1', '32.co1.a1', '32.cp1.a2', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.ea1', '32.hk1.eb1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 1952, -1, 9564, -1, 1950, -1], 'generators': [1, 138, 4, 128], 'label': '256.30836.16.en1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.i1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879409
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.gf1.b1', '8.gl1.b1'], 'contains': ['32.ci1.c1', '32.cj1.f1', '32.ck1.d1', '32.cl1.a1', '32.cm1.b1', '32.co1.b1', '32.cp1.b2', '32.hk1.bq1', '32.hk1.br1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.de1', '32.hk1.df1', '32.hk1.ec1', '32.hk1.ed1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 1590, -1, 9564, -1, 1589, -1], 'generators': [1, 34, 4, 128], 'label': '256.30836.16.en1.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.j1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879410
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.gf1.b1', '8.gl1.a1'], 'contains': ['32.ci1.c1', '32.cj1.g1', '32.ck1.c1', '32.cl1.b1', '32.cm1.a1', '32.co1.c1', '32.cp1.a1', '32.hk1.bs1', '32.hk1.bt1', '32.hk1.ca1', '32.hk1.cb1', '32.hk1.dg1', '32.hk1.dh1', '32.hk1.ee1', '32.hk1.ef1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 3060, -1, 9564, -1, 3054, -1], 'generators': [1, 138, 140, 128], 'label': '256.30836.16.en1.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.k1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879411
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.gf1.b1', '8.gl1.b1'], 'contains': ['32.ci1.c1', '32.cj1.h1', '32.ck1.d1', '32.cl1.b1', '32.cm1.b1', '32.co1.d1', '32.cp1.b1', '32.hk1.bu1', '32.hk1.bv1', '32.hk1.cc1', '32.hk1.cd1', '32.hk1.di1', '32.hk1.dj1', '32.hk1.eg1', '32.hk1.eh1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 2257, -1, 9564, -1, 2255, -1], 'generators': [1, 34, 140, 128], 'label': '256.30836.16.en1.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.l1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879412
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.gf1.b1', '8.gl1.c1'], 'contains': ['32.ci1.d1', '32.cj1.e1', '32.ck1.d1', '32.cl1.c1', '32.cm1.c1', '32.co1.b1', '32.cp1.a1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.eq1', '32.hk1.er1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 1646, -1, 9564, -1, 1644, -1], 'generators': [33, 138, 4, 128], 'label': '256.30836.16.en1.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.m1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879413
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.gf1.b1', '8.gl1.d1'], 'contains': ['32.ci1.d1', '32.cj1.f1', '32.ck1.c1', '32.cl1.c1', '32.cm1.d1', '32.co1.a1', '32.cp1.b1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.es1', '32.hk1.et1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 1938, -1, 9564, -1, 1936, -1], 'generators': [33, 34, 4, 128], 'label': '256.30836.16.en1.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.n1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879414
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.j1.a1', '128.j1.b1', '128.l1.a1', '128.l1.b1', '128.k1.a1', '128.k1.b1', '128.n1.a1', '128.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.f1.a1', '4.v1.a1', '4.w1.a1', '4.bh1.a1', '4.bi1.a1', '4.bx1.a1', '4.by1.a1', '4.ch1.a1', '4.ci1.a1', '4.ev1.a1', '4.ew1.a1', '4.fh1.a1', '4.fi1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6509, 3436, 6287, 7438, 6512, 3435, 6287, 7454], 'generators': [1, 2, 68, 80], 'label': '256.30836.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.f1.a1', '4.bx1.a1', '4.by1.a1', '4.ch1.a1', '4.ci1.a1', '4.w1.a1', '4.v1.a1', '4.bi1.a1', '4.bh1.a1', '4.ew1.a1', '4.ev1.a1', '4.fi1.a1', '4.fh1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879415
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bb1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.o1', '64.dl1.d1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.c1', '64.dl1.p1', '64.do1.a1', '64.do1.c2', '64.do1.d2', '64.do1.b1', '64.do1.d1', '64.do1.b2', '64.do1.a2', '64.do1.c1', '64.do1.e1', '64.do1.g2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.f2', '64.do1.e2', '64.do1.g1', '64.dn1.a1', '64.dn1.b2', '64.dn1.d1', '64.dn1.c2', '64.dn1.c1', '64.dn1.d2', '64.dn1.b1', '64.dn1.a2', '64.dn1.e2', '64.dn1.f1', '64.dn1.h2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.f2', '64.dn1.e1', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.h1', '64.dm1.b2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dm1.d2', '64.dm1.b1', '64.dm1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.a1', '2.n1.a1'], 'contains': ['8.f1.a1', '8.n1.a1', '8.o1.a1', '8.eg1.a1', '8.eh1.a1', '8.ft1.a1', '8.fu1.a1', '8.gz1.a1', '8.gz1.b1'], 'core': '4.bb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2800, 9743, 6331, 3153, 2801, 9739, 6326, 3160], 'generators': [69, 2, 16, 128], 'label': '256.30836.4.bb1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bb1.a1', 'normal_contained_in': ['2.g1.a1', '2.i1.a1', '2.n1.a1'], 'normal_contains': ['8.f1.a1', '8.n1.a1', '8.o1.a1', '8.eg1.a1', '8.eh1.a1', '8.ft1.a1', '8.fu1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bb1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879416
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.gf1.b1', '8.gl1.c1'], 'contains': ['32.ci1.d1', '32.cj1.g1', '32.ck1.d1', '32.cl1.d1', '32.cm1.c1', '32.co1.d1', '32.cp1.a2', '32.hk1.do1', '32.hk1.dp1', '32.hk1.dw1', '32.hk1.dx1', '32.hk1.em1', '32.hk1.en1', '32.hk1.eu1', '32.hk1.ev1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 2403, -1, 9564, -1, 2402, -1], 'generators': [33, 138, 140, 128], 'label': '256.30836.16.en1.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.o1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879417
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.en1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.gf1.b1', '8.gl1.d1'], 'contains': ['32.ci1.d1', '32.cj1.h1', '32.ck1.c1', '32.cl1.d1', '32.cm1.d1', '32.co1.c1', '32.cp1.b2', '32.hk1.dq1', '32.hk1.dr1', '32.hk1.dy1', '32.hk1.dz1', '32.hk1.eo1', '32.hk1.ep1', '32.hk1.ew1', '32.hk1.ex1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9558, -1, 3046, -1, 9564, -1, 3040, -1], 'generators': [33, 34, 140, 128], 'label': '256.30836.16.en1.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.en1.p1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.en1.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 30879418
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eo1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.go1.a1', '8.gp1.a1'], 'contains': ['32.g1.a1', '32.cr1.a1', '32.cv1.a1', '32.eb1.a1', '32.eb1.c1', '32.fe1.a1', '32.fe1.c1', '32.gt1.a1', '32.gt1.c1', '32.gt1.e1', '32.gt1.g1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8521, -1, 4120, -1, 8525, -1, 4116, -1], 'generators': [1, 2, 136, 32], 'label': '256.30836.16.eo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.eo1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eo1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30879419
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eo1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.go1.b1', '8.gp1.b1'], 'contains': ['32.g1.b1', '32.cr1.a1', '32.cv1.a1', '32.eb1.b1', '32.eb1.d1', '32.fe1.b1', '32.fe1.d1', '32.gt1.b1', '32.gt1.d1', '32.gt1.f1', '32.gt1.h1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8521, -1, 4244, -1, 8525, -1, 4241, -1], 'generators': [129, 2, 136, 32], 'label': '256.30836.16.eo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.eo1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eo1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30879420
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ep1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.go1.a1', '8.go1.b1'], 'contains': ['32.cr1.a1', '32.cs1.a1', '32.ct1.a1', '32.ec1.a1', '32.ec1.b1', '32.ec1.c1', '32.ec1.d1', '32.ff1.a1', '32.ff1.a2', '32.ff1.b1', '32.ff1.b2', '32.gu1.a1', '32.gu1.b1', '32.gu1.c1', '32.gu1.d1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8574, -1, 3268, -1, 8579, -1, 3262, -1], 'generators': [2, 4, 136, 32], 'label': '256.30836.16.ep1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ep1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ep1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 30879421
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.go1.a1', '8.go1.b1'], 'contains': ['32.cr1.a1', '32.cu1.a1', '32.cw1.a1', '32.ed1.a1', '32.ed1.a2', '32.ed1.b1', '32.ed1.b2', '32.fg1.a1', '32.fg1.b1', '32.fg1.c1', '32.fg1.d1', '32.gv1.a1', '32.gv1.b1', '32.gv1.c1', '32.gv1.d1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8814, -1, 3198, -1, 8818, -1, 3192, -1], 'generators': [5, 2, 136, 32], 'label': '256.30836.16.eq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.eq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eq1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 30879422
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.er1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.gp1.a1', '8.gp1.b1'], 'contains': ['32.cr1.a1', '32.cy1.a1', '32.dd1.a1', '32.ee1.a1', '32.ee1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1860, -1, 7194, -1, 1861, -1, 7188, -1], 'generators': [2, 16, 136], 'label': '256.30836.16.er1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.er1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.er1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30879423
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.es1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.gp1.a1', '8.gp1.b1'], 'contains': ['32.cr1.a1', '32.da1.a1', '32.dg1.a1', '32.fh1.a1', '32.fh1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1504, -1, 7677, -1, 1504, -1, 7671, -1], 'generators': [17, 2, 32], 'label': '256.30836.16.es1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.es1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.es1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30879424
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.et1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.go1.a1', '8.gq1.a1'], 'contains': ['32.g1.a1', '32.cs1.a1', '32.cu1.a1', '32.ef1.a1', '32.ef1.b1', '32.fi1.a1', '32.fi1.b1', '32.gw1.a1', '32.gw1.c1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8601, -1, 3129, -1, 8605, -1, 3123, -1], 'generators': [1, 4, 136, 32], 'label': '256.30836.16.et1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.et1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.et1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879425
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.et1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.go1.b1', '8.gq1.b1'], 'contains': ['32.g1.b1', '32.cs1.a1', '32.cu1.a1', '32.ef1.c1', '32.ef1.d1', '32.fi1.c1', '32.fi1.d1', '32.gw1.b1', '32.gw1.d1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8601, -1, 3717, -1, 8605, -1, 3713, -1], 'generators': [129, 4, 136, 32], 'label': '256.30836.16.et1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.et1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.et1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879426
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bc1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.d1', '64.dl1.o1', '64.dl1.p1', '64.dl1.c1', '64.dl1.g1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.b2', '64.dm1.h1', '64.dm1.h2', '64.dm1.b1', '64.dm1.d2', '64.dm1.f1', '64.dm1.f2', '64.dm1.d1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.f1', '64.dn1.e2', '64.dn1.e1', '64.dn1.f2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.h2', '64.do1.a1', '64.do1.c2', '64.do1.a2', '64.do1.c1', '64.do1.d1', '64.do1.b2', '64.do1.d2', '64.do1.b1', '64.do1.g2', '64.do1.e1', '64.do1.g1', '64.do1.e2', '64.do1.f2', '64.do1.h1', '64.do1.f1', '64.do1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.k1.a1', '2.o1.a1'], 'contains': ['8.g1.a1', '8.h1.a1', '8.k1.a1', '8.eo1.a1', '8.et1.a1', '8.eu1.a1', '8.fe1.a1'], 'core': '4.bc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2611, 1457, 8492, 8906, 2613, 1457, 8485, 8925], 'generators': [65, 2, 80], 'label': '256.30836.4.bc1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bc1.a1', 'normal_contained_in': ['2.d1.a1', '2.k1.a1', '2.o1.a1'], 'normal_contains': ['8.g1.a1', '8.h1.a1', '8.k1.a1', '8.eu1.a1', '8.fe1.a1', '8.eo1.a1', '8.et1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bc1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879427
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.go1.a1', '8.gr1.a1'], 'contains': ['32.g1.a1', '32.ct1.a1', '32.cw1.a1', '32.eg1.a1', '32.eg1.a2', '32.fj1.a1', '32.fj1.a2', '32.gx1.a1', '32.gx1.b1', '32.gx1.e1', '32.gx1.f1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8627, -1, 3981, -1, 8632, -1, 3977, -1], 'generators': [1, 6, 136, 32], 'label': '256.30836.16.eu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.eu1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eu1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879428
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.eu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.go1.b1', '8.gr1.b1'], 'contains': ['32.g1.b1', '32.ct1.a1', '32.cw1.a1', '32.eg1.b1', '32.eg1.b2', '32.fj1.b1', '32.fj1.b2', '32.gx1.c1', '32.gx1.d1', '32.gx1.g1', '32.gx1.h1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8627, -1, 4078, -1, 8632, -1, 4074, -1], 'generators': [129, 6, 136, 32], 'label': '256.30836.16.eu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.eu1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.eu1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879437
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bd1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.n1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.m1', '64.dl1.b1', '64.dl1.f1', '64.dl1.i1', '64.dl1.j1', '64.dl1.e1', '64.dl1.d1', '64.dl1.o1', '64.dl1.p1', '64.dl1.c1', '64.dl1.g1', '64.dl1.l1', '64.dl1.k1', '64.dl1.h1', '64.dm1.a1', '64.dm1.g2', '64.dm1.g1', '64.dm1.a2', '64.dm1.c1', '64.dm1.e2', '64.dm1.e1', '64.dm1.c2', '64.dm1.b2', '64.dm1.h1', '64.dm1.h2', '64.dm1.b1', '64.dm1.d2', '64.dm1.f1', '64.dm1.f2', '64.dm1.d1', '64.dn1.a1', '64.dn1.b2', '64.dn1.b1', '64.dn1.a2', '64.dn1.c1', '64.dn1.d2', '64.dn1.d1', '64.dn1.c2', '64.dn1.f1', '64.dn1.e2', '64.dn1.e1', '64.dn1.f2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.h2', '64.do1.a1', '64.do1.c2', '64.do1.a2', '64.do1.c1', '64.do1.d1', '64.do1.b2', '64.do1.d2', '64.do1.b1', '64.do1.g2', '64.do1.e1', '64.do1.g1', '64.do1.e2', '64.do1.f2', '64.do1.h1', '64.do1.f1', '64.do1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.a1', '2.o1.a1'], 'contains': ['8.g1.a1', '8.i1.a1', '8.o1.a1', '8.ep1.a1', '8.er1.a1', '8.ez1.a1', '8.ff1.a1'], 'core': '4.bd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6011, 6047, 6406, 3987, 6014, 6045, 6400, 3996], 'generators': [65, 2, 20], 'label': '256.30836.4.bd1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bd1.a1', 'normal_contained_in': ['2.f1.a1', '2.i1.a1', '2.o1.a1'], 'normal_contains': ['8.g1.a1', '8.i1.a1', '8.o1.a1', '8.ez1.a1', '8.ff1.a1', '8.ep1.a1', '8.er1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bd1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879438
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ez1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.gp1.a1', '8.gt1.a1'], 'contains': ['32.g1.a1', '32.dd1.a1', '32.dg1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1224, -1, 7152, -1, 1225, -1, 7146, -1], 'generators': [1, 18], 'label': '256.30836.16.ez1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '16.ez1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ez1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879439
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ez1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.z1.a1', '8.gp1.b1', '8.gt1.b1'], 'contains': ['32.g1.b1', '32.dd1.a1', '32.dg1.a1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1224, -1, 7171, -1, 1225, -1, 7165, -1], 'generators': [129, 18], 'label': '256.30836.16.ez1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '16.ez1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ez1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879440
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fa1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '8.gq1.a1', '8.gt1.a1'], 'contains': ['32.g1.a1', '32.dh1.a1', '32.di1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1584, -1, 6110, -1, 1585, -1, 6104, -1], 'generators': [1, 86], 'label': '256.30836.16.fa1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.p1.a1', 'old_label': '16.fa1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fa1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879441
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fa1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bc1.a1', '8.gq1.b1', '8.gt1.b1'], 'contains': ['32.g1.b1', '32.dh1.a1', '32.di1.a1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1584, -1, 6129, -1, 1585, -1, 6123, -1], 'generators': [129, 86], 'label': '256.30836.16.fa1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.p1.a1', 'old_label': '16.fa1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fa1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879442
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.go1.a1', '8.go1.b1'], 'contains': ['32.cs1.a1', '32.cv1.a1', '32.cw1.a1', '32.ei1.a1', '32.ei1.a2', '32.ei1.b1', '32.ei1.b2', '32.fl1.a1', '32.fl1.a2', '32.fl1.a3', '32.fl1.a4', '32.gz1.a1', '32.gz1.b1', '32.gz1.c1', '32.gz1.d1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8893, -1, 2514, -1, 8898, -1, 2513, -1], 'generators': [3, 4, 136, 32], 'label': '256.30836.16.fb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.fb1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fb1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879443
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.gq1.a1', '8.gq1.b1'], 'contains': ['32.cs1.a1', '32.cx1.a1', '32.di1.a1', '32.ej1.a1', '32.ej1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1662, -1, 5443, -1, 1662, -1, 5439, -1], 'generators': [83, 4, 136], 'label': '256.30836.16.fc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '16.fc1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879444
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bo1.a1', '8.gq1.a1', '8.gq1.b1'], 'contains': ['32.cs1.a1', '32.de1.a1', '32.dh1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2154, -1, 5465, -1, 2155, -1, 5460, -1], 'generators': [82, 4], 'label': '256.30836.16.fd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bo1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '16.fd1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879445
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fe1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bq1.a1', '8.go1.a1', '8.go1.b1'], 'contains': ['32.ct1.a1', '32.cu1.a1', '32.cv1.a1', '32.ek1.a1', '32.ek1.a2', '32.ek1.a3', '32.ek1.a4', '32.fm1.a1', '32.fm1.a2', '32.fm1.b1', '32.fm1.b2', '32.ha1.a1', '32.ha1.b1', '32.ha1.c1', '32.ha1.d1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8548, -1, 2445, -1, 8552, -1, 2443, -1], 'generators': [5, 6, 136, 32], 'label': '256.30836.16.fe1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.fe1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fe1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879446
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ff1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bu1.a1', '8.gr1.a1', '8.gr1.b1'], 'contains': ['32.ct1.a1', '32.cz1.a1', '32.dc1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1986, -1, 6258, -1, 1986, -1, 6253, -1], 'generators': [66, 68], 'label': '256.30836.16.ff1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bu1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bs1.a1', 'old_label': '16.ff1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ff1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879447
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bx1.a1', '8.gr1.a1', '8.gr1.b1'], 'contains': ['32.ct1.a1', '32.db1.a1', '32.df1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1621, -1, 6220, -1, 1622, -1, 6215, -1], 'generators': [69, 6], 'label': '256.30836.16.fg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bx1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bs1.a1', 'old_label': '16.fg1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879448
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.be1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.p1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.o1', '64.dl1.d1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.c1', '64.dl1.p1', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.h1', '64.dm1.b2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dm1.d2', '64.dm1.b1', '64.dm1.h2', '64.do1.a1', '64.do1.c2', '64.do1.d2', '64.do1.b1', '64.do1.d1', '64.do1.b2', '64.do1.a2', '64.do1.c1', '64.do1.e1', '64.do1.g2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.f2', '64.do1.e2', '64.do1.g1', '64.dn1.a1', '64.dn1.b2', '64.dn1.d1', '64.dn1.c2', '64.dn1.c1', '64.dn1.d2', '64.dn1.b1', '64.dn1.a2', '64.dn1.e2', '64.dn1.f1', '64.dn1.h2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.f2', '64.dn1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.k1.a1', '2.m1.a1'], 'contains': ['8.g1.a1', '8.j1.a1', '8.m1.a1', '8.eq1.a1', '8.es1.a1', '8.fd1.a1', '8.fh1.a1', '8.gk1.a1', '8.gk1.b1'], 'core': '4.be1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2480, 6532, 9149, 3459, 2482, 6529, 9140, 3467], 'generators': [65, 2, 84, 32], 'label': '256.30836.4.be1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.be1.a1', 'normal_contained_in': ['2.f1.a1', '2.k1.a1', '2.m1.a1'], 'normal_contains': ['8.g1.a1', '8.j1.a1', '8.m1.a1', '8.fd1.a1', '8.fh1.a1', '8.eq1.a1', '8.es1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.be1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.be1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879449
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cd1.a1', '8.gq1.a1', '8.gq1.b1'], 'contains': ['32.cu1.a1', '32.cx1.a1', '32.dh1.a1', '32.fn1.a1', '32.fn1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2026, -1, 5945, -1, 2027, -1, 5940, -1], 'generators': [5, 86, 32], 'label': '256.30836.16.fh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '16.fh1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fh1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879456
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fo1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dp1.a1', '8.gs1.a1', '8.gs1.b1'], 'contains': ['32.cx1.a1', '32.cz1.a1', '32.da1.a1', '32.fo1.a1', '32.fo1.a2'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1298, -1, 8515, -1, 1299, -1, 8507, -1], 'generators': [17, 66, 32], 'label': '256.30836.16.fo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '16.fo1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fo1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879457
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.ec1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ec1.a1', '8.gs1.a1', '8.gs1.b1'], 'contains': ['32.cy1.a1', '32.cz1.a1', '32.de1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1821, -1, 8267, -1, 1822, -1, 8260, -1], 'generators': [66, 16], 'label': '256.30836.16.fp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ec1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '16.fp1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879458
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.eu1.a1', '8.gs1.a1', '8.gs1.b1'], 'contains': ['32.da1.a1', '32.db1.a1', '32.de1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1376, -1, 8301, -1, 1376, -1, 8294, -1], 'generators': [17, 82], 'label': '256.30836.16.fq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.eu1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bw1.a1', 'old_label': '16.fq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879459
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bf1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.b1', '64.dl1.f1', '64.dl1.n1', '64.dl1.m1', '64.dl1.e1', '64.dl1.c1', '64.dl1.k1', '64.dl1.l1', '64.dl1.d1', '64.dl1.h1', '64.dl1.p1', '64.dl1.o1', '64.dl1.g1', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.f1', '64.dn1.h2', '64.dn1.e1', '64.dn1.e2', '64.dn1.h1', '64.dm1.a1', '64.dm1.e2', '64.dm1.e1', '64.dm1.a2', '64.dm1.c1', '64.dm1.g2', '64.dm1.g1', '64.dm1.c2', '64.dm1.b1', '64.dm1.f2', '64.dm1.f1', '64.dm1.b2', '64.dm1.d1', '64.dm1.h2', '64.dm1.h1', '64.dm1.d2', '64.do1.a1', '64.do1.b2', '64.do1.d2', '64.do1.c1', '64.do1.d1', '64.do1.c2', '64.do1.a2', '64.do1.b1', '64.do1.e2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.h2', '64.do1.g1', '64.do1.e1', '64.do1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.a1', '2.o1.a1'], 'contains': ['8.h1.a1', '8.l1.a1', '8.o1.a1', '8.ev1.a1', '8.ex1.a1', '8.fp1.a1', '8.fx1.a1'], 'core': '4.bf1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2343, 6669, 7479, 9868, 2344, 6668, 7472, 9889], 'generators': [17, 2, 68], 'label': '256.30836.4.bf1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bf1.a1', 'normal_contained_in': ['2.g1.a1', '2.h1.a1', '2.o1.a1'], 'normal_contains': ['8.h1.a1', '8.o1.a1', '8.l1.a1', '8.ev1.a1', '8.ex1.a1', '8.fx1.a1', '8.fp1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bf1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879460
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fn1.a1', '8.gt1.a1', '8.gt1.b1'], 'contains': ['32.dc1.a1', '32.dd1.a1', '32.dh1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1191, -1, 6407, -1, 1191, -1, 6401, -1], 'generators': [18, 68], 'label': '256.30836.16.fr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fn1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cj1.a1', 'old_label': '16.fr1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fr1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879461
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fp1.a1', '8.gt1.a1', '8.gt1.b1'], 'contains': ['32.dc1.a1', '32.dg1.a1', '32.di1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1257, -1, 6375, -1, 1258, -1, 6370, -1], 'generators': [19, 68], 'label': '256.30836.16.fs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cj1.a1', 'old_label': '16.fs1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879462
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ft1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ft1.a1', '8.gt1.a1', '8.gt1.b1'], 'contains': ['32.dd1.a1', '32.df1.a1', '32.di1.a1', '32.el1.a1', '32.el1.a2'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1124, -1, 6279, -1, 1124, -1, 6274, -1], 'generators': [69, 18, 136], 'label': '256.30836.16.ft1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ft1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cj1.a1', 'old_label': '16.ft1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ft1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879463
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fy1.a1', '8.gt1.a1', '8.gt1.b1'], 'contains': ['32.df1.a1', '32.dg1.a1', '32.dh1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1161, -1, 6391, -1, 1162, -1, 6385, -1], 'generators': [69, 86], 'label': '256.30836.16.fu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fy1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.cj1.a1', 'old_label': '16.fu1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879464
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.gu1.a1', '8.gv1.a1'], 'contains': ['32.h1.a1', '32.dj1.a1', '32.dn1.a1', '32.eb1.a1', '32.eb1.b1', '32.gk1.a1', '32.gk1.b1', '32.gk1.d1', '32.gk1.g1', '32.hb1.a1', '32.hb1.b1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8761, -1, 4203, -1, 8765, -1, 4199, -1], 'generators': [1, 2, 8, 32], 'label': '256.30836.16.fv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.fv1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fv1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879465
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.gu1.b1', '8.gv1.b1'], 'contains': ['32.h1.b1', '32.dj1.a1', '32.dn1.a1', '32.eb1.c1', '32.eb1.d1', '32.gk1.c1', '32.gk1.e1', '32.gk1.f1', '32.gk1.h1', '32.hb1.c1', '32.hb1.d1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8761, -1, 4217, -1, 8765, -1, 4213, -1], 'generators': [1, 130, 8, 32], 'label': '256.30836.16.fv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.fv1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fv1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879466
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.gu1.a1', '8.gw1.a1'], 'contains': ['32.h1.a1', '32.dk1.a1', '32.dl1.a1', '32.ec1.a1', '32.ec1.b1', '32.gl1.a1', '32.gl1.c1', '32.hc1.a1', '32.hc1.b1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8787, -1, 3772, -1, 8792, -1, 3769, -1], 'generators': [2, 4, 8, 32], 'label': '256.30836.16.fw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.fw1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879467
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.gu1.b1', '8.gw1.b1'], 'contains': ['32.h1.b1', '32.dk1.a1', '32.dl1.a1', '32.ec1.c1', '32.ec1.d1', '32.gl1.b1', '32.gl1.d1', '32.hc1.c1', '32.hc1.d1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8787, -1, 3828, -1, 8792, -1, 3824, -1], 'generators': [130, 4, 8, 32], 'label': '256.30836.16.fw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.fw1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fw1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879468
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.gu1.a1', '8.gx1.a1'], 'contains': ['32.h1.a1', '32.dm1.a1', '32.do1.a1', '32.ed1.a1', '32.ed1.a2', '32.gm1.a1', '32.gm1.c1', '32.hd1.a1', '32.hd1.b1', '32.hd1.c1', '32.hd1.d1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8867, -1, 3744, -1, 8871, -1, 3741, -1], 'generators': [5, 2, 8, 32], 'label': '256.30836.16.fx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.fx1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fx1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879469
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.gu1.b1', '8.gx1.b1'], 'contains': ['32.h1.b1', '32.dm1.a1', '32.do1.a1', '32.ed1.b1', '32.ed1.b2', '32.gm1.b1', '32.gm1.d1', '32.hd1.e1', '32.hd1.f1', '32.hd1.g1', '32.hd1.h1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8867, -1, 3814, -1, 8871, -1, 3810, -1], 'generators': [5, 130, 8, 32], 'label': '256.30836.16.fx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.fx1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fx1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879483
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.gw1.b1', '8.gz1.b1'], 'contains': ['32.h1.b1', '32.dy1.a1', '32.ea1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3771, -1, 6648, -1, 3773, -1, 6643, -1], 'generators': [85, 130], 'label': '256.30836.16.gd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '16.gd1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gd1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879470
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bg1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.i1', '64.dl1.m1', '64.dl1.e1', '64.dl1.f1', '64.dl1.n1', '64.dl1.j1', '64.dl1.b1', '64.dl1.c1', '64.dl1.k1', '64.dl1.o1', '64.dl1.g1', '64.dl1.h1', '64.dl1.p1', '64.dl1.l1', '64.dl1.d1', '64.do1.a1', '64.do1.b2', '64.do1.a2', '64.do1.b1', '64.do1.d1', '64.do1.c2', '64.do1.d2', '64.do1.c1', '64.do1.e2', '64.do1.f1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.g1', '64.do1.h1', '64.do1.g2', '64.dm1.a1', '64.dm1.e2', '64.dm1.g1', '64.dm1.c2', '64.dm1.c1', '64.dm1.g2', '64.dm1.e1', '64.dm1.a2', '64.dm1.b1', '64.dm1.f2', '64.dm1.h1', '64.dm1.d2', '64.dm1.d1', '64.dm1.h2', '64.dm1.f1', '64.dm1.b2', '64.dn1.a1', '64.dn1.d2', '64.dn1.b1', '64.dn1.c2', '64.dn1.c1', '64.dn1.b2', '64.dn1.d1', '64.dn1.a2', '64.dn1.f2', '64.dn1.g1', '64.dn1.e2', '64.dn1.h1', '64.dn1.h2', '64.dn1.e1', '64.dn1.g2', '64.dn1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.k1.a1', '2.l1.a1'], 'contains': ['8.h1.a1', '8.m1.a1', '8.n1.a1', '8.ew1.a1', '8.ey1.a1', '8.fv1.a1', '8.fy1.a1'], 'core': '4.bg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1487, 4513, 8748, 5770, 1488, 4511, 8741, 5782], 'generators': [17, 2, 84], 'label': '256.30836.4.bg1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bg1.a1', 'normal_contained_in': ['2.g1.a1', '2.k1.a1', '2.l1.a1'], 'normal_contains': ['8.h1.a1', '8.n1.a1', '8.m1.a1', '8.ew1.a1', '8.ey1.a1', '8.fy1.a1', '8.fv1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bg1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879471
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.gw1.a1', '8.gy1.a1'], 'contains': ['32.h1.a1', '32.dp1.a1', '32.dv1.a1', '32.gn1.a1', '32.gn1.c1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3038, -1, 8780, -1, 3040, -1, 8773, -1], 'generators': [81, 2, 32], 'label': '256.30836.16.fy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.fy1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fy1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879472
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.gw1.b1', '8.gy1.b1'], 'contains': ['32.h1.b1', '32.dp1.a1', '32.dv1.a1', '32.gn1.b1', '32.gn1.d1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3038, -1, 8804, -1, 3040, -1, 8796, -1], 'generators': [81, 130, 32], 'label': '256.30836.16.fy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.fy1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fy1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879473
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.gx1.a1', '8.gz1.a1'], 'contains': ['32.h1.a1', '32.dq1.a1', '32.dt1.a1', '32.ee1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3404, -1, 6451, -1, 3405, -1, 6445, -1], 'generators': [2, 16, 8], 'label': '256.30836.16.fz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '16.fz1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fz1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879474
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.fz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.gx1.b1', '8.gz1.b1'], 'contains': ['32.h1.b1', '32.dq1.a1', '32.dt1.a1', '32.ee1.b1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3404, -1, 6478, -1, 3405, -1, 6472, -1], 'generators': [130, 16, 8], 'label': '256.30836.16.fz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '16.fz1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.fz1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879475
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ga1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.gx1.a1', '8.gy1.a1'], 'contains': ['32.h1.a1', '32.dr1.a1', '32.dx1.a1', '32.go1.a1', '32.go1.c1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3728, -1, 8594, -1, 3729, -1, 8587, -1], 'generators': [21, 2, 32], 'label': '256.30836.16.ga1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '16.ga1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ga1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879476
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ga1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.gx1.b1', '8.gy1.b1'], 'contains': ['32.h1.b1', '32.dr1.a1', '32.dx1.a1', '32.go1.b1', '32.go1.d1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3728, -1, 8621, -1, 3729, -1, 8613, -1], 'generators': [21, 130, 32], 'label': '256.30836.16.ga1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '16.ga1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ga1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879477
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.gv1.a1', '8.gy1.a1'], 'contains': ['32.h1.a1', '32.ds1.a1', '32.du1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6252, -1, 7504, -1, 6255, -1, 7497, -1], 'generators': [2, 68], 'label': '256.30836.16.gb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.gb1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879478
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '8.gv1.b1', '8.gy1.b1'], 'contains': ['32.h1.b1', '32.ds1.a1', '32.du1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6252, -1, 7523, -1, 6255, -1, 7516, -1], 'generators': [130, 68], 'label': '256.30836.16.gb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.gb1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gb1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879479
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.gv1.a1', '8.gz1.a1'], 'contains': ['32.h1.a1', '32.dw1.a1', '32.dz1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4248, -1, 7095, -1, 4251, -1, 7088, -1], 'generators': [69, 2], 'label': '256.30836.16.gc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '16.gc1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879480
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '8.gv1.b1', '8.gz1.b1'], 'contains': ['32.h1.b1', '32.dw1.a1', '32.dz1.a1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4248, -1, 7114, -1, 4251, -1, 7107, -1], 'generators': [69, 130], 'label': '256.30836.16.gc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '16.gc1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gc1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879481
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bh1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.d1', '64.dl1.o1', '64.dl1.k1', '64.dl1.h1', '64.dl1.g1', '64.dl1.l1', '64.dl1.p1', '64.dl1.c1', '64.dn1.a1', '64.dn1.b2', '64.dn1.d1', '64.dn1.c2', '64.dn1.c1', '64.dn1.d2', '64.dn1.b1', '64.dn1.a2', '64.dn1.f1', '64.dn1.e2', '64.dn1.g1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.e1', '64.dn1.f2', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.b2', '64.dm1.h1', '64.dm1.f2', '64.dm1.d1', '64.dm1.d2', '64.dm1.f1', '64.dm1.h2', '64.dm1.b1', '64.do1.a1', '64.do1.c2', '64.do1.d2', '64.do1.b1', '64.do1.d1', '64.do1.b2', '64.do1.a2', '64.do1.c1', '64.do1.g2', '64.do1.e1', '64.do1.f1', '64.do1.h2', '64.do1.f2', '64.do1.h1', '64.do1.g1', '64.do1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.j1.a1', '2.o1.a1'], 'contains': ['8.i1.a1', '8.k1.a1', '8.l1.a1', '8.fa1.a1', '8.fb1.a1', '8.fl1.a1', '8.fq1.a1'], 'core': '4.bh1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8548, 822, 5349, 8444, 8552, 822, 5344, 8462], 'generators': [2, 68, 80], 'label': '256.30836.4.bh1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bh1.a1', 'normal_contained_in': ['2.e1.a1', '2.j1.a1', '2.o1.a1'], 'normal_contains': ['8.i1.a1', '8.l1.a1', '8.k1.a1', '8.fa1.a1', '8.fb1.a1', '8.fq1.a1', '8.fl1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bh1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879482
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '8.gw1.a1', '8.gz1.a1'], 'contains': ['32.h1.a1', '32.dy1.a1', '32.ea1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3771, -1, 6629, -1, 3773, -1, 6624, -1], 'generators': [85, 2], 'label': '256.30836.16.gd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '16.gd1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879484
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ge1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.gu1.a1', '8.gu1.b1'], 'contains': ['32.dj1.a1', '32.dk1.a1', '32.dm1.a1', '32.ef1.a1', '32.ef1.b1', '32.ef1.c1', '32.ef1.d1', '32.gp1.a1', '32.gp1.a2', '32.gp1.b1', '32.gp1.b2', '32.he1.a1', '32.he1.b1', '32.he1.c1', '32.he1.d1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9001, -1, 2007, -1, 9005, -1, 2005, -1], 'generators': [1, 4, 8, 32], 'label': '256.30836.16.ge1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ge1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ge1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879485
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.gu1.a1', '8.gu1.b1'], 'contains': ['32.dj1.a1', '32.dl1.a1', '32.do1.a1', '32.eg1.a1', '32.eg1.a2', '32.eg1.b1', '32.eg1.b2', '32.gq1.a1', '32.gq1.a2', '32.gq1.b1', '32.gq1.b2', '32.hf1.a1', '32.hf1.b1', '32.hf1.c1', '32.hf1.d1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9027, -1, 2313, -1, 9031, -1, 2311, -1], 'generators': [1, 6, 8, 32], 'label': '256.30836.16.gf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.gf1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879486
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.x1.a1', '8.gv1.a1', '8.gv1.b1'], 'contains': ['32.dj1.a1', '32.ds1.a1', '32.dw1.a1', '32.eh1.a1', '32.eh1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4838, -1, 6821, -1, 4841, -1, 6815, -1], 'generators': [1, 68, 8], 'label': '256.30836.16.gg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '16.gg1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879487
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.gv1.a1', '8.gv1.b1'], 'contains': ['32.dj1.a1', '32.du1.a1', '32.dz1.a1', '32.hg1.a1', '32.hg1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7543, -1, 7381, -1, 7546, -1, 7375, -1], 'generators': [1, 70, 32], 'label': '256.30836.16.gh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '16.gh1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gh1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879488
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.gu1.a1', '8.gu1.b1'], 'contains': ['32.dk1.a1', '32.dn1.a1', '32.do1.a1', '32.ei1.a1', '32.ei1.a2', '32.ei1.b1', '32.ei1.b2', '32.gr1.a1', '32.gr1.a2', '32.gr1.b1', '32.gr1.b2', '32.hh1.a1', '32.hh1.a2', '32.hh1.b1', '32.hh1.b2'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, -1, 2244, -1, 9111, -1, 2241, -1], 'generators': [3, 4, 8, 32], 'label': '256.30836.16.gi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.gi1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gi1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879489
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.be1.a1', '8.gw1.a1', '8.gw1.b1'], 'contains': ['32.dk1.a1', '32.dp1.a1', '32.ea1.a1', '32.ej1.a1', '32.ej1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2401, -1, 6355, -1, 2402, -1, 6350, -1], 'generators': [83, 4, 8], 'label': '256.30836.16.gj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.gj1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gj1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879490
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bp1.a1', '8.gw1.a1', '8.gw1.b1'], 'contains': ['32.dk1.a1', '32.dv1.a1', '32.dy1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5065, -1, 6668, -1, 5068, -1, 6662, -1], 'generators': [81, 4], 'label': '256.30836.16.gk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.gk1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gk1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879491
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bq1.a1', '8.gu1.a1', '8.gu1.b1'], 'contains': ['32.dl1.a1', '32.dm1.a1', '32.dn1.a1', '32.ek1.a1', '32.ek1.a2', '32.ek1.a3', '32.ek1.a4', '32.gs1.a1', '32.gs1.a2', '32.gs1.b1', '32.gs1.b2', '32.hi1.a1', '32.hi1.b1', '32.hi1.c1', '32.hi1.d1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8840, -1, 1895, -1, 8845, -1, 1894, -1], 'generators': [5, 6, 8, 32], 'label': '256.30836.16.gl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.gl1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879492
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bi1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dl1.a1', '64.dl1.n1', '64.dl1.j1', '64.dl1.e1', '64.dl1.f1', '64.dl1.i1', '64.dl1.m1', '64.dl1.b1', '64.dl1.o1', '64.dl1.d1', '64.dl1.h1', '64.dl1.k1', '64.dl1.l1', '64.dl1.g1', '64.dl1.c1', '64.dl1.p1', '64.do1.a1', '64.do1.c2', '64.do1.d2', '64.do1.b1', '64.do1.d1', '64.do1.b2', '64.do1.a2', '64.do1.c1', '64.do1.e1', '64.do1.g2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.f2', '64.do1.e2', '64.do1.g1', '64.dn1.a1', '64.dn1.b2', '64.dn1.d1', '64.dn1.c2', '64.dn1.c1', '64.dn1.d2', '64.dn1.b1', '64.dn1.a2', '64.dn1.e2', '64.dn1.f1', '64.dn1.h2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.f2', '64.dn1.e1', '64.dm1.a1', '64.dm1.g2', '64.dm1.e1', '64.dm1.c2', '64.dm1.c1', '64.dm1.e2', '64.dm1.g1', '64.dm1.a2', '64.dm1.h1', '64.dm1.b2', '64.dm1.d1', '64.dm1.f2', '64.dm1.f1', '64.dm1.d2', '64.dm1.b1', '64.dm1.h2'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.k1.a1', '2.n1.a1'], 'contains': ['8.j1.a1', '8.k1.a1', '8.n1.a1', '8.fi1.a1', '8.fj1.a1', '8.fm1.a1', '8.fw1.a1'], 'core': '4.bi1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4310, 1030, 6684, 5700, 4312, 1030, 6679, 5712], 'generators': [69, 2, 80], 'label': '256.30836.4.bi1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bi1.a1', 'normal_contained_in': ['2.e1.a1', '2.k1.a1', '2.n1.a1'], 'normal_contains': ['8.j1.a1', '8.n1.a1', '8.k1.a1', '8.fj1.a1', '8.fi1.a1', '8.fm1.a1', '8.fw1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bi1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879493
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.br1.a1', '8.gw1.a1', '8.gw1.b1'], 'contains': ['32.dl1.a1', '32.dp1.a1', '32.dy1.a1', '32.hj1.a1', '32.hj1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4602, -1, 6708, -1, 4603, -1, 6702, -1], 'generators': [85, 6, 32], 'label': '256.30836.16.gm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.br1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.gm1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879494
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cb1.a1', '8.gw1.a1', '8.gw1.b1'], 'contains': ['32.dl1.a1', '32.dv1.a1', '32.ea1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4131, -1, 6687, -1, 4133, -1, 6681, -1], 'generators': [81, 6], 'label': '256.30836.16.gn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.h1.a1', 'old_label': '16.gn1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879495
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.go1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cf1.a1', '8.gx1.a1', '8.gx1.b1'], 'contains': ['32.dm1.a1', '32.dq1.a1', '32.dx1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4693, -1, 5985, -1, 4695, -1, 5980, -1], 'generators': [5, 16], 'label': '256.30836.16.go1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '16.go1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.go1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879496
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cl1.a1', '8.gx1.a1', '8.gx1.b1'], 'contains': ['32.dm1.a1', '32.dr1.a1', '32.dt1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4286, -1, 6004, -1, 4287, -1, 5999, -1], 'generators': [5, 18], 'label': '256.30836.16.gp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cl1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.p1.a1', 'old_label': '16.gp1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gp1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879497
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cw1.a1', '8.gv1.a1', '8.gv1.b1'], 'contains': ['32.dn1.a1', '32.ds1.a1', '32.dz1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6442, -1, 7313, -1, 6445, -1, 7307, -1], 'generators': [3, 68], 'label': '256.30836.16.gq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cw1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '16.gq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879498
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gr1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cz1.a1', '8.gv1.a1', '8.gv1.b1'], 'contains': ['32.dn1.a1', '32.du1.a1', '32.dw1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6535, -1, 7133, -1, 6539, -1, 7126, -1], 'generators': [69, 70], 'label': '256.30836.16.gr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cz1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '16.gr1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gr1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879503
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bj1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.p1.a1', '2.q1.a1'], 'contains': ['8.p1.a1', '8.r1.a1', '8.bc1.a1', '8.be1.a1', '8.bo1.a1', '8.cd1.a1', '8.co1.a1', '8.gq1.a1', '8.gq1.b1'], 'core': '4.bj1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2183, 5178, 5259, 1422, 2185, 5176, 5255, 1425], 'generators': [1, 82, 4, 128], 'label': '256.30836.4.bj1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bj1.a1', 'normal_contained_in': ['2.a1.a1', '2.q1.a1', '2.p1.a1'], 'normal_contains': ['8.p1.a1', '8.r1.a1', '8.bc1.a1', '8.be1.a1', '8.bo1.a1', '8.cd1.a1', '8.co1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bj1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879504
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.eg1.a1', '8.gz1.a1', '8.gz1.b1'], 'contains': ['32.dq1.a1', '32.dw1.a1', '32.dy1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3488, -1, 6525, -1, 3490, -1, 6520, -1], 'generators': [69, 16], 'label': '256.30836.16.gw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.eg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '16.gw1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879505
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.eh1.a1', '8.gz1.a1', '8.gz1.b1'], 'contains': ['32.dq1.a1', '32.dz1.a1', '32.ea1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3362, -1, 6596, -1, 3364, -1, 6591, -1], 'generators': [71, 16], 'label': '256.30836.16.gx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.eh1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '16.gx1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gx1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879506
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fk1.a1', '8.gy1.a1', '8.gy1.b1'], 'contains': ['32.dr1.a1', '32.du1.a1', '32.dv1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3892, -1, 8761, -1, 3894, -1, 8753, -1], 'generators': [81, 70], 'label': '256.30836.16.gy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fk1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.w1.a1', 'old_label': '16.gy1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gy1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879507
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.gz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fo1.a1', '8.gy1.a1', '8.gy1.b1'], 'contains': ['32.ds1.a1', '32.dv1.a1', '32.dx1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3555, -1, 8688, -1, 3557, -1, 8680, -1], 'generators': [81, 68], 'label': '256.30836.16.gz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fo1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.w1.a1', 'old_label': '16.gz1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.gz1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879508
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ha1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ft1.a1', '8.gz1.a1', '8.gz1.b1'], 'contains': ['32.dt1.a1', '32.dw1.a1', '32.ea1.a1', '32.el1.a1', '32.el1.a2'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2313, -1, 6426, -1, 2314, -1, 6420, -1], 'generators': [69, 18, 8], 'label': '256.30836.16.ha1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ft1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '16.ha1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ha1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879509
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fu1.a1', '8.gz1.a1', '8.gz1.b1'], 'contains': ['32.dt1.a1', '32.dy1.a1', '32.dz1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4215, -1, 6612, -1, 4217, -1, 6606, -1], 'generators': [85, 18], 'label': '256.30836.16.hb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fu1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bb1.a1', 'old_label': '16.hb1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879510
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.go1.a1', '8.gu1.a1'], 'contains': ['32.eb1.a1', '32.ec1.a1', '32.ed1.a1', '32.ef1.a1', '32.eg1.a1', '32.ei1.a1', '32.ek1.a1', '32.hk1.a1', '32.hk1.d1', '32.hk1.r1', '32.hk1.s1', '32.hk1.bp1', '32.hk1.bq1', '32.hk1.dk1', '32.hk1.dn1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 638, -1, 9431, -1, 637, -1], 'generators': [1, 2, 4, 32], 'label': '256.30836.16.hc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879511
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.go1.a1', '8.gu1.a1'], 'contains': ['32.eb1.a1', '32.ec1.a1', '32.ed1.a2', '32.ef1.a1', '32.eg1.a2', '32.ei1.a2', '32.ek1.a2', '32.hk1.b1', '32.hk1.c1', '32.hk1.q1', '32.hk1.t1', '32.hk1.bo1', '32.hk1.br1', '32.hk1.dl1', '32.hk1.dm1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 666, -1, 9431, -1, 665, -1], 'generators': [137, 2, 4, 32], 'label': '256.30836.16.hc1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879512
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.go1.a1', '8.gu1.a1'], 'contains': ['32.eb1.a1', '32.ec1.b1', '32.ed1.a1', '32.ef1.b1', '32.eg1.a2', '32.ei1.b1', '32.ek1.a3', '32.hk1.e1', '32.hk1.h1', '32.hk1.v1', '32.hk1.w1', '32.hk1.bt1', '32.hk1.bu1', '32.hk1.do1', '32.hk1.dr1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 1492, -1, 9431, -1, 1491, -1], 'generators': [137, 2, 140, 32], 'label': '256.30836.16.hc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879513
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.go1.a1', '8.gu1.a1'], 'contains': ['32.eb1.a1', '32.ec1.b1', '32.ed1.a2', '32.ef1.b1', '32.eg1.a1', '32.ei1.b2', '32.ek1.a4', '32.hk1.f1', '32.hk1.g1', '32.hk1.u1', '32.hk1.x1', '32.hk1.bs1', '32.hk1.bv1', '32.hk1.dp1', '32.hk1.dq1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 1563, -1, 9431, -1, 1561, -1], 'generators': [1, 2, 140, 32], 'label': '256.30836.16.hc1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.b2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879514
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bk1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.p1.a1', '2.r1.a1'], 'contains': ['8.p1.a1', '8.s1.a1', '8.x1.a1', '8.bf1.a1', '8.bi1.a1', '8.ce1.a1', '8.ch1.a1', '8.gb1.a1', '8.gb1.b1'], 'core': '4.bk1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6793, 7657, 5317, 633, 6797, 7655, 5313, 634], 'generators': [1, 4, 64, 136], 'label': '256.30836.4.bk1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bk1.a1', 'normal_contained_in': ['2.b1.a1', '2.p1.a1', '2.r1.a1'], 'normal_contains': ['8.p1.a1', '8.s1.a1', '8.x1.a1', '8.bi1.a1', '8.bf1.a1', '8.ch1.a1', '8.ce1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bk1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879515
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.go1.b1', '8.gu1.a1'], 'contains': ['32.eb1.b1', '32.ec1.a1', '32.ed1.a2', '32.ef1.c1', '32.eg1.b1', '32.ei1.a1', '32.ek1.a3', '32.hk1.j1', '32.hk1.k1', '32.hk1.y1', '32.hk1.bb1', '32.hk1.dc1', '32.hk1.df1', '32.hk1.dt1', '32.hk1.du1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 1451, -1, 9431, -1, 1450, -1], 'generators': [129, 2, 4, 32], 'label': '256.30836.16.hc1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.c1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879516
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.go1.b1', '8.gu1.a1'], 'contains': ['32.eb1.b1', '32.ec1.a1', '32.ed1.a1', '32.ef1.c1', '32.eg1.b2', '32.ei1.a2', '32.ek1.a4', '32.hk1.i1', '32.hk1.l1', '32.hk1.z1', '32.hk1.ba1', '32.hk1.dd1', '32.hk1.de1', '32.hk1.ds1', '32.hk1.dv1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 1465, -1, 9431, -1, 1464, -1], 'generators': [9, 2, 4, 32], 'label': '256.30836.16.hc1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.c2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879517
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.go1.b1', '8.gu1.a1'], 'contains': ['32.eb1.b1', '32.ec1.b1', '32.ed1.a2', '32.ef1.d1', '32.eg1.b2', '32.ei1.b1', '32.ek1.a1', '32.hk1.n1', '32.hk1.o1', '32.hk1.bc1', '32.hk1.bf1', '32.hk1.dg1', '32.hk1.dj1', '32.hk1.dx1', '32.hk1.dy1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 2537, -1, 9431, -1, 2534, -1], 'generators': [9, 2, 140, 32], 'label': '256.30836.16.hc1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879518
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.go1.b1', '8.gu1.a1'], 'contains': ['32.eb1.b1', '32.ec1.b1', '32.ed1.a1', '32.ef1.d1', '32.eg1.b1', '32.ei1.b2', '32.ek1.a2', '32.hk1.m1', '32.hk1.p1', '32.hk1.bd1', '32.hk1.be1', '32.hk1.dh1', '32.hk1.di1', '32.hk1.dw1', '32.hk1.dz1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 2588, -1, 9431, -1, 2586, -1], 'generators': [129, 2, 140, 32], 'label': '256.30836.16.hc1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.d2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.d2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879519
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.go1.a1', '8.gu1.b1'], 'contains': ['32.eb1.c1', '32.ec1.c1', '32.ed1.b1', '32.ef1.a1', '32.eg1.a1', '32.ei1.a2', '32.ek1.a3', '32.hk1.bh1', '32.hk1.bi1', '32.hk1.bw1', '32.hk1.bz1', '32.hk1.cm1', '32.hk1.cp1', '32.hk1.ej1', '32.hk1.ek1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 749, -1, 9431, -1, 755, -1], 'generators': [1, 138, 4, 32], 'label': '256.30836.16.hc1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.e1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879520
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.go1.a1', '8.gu1.b1'], 'contains': ['32.eb1.c1', '32.ec1.c1', '32.ed1.b2', '32.ef1.a1', '32.eg1.a2', '32.ei1.a1', '32.ek1.a4', '32.hk1.bg1', '32.hk1.bj1', '32.hk1.bx1', '32.hk1.by1', '32.hk1.cn1', '32.hk1.co1', '32.hk1.ei1', '32.hk1.el1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 770, -1, 9431, -1, 776, -1], 'generators': [137, 138, 4, 32], 'label': '256.30836.16.hc1.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.e2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.e2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879521
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.go1.a1', '8.gu1.b1'], 'contains': ['32.eb1.c1', '32.ec1.d1', '32.ed1.b1', '32.ef1.b1', '32.eg1.a2', '32.ei1.b2', '32.ek1.a1', '32.hk1.bl1', '32.hk1.bm1', '32.hk1.ca1', '32.hk1.cd1', '32.hk1.cq1', '32.hk1.ct1', '32.hk1.en1', '32.hk1.eo1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 1604, -1, 9431, -1, 1602, -1], 'generators': [137, 138, 140, 32], 'label': '256.30836.16.hc1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.f1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879522
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.go1.a1', '8.gu1.b1'], 'contains': ['32.eb1.c1', '32.ec1.d1', '32.ed1.b2', '32.ef1.b1', '32.eg1.a1', '32.ei1.b1', '32.ek1.a2', '32.hk1.bk1', '32.hk1.bn1', '32.hk1.cb1', '32.hk1.cc1', '32.hk1.cr1', '32.hk1.cs1', '32.hk1.em1', '32.hk1.ep1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 1618, -1, 9431, -1, 1616, -1], 'generators': [1, 138, 140, 32], 'label': '256.30836.16.hc1.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.f2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.f2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879523
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.go1.b1', '8.gu1.b1'], 'contains': ['32.eb1.d1', '32.ec1.c1', '32.ed1.b2', '32.ef1.c1', '32.eg1.b1', '32.ei1.a2', '32.ek1.a1', '32.hk1.ce1', '32.hk1.ch1', '32.hk1.cv1', '32.hk1.cw1', '32.hk1.eb1', '32.hk1.ec1', '32.hk1.eq1', '32.hk1.et1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 1548, -1, 9431, -1, 1547, -1], 'generators': [129, 138, 4, 32], 'label': '256.30836.16.hc1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.g1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879524
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.go1.b1', '8.gu1.b1'], 'contains': ['32.eb1.d1', '32.ec1.c1', '32.ed1.b1', '32.ef1.c1', '32.eg1.b2', '32.ei1.a1', '32.ek1.a2', '32.hk1.cf1', '32.hk1.cg1', '32.hk1.cu1', '32.hk1.cx1', '32.hk1.ea1', '32.hk1.ed1', '32.hk1.er1', '32.hk1.es1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 1506, -1, 9431, -1, 1505, -1], 'generators': [9, 138, 4, 32], 'label': '256.30836.16.hc1.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.g2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.g2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879525
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.j1.a1', '128.j1.b1', '128.l1.a1', '128.l1.b1', '128.k1.a1', '128.k1.b1', '128.n1.a1', '128.n1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.g1.a1', '4.y1.a1', '4.z1.a1', '4.bd1.a1', '4.be1.a1', '4.ca1.a1', '4.cb1.a1', '4.ce1.a1', '4.cg1.a1', '4.ey1.a1', '4.ez1.a1', '4.fd1.a1', '4.fe1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5631, 6084, 7924, 4225, 5634, 6082, 7932, 4360], 'generators': [1, 2, 20, 64], 'label': '256.30836.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.g1.a1', '4.ce1.a1', '4.cg1.a1', '4.ca1.a1', '4.cb1.a1', '4.be1.a1', '4.bd1.a1', '4.z1.a1', '4.y1.a1', '4.ez1.a1', '4.ey1.a1', '4.fe1.a1', '4.fd1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879526
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bl1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.q1.a1', '2.r1.a1'], 'contains': ['8.p1.a1', '8.t1.a1', '8.y1.a1', '8.bg1.a1', '8.bj1.a1', '8.cf1.a1', '8.ci1.a1'], 'core': '4.bl1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6658, 5248, 5944, 4895, 6661, 5246, 5939, 4906], 'generators': [1, 4, 16], 'label': '256.30836.4.bl1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bl1.a1', 'normal_contained_in': ['2.c1.a1', '2.q1.a1', '2.r1.a1'], 'normal_contains': ['8.p1.a1', '8.t1.a1', '8.y1.a1', '8.bg1.a1', '8.bj1.a1', '8.cf1.a1', '8.ci1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bl1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879527
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.go1.b1', '8.gu1.b1'], 'contains': ['32.eb1.d1', '32.ec1.d1', '32.ed1.b2', '32.ef1.d1', '32.eg1.b2', '32.ei1.b2', '32.ek1.a3', '32.hk1.ci1', '32.hk1.cl1', '32.hk1.cz1', '32.hk1.da1', '32.hk1.ef1', '32.hk1.eg1', '32.hk1.eu1', '32.hk1.ex1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 2550, -1, 9431, -1, 2548, -1], 'generators': [9, 138, 140, 32], 'label': '256.30836.16.hc1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.h1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879528
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.hc1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.go1.b1', '8.gu1.b1'], 'contains': ['32.eb1.d1', '32.ec1.d1', '32.ed1.b1', '32.ef1.d1', '32.eg1.b1', '32.ei1.b1', '32.ek1.a4', '32.hk1.cj1', '32.hk1.ck1', '32.hk1.cy1', '32.hk1.db1', '32.hk1.ee1', '32.hk1.eh1', '32.hk1.ev1', '32.hk1.ew1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9426, -1, 2566, -1, 9431, -1, 2566, -1], 'generators': [129, 138, 140, 32], 'label': '256.30836.16.hc1.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hc1.h2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hc1.h2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879529
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.ha1.a1', '8.ha1.b1'], 'contains': ['32.em1.a1', '32.en1.a1', '32.eq1.a1', '32.fe1.a1', '32.fe1.b1', '32.fe1.c1', '32.fe1.d1', '32.gb1.a1', '32.gb1.b1', '32.gb1.c1', '32.gb1.d1', '32.hb1.a1', '32.hb1.b1', '32.hb1.c1', '32.hb1.d1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9293, -1, 3689, -1, 9298, -1, 3685, -1], 'generators': [1, 2, 8, 160], 'label': '256.30836.16.hd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hd1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879530
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.he1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.ha1.a1', '8.ha1.b1'], 'contains': ['32.em1.a1', '32.eo1.a1', '32.ep1.a1', '32.ff1.a1', '32.ff1.a2', '32.ff1.b1', '32.ff1.b2', '32.gc1.a1', '32.gc1.b1', '32.gc1.c1', '32.gc1.d1', '32.hc1.a1', '32.hc1.b1', '32.hc1.c1', '32.hc1.d1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9320, -1, 3528, -1, 9324, -1, 3526, -1], 'generators': [2, 4, 8, 160], 'label': '256.30836.16.he1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.he1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.he1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879531
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.ha1.a1', '8.hb1.a1'], 'contains': ['32.i1.a1', '32.em1.a1', '32.er1.a1', '32.fg1.a1', '32.fg1.c1', '32.gd1.a1', '32.gd1.c1', '32.hd1.a1', '32.hd1.b1', '32.hd1.e1', '32.hd1.f1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9452, -1, 4050, -1, 9457, -1, 4046, -1], 'generators': [5, 2, 8, 160], 'label': '256.30836.16.hf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.hf1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879532
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.ha1.b1', '8.hb1.b1'], 'contains': ['32.i1.b1', '32.em1.a1', '32.er1.a1', '32.fg1.b1', '32.fg1.d1', '32.gd1.b1', '32.gd1.d1', '32.hd1.c1', '32.hd1.d1', '32.hd1.g1', '32.hd1.h1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9452, -1, 3758, -1, 9457, -1, 3755, -1], 'generators': [133, 2, 8, 160], 'label': '256.30836.16.hf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.hf1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hf1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879533
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.hb1.a1', '8.hb1.b1'], 'contains': ['32.em1.a1', '32.eu1.a1', '32.fa1.a1', '32.fh1.a1', '32.fh1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5021, -1, 6197, -1, 5024, -1, 6192, -1], 'generators': [17, 2, 160], 'label': '256.30836.16.hg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.hg1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879534
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.hb1.a1', '8.hb1.b1'], 'contains': ['32.em1.a1', '32.ev1.a1', '32.ey1.a1', '32.ge1.a1', '32.ge1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8124, -1, 5487, -1, 8127, -1, 5483, -1], 'generators': [2, 20, 8], 'label': '256.30836.16.hh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.hh1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hh1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879535
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.ha1.a1', '8.hc1.a1'], 'contains': ['32.i1.a1', '32.en1.a1', '32.eo1.a1', '32.fi1.a1', '32.fi1.c1', '32.gf1.a1', '32.gf1.c1', '32.gf1.e1', '32.gf1.g1', '32.he1.a1', '32.he1.c1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9346, -1, 4064, -1, 9351, -1, 4060, -1], 'generators': [1, 4, 8, 160], 'label': '256.30836.16.hi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.hi1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hi1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879536
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.ha1.b1', '8.hc1.b1'], 'contains': ['32.i1.b1', '32.en1.a1', '32.eo1.a1', '32.fi1.b1', '32.fi1.d1', '32.gf1.b1', '32.gf1.d1', '32.gf1.f1', '32.gf1.h1', '32.he1.b1', '32.he1.d1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9346, -1, 3731, -1, 9351, -1, 3727, -1], 'generators': [129, 4, 8, 160], 'label': '256.30836.16.hi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.hi1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hi1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879537
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bm1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.q1.a1', '2.s1.a1'], 'contains': ['8.p1.a1', '8.u1.a1', '8.bb1.a1', '8.bh1.a1', '8.bl1.a1', '8.cg1.a1', '8.ck1.a1', '8.hc1.a1', '8.hc1.b1'], 'core': '4.bm1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7882, 5777, 8849, 124, 7886, 5775, 8841, 124], 'generators': [1, 66, 4, 128], 'label': '256.30836.4.bm1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bm1.a1', 'normal_contained_in': ['2.b1.a1', '2.q1.a1', '2.s1.a1'], 'normal_contains': ['8.p1.a1', '8.u1.a1', '8.bb1.a1', '8.bl1.a1', '8.bh1.a1', '8.ck1.a1', '8.cg1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bm1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879538
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.ha1.a1', '8.ha1.b1'], 'contains': ['32.en1.a1', '32.ep1.a1', '32.er1.a1', '32.fj1.a1', '32.fj1.a2', '32.fj1.b1', '32.fj1.b2', '32.gg1.a1', '32.gg1.a2', '32.gg1.b1', '32.gg1.b2', '32.hf1.a1', '32.hf1.b1', '32.hf1.c1', '32.hf1.d1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9479, -1, 3226, -1, 9484, -1, 3220, -1], 'generators': [1, 6, 8, 160], 'label': '256.30836.16.hj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hj1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879539
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.u1.a1', '8.hc1.a1', '8.hc1.b1'], 'contains': ['32.en1.a1', '32.et1.a1', '32.ew1.a1', '32.fk1.a1', '32.fk1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5161, -1, 8465, -1, 5163, -1, 8457, -1], 'generators': [1, 66, 160], 'label': '256.30836.16.hk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bm1.a1', 'old_label': '16.hk1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hk1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879540
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hl1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bb1.a1', '8.hc1.a1', '8.hc1.b1'], 'contains': ['32.en1.a1', '32.ez1.a1', '32.fd1.a1', '32.hg1.a1', '32.hg1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7757, -1, 8247, -1, 7761, -1, 8240, -1], 'generators': [1, 70, 160], 'label': '256.30836.16.hl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bm1.a1', 'old_label': '16.hl1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879541
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hm1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.ha1.a1', '8.ha1.b1'], 'contains': ['32.eo1.a1', '32.eq1.a1', '32.er1.a1', '32.fl1.a1', '32.fl1.a2', '32.fl1.a3', '32.fl1.a4', '32.gh1.a1', '32.gh1.b1', '32.gh1.c1', '32.gh1.d1', '32.hh1.a1', '32.hh1.a2', '32.hh1.b1', '32.hh1.b2'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9506, -1, 2990, -1, 9510, -1, 2984, -1], 'generators': [3, 4, 8, 160], 'label': '256.30836.16.hm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.hm1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879542
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hn1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bh1.a1', '8.hc1.a1', '8.hc1.b1'], 'contains': ['32.eo1.a1', '32.et1.a1', '32.ez1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7498, -1, 8205, -1, 7503, -1, 8198, -1], 'generators': [66, 4], 'label': '256.30836.16.hn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bh1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bm1.a1', 'old_label': '16.hn1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hn1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879543
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ho1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bl1.a1', '8.hc1.a1', '8.hc1.b1'], 'contains': ['32.eo1.a1', '32.ew1.a1', '32.fd1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5968, -1, 8224, -1, 5971, -1, 8217, -1], 'generators': [67, 4], 'label': '256.30836.16.ho1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bl1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bm1.a1', 'old_label': '16.ho1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ho1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879544
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bq1.a1', '8.ha1.a1', '8.hd1.a1'], 'contains': ['32.i1.a1', '32.ep1.a1', '32.eq1.a1', '32.fm1.a1', '32.fm1.a2', '32.gi1.a1', '32.gi1.b1', '32.hi1.a1', '32.hi1.c1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9267, -1, 4092, -1, 9271, -1, 4088, -1], 'generators': [5, 6, 8, 160], 'label': '256.30836.16.hp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.hp1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879545
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bq1.a1', '8.ha1.b1', '8.hd1.b1'], 'contains': ['32.i1.b1', '32.ep1.a1', '32.eq1.a1', '32.fm1.b1', '32.fm1.b2', '32.gi1.c1', '32.gi1.d1', '32.hi1.b1', '32.hi1.d1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9267, -1, 3157, -1, 9271, -1, 3151, -1], 'generators': [133, 6, 8, 160], 'label': '256.30836.16.hp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.hp1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hp1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879546
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.br1.a1', '8.hd1.a1', '8.hd1.b1'], 'contains': ['32.ep1.a1', '32.es1.a1', '32.fc1.a1', '32.hj1.a1', '32.hj1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6039, -1, 6959, -1, 6042, -1, 6953, -1], 'generators': [85, 6, 160], 'label': '256.30836.16.hq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.br1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.dh1.a1', 'old_label': '16.hq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879548
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bn1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.p1.a1', '2.s1.a1'], 'contains': ['8.p1.a1', '8.v1.a1', '8.z1.a1', '8.bk1.a1', '8.bm1.a1', '8.cj1.a1', '8.cl1.a1'], 'core': '4.bn1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7401, 8616, 5612, 901, 7405, 8613, 5608, 903], 'generators': [1, 18, 4], 'label': '256.30836.4.bn1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bn1.a1', 'normal_contained_in': ['2.c1.a1', '2.p1.a1', '2.s1.a1'], 'normal_contains': ['8.p1.a1', '8.v1.a1', '8.z1.a1', '8.bm1.a1', '8.bk1.a1', '8.cl1.a1', '8.cj1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bn1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879549
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cd1.a1', '8.hd1.a1', '8.he1.a1'], 'contains': ['32.i1.a1', '32.es1.a1', '32.fb1.a1', '32.fn1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3325, -1, 7871, -1, 3327, -1, 7864, -1], 'generators': [5, 86, 160], 'label': '256.30836.16.hs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.bc1.a1', 'old_label': '16.hs1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hs1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879550
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cd1.a1', '8.hd1.b1', '8.he1.b1'], 'contains': ['32.i1.b1', '32.es1.a1', '32.fb1.a1', '32.fn1.b1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3325, -1, 7848, -1, 3327, -1, 7841, -1], 'generators': [133, 86, 160], 'label': '256.30836.16.hs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.bc1.a1', 'old_label': '16.hs1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hs1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879551
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ht1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cg1.a1', '8.hc1.a1', '8.he1.a1'], 'contains': ['32.i1.a1', '32.et1.a1', '32.fd1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5204, -1, 8425, -1, 5207, -1, 8419, -1], 'generators': [5, 66], 'label': '256.30836.16.ht1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.q1.a1', 'old_label': '16.ht1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ht1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879552
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ht1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cg1.a1', '8.hc1.b1', '8.he1.b1'], 'contains': ['32.i1.b1', '32.et1.a1', '32.fd1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5204, -1, 8372, -1, 5207, -1, 8365, -1], 'generators': [133, 66], 'label': '256.30836.16.ht1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.q1.a1', 'old_label': '16.ht1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ht1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879553
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ci1.a1', '8.hb1.a1', '8.he1.a1'], 'contains': ['32.i1.a1', '32.eu1.a1', '32.ey1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5680, -1, 7294, -1, 5683, -1, 7288, -1], 'generators': [17, 20], 'label': '256.30836.16.hu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ci1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.l1.a1', 'old_label': '16.hu1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hu1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879554
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ci1.a1', '8.hb1.b1', '8.he1.b1'], 'contains': ['32.i1.b1', '32.eu1.a1', '32.ey1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5680, -1, 7275, -1, 5683, -1, 7268, -1], 'generators': [145, 20], 'label': '256.30836.16.hu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ci1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.l1.a1', 'old_label': '16.hu1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hu1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879555
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cj1.a1', '8.hb1.a1', '8.hf1.a1'], 'contains': ['32.i1.a1', '32.ev1.a1', '32.fa1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7911, -1, 6772, -1, 7915, -1, 6766, -1], 'generators': [5, 22], 'label': '256.30836.16.hv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cj1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '16.hv1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879556
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cj1.a1', '8.hb1.b1', '8.hf1.b1'], 'contains': ['32.i1.b1', '32.ev1.a1', '32.fa1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7911, -1, 6753, -1, 7915, -1, 6747, -1], 'generators': [133, 22], 'label': '256.30836.16.hv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cj1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '16.hv1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hv1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879557
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ck1.a1', '8.hc1.a1', '8.hf1.a1'], 'contains': ['32.i1.a1', '32.ew1.a1', '32.ez1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7405, -1, 7655, -1, 7409, -1, 7648, -1], 'generators': [5, 70], 'label': '256.30836.16.hw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ck1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.s1.a1', 'old_label': '16.hw1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879558
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ck1.a1', '8.hc1.b1', '8.hf1.b1'], 'contains': ['32.i1.b1', '32.ew1.a1', '32.ez1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7405, -1, 7485, -1, 7409, -1, 7478, -1], 'generators': [133, 70], 'label': '256.30836.16.hw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ck1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.s1.a1', 'old_label': '16.hw1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hw1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879559
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bo1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.r1.a1', '2.s1.a1'], 'contains': ['8.p1.a1', '8.w1.a1', '8.ba1.a1', '8.bn1.a1', '8.bp1.a1', '8.cm1.a1', '8.cn1.a1'], 'core': '4.bo1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8441, 1298, 5520, 5111, 8445, 1298, 5515, 5123], 'generators': [1, 4, 80], 'label': '256.30836.4.bo1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bo1.a1', 'normal_contained_in': ['2.a1.a1', '2.s1.a1', '2.r1.a1'], 'normal_contains': ['8.p1.a1', '8.ba1.a1', '8.w1.a1', '8.bp1.a1', '8.bn1.a1', '8.cm1.a1', '8.cn1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bo1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879560
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cm1.a1', '8.hd1.a1', '8.hf1.a1'], 'contains': ['32.i1.a1', '32.ex1.a1', '32.fc1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7369, -1, 6871, -1, 7372, -1, 6865, -1], 'generators': [5, 80], 'label': '256.30836.16.hx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cm1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.bb1.a1', 'old_label': '16.hx1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879561
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cm1.a1', '8.hd1.b1', '8.hf1.b1'], 'contains': ['32.i1.b1', '32.ex1.a1', '32.fc1.a1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7369, -1, 6999, -1, 7372, -1, 6994, -1], 'generators': [133, 80], 'label': '256.30836.16.hx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cm1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.bb1.a1', 'old_label': '16.hx1.b1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hx1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879562
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cp1.a1', '8.hd1.a1', '8.hd1.b1'], 'contains': ['32.eq1.a1', '32.es1.a1', '32.ex1.a1', '32.gj1.a1', '32.gj1.b1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6083, -1, 6732, -1, 6086, -1, 6726, -1], 'generators': [3, 80, 8], 'label': '256.30836.16.hy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.dh1.a1', 'old_label': '16.hy1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hy1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879563
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.hz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.da1.a1', '8.hd1.a1', '8.hd1.b1'], 'contains': ['32.eq1.a1', '32.fb1.a1', '32.fc1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6572, -1, 7061, -1, 6575, -1, 7055, -1], 'generators': [85, 86], 'label': '256.30836.16.hz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.da1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.dh1.a1', 'old_label': '16.hz1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.hz1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879564
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ia1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dg1.a1', '8.hb1.a1', '8.hb1.b1'], 'contains': ['32.er1.a1', '32.eu1.a1', '32.ev1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7978, -1, 6043, -1, 7982, -1, 6038, -1], 'generators': [17, 22], 'label': '256.30836.16.ia1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.ia1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ia1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879565
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ib1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dj1.a1', '8.hb1.a1', '8.hb1.b1'], 'contains': ['32.er1.a1', '32.ey1.a1', '32.fa1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7677, -1, 6063, -1, 7681, -1, 6057, -1], 'generators': [19, 20], 'label': '256.30836.16.ib1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dj1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.r1.a1', 'old_label': '16.ib1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ib1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879566
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ic1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.dp1.a1', '8.he1.a1', '8.he1.b1'], 'contains': ['32.es1.a1', '32.et1.a1', '32.eu1.a1', '32.fo1.a1', '32.fo1.a2'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2449, -1, 8541, -1, 2450, -1, 8534, -1], 'generators': [17, 66, 160], 'label': '256.30836.16.ic1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.dp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.ef1.a1', 'old_label': '16.ic1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ic1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879570
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bp1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.t1.a1', '2.u1.a1'], 'contains': ['8.q1.a1', '8.r1.a1', '8.ba1.a1', '8.br1.a1', '8.ca1.a1', '8.db1.a1', '8.dl1.a1', '8.gm1.a1', '8.gm1.b1', '8.gm1.c1', '8.gm1.d1'], 'core': '4.bp1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8083, 7465, 5156, 9680, 8087, 7463, 5152, 9701], 'generators': [1, 82, 84, 32], 'label': '256.30836.4.bp1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bp1.a1', 'normal_contained_in': ['2.a1.a1', '2.u1.a1', '2.t1.a1'], 'normal_contains': ['8.q1.a1', '8.r1.a1', '8.ba1.a1', '8.br1.a1', '8.ca1.a1', '8.db1.a1', '8.dl1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bp1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879571
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ig1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.ez1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.ez1.a1', '8.hf1.a1', '8.hf1.b1'], 'contains': ['32.ev1.a1', '32.ew1.a1', '32.fc1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7467, -1, 7078, -1, 7471, -1, 7072, -1], 'generators': [85, 22], 'label': '256.30836.16.ig1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.ez1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.er1.a1', 'old_label': '16.ig1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ig1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879572
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ih1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fa1.a1', '8.hf1.a1', '8.hf1.b1'], 'contains': ['32.ev1.a1', '32.ex1.a1', '32.ez1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7945, -1, 7043, -1, 7948, -1, 7038, -1], 'generators': [70, 80], 'label': '256.30836.16.ih1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fa1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.er1.a1', 'old_label': '16.ih1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ih1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879573
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ii1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fe1.a1', '8.hf1.a1', '8.hf1.b1'], 'contains': ['32.ew1.a1', '32.ex1.a1', '32.fa1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6001, -1, 7242, -1, 6004, -1, 7235, -1], 'generators': [67, 80], 'label': '256.30836.16.ii1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fe1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.er1.a1', 'old_label': '16.ii1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ii1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879574
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ij1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fx1.a1', '8.hf1.a1', '8.hf1.b1'], 'contains': ['32.ez1.a1', '32.fa1.a1', '32.fc1.a1'], 'core': '64.f1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7439, -1, 7257, -1, 7443, -1, 7251, -1], 'generators': [85, 70], 'label': '256.30836.16.ij1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.fx1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.er1.a1', 'old_label': '16.ij1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ij1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879575
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.go1.a1', '8.ha1.a1'], 'contains': ['32.fe1.a1', '32.ff1.a1', '32.fg1.a1', '32.fi1.a1', '32.fj1.a1', '32.fl1.a1', '32.fm1.a1', '32.hk1.a1', '32.hk1.g1', '32.hk1.q1', '32.hk1.w1', '32.hk1.bi1', '32.hk1.bk1', '32.hk1.co1', '32.hk1.cq1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 2021, -1, 9537, -1, 2019, -1], 'generators': [1, 2, 4, 168], 'label': '256.30836.16.ik1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.a1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879576
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.go1.a1', '8.ha1.a1'], 'contains': ['32.fe1.a1', '32.ff1.a2', '32.fg1.a1', '32.fi1.a1', '32.fj1.a2', '32.fl1.a2', '32.fm1.a2', '32.hk1.c1', '32.hk1.e1', '32.hk1.s1', '32.hk1.u1', '32.hk1.bg1', '32.hk1.bm1', '32.hk1.cm1', '32.hk1.cs1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 2035, -1, 9537, -1, 2033, -1], 'generators': [1, 130, 4, 168], 'label': '256.30836.16.ik1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.a2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879577
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.go1.a1', '8.ha1.b1'], 'contains': ['32.fe1.a1', '32.ff1.a1', '32.fg1.b1', '32.fi1.b1', '32.fj1.a2', '32.fl1.a3', '32.fm1.b1', '32.hk1.b1', '32.hk1.h1', '32.hk1.r1', '32.hk1.x1', '32.hk1.bj1', '32.hk1.bl1', '32.hk1.cp1', '32.hk1.cr1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 1138, -1, 9537, -1, 1137, -1], 'generators': [33, 2, 4, 168], 'label': '256.30836.16.ik1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879578
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.go1.a1', '8.ha1.b1'], 'contains': ['32.fe1.a1', '32.ff1.a2', '32.fg1.b1', '32.fi1.b1', '32.fj1.a1', '32.fl1.a4', '32.fm1.b2', '32.hk1.d1', '32.hk1.f1', '32.hk1.t1', '32.hk1.v1', '32.hk1.bh1', '32.hk1.bn1', '32.hk1.cn1', '32.hk1.ct1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 1312, -1, 9537, -1, 1311, -1], 'generators': [33, 130, 4, 168], 'label': '256.30836.16.ik1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.b2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879579
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.go1.b1', '8.ha1.a1'], 'contains': ['32.fe1.b1', '32.ff1.a1', '32.fg1.a1', '32.fi1.c1', '32.fj1.b1', '32.fl1.a4', '32.fm1.a2', '32.hk1.i1', '32.hk1.o1', '32.hk1.y1', '32.hk1.be1', '32.hk1.cg1', '32.hk1.ci1', '32.hk1.cw1', '32.hk1.cy1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 2638, -1, 9537, -1, 2640, -1], 'generators': [161, 2, 4, 168], 'label': '256.30836.16.ik1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.c1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879580
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.go1.b1', '8.ha1.a1'], 'contains': ['32.fe1.b1', '32.ff1.a2', '32.fg1.a1', '32.fi1.c1', '32.fj1.b2', '32.fl1.a3', '32.fm1.a1', '32.hk1.k1', '32.hk1.m1', '32.hk1.ba1', '32.hk1.bc1', '32.hk1.ce1', '32.hk1.ck1', '32.hk1.cu1', '32.hk1.da1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 2865, -1, 9537, -1, 2859, -1], 'generators': [161, 130, 4, 168], 'label': '256.30836.16.ik1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.c2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879581
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bq1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.t1.a1', '2.v1.a1'], 'contains': ['8.q1.a1', '8.s1.a1', '8.bb1.a1', '8.bs1.a1', '8.bv1.a1', '8.dc1.a1', '8.df1.a1', '8.gn1.a1', '8.gn1.b1', '8.gn1.c1', '8.gn1.d1'], 'core': '4.bq1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8743, 7981, 8779, 8160, 8747, 7979, 8772, 8178], 'generators': [1, 6, 64, 32], 'label': '256.30836.4.bq1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bq1.a1', 'normal_contained_in': ['2.b1.a1', '2.t1.a1', '2.v1.a1'], 'normal_contains': ['8.q1.a1', '8.s1.a1', '8.bb1.a1', '8.bv1.a1', '8.bs1.a1', '8.df1.a1', '8.dc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bq1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879582
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.go1.b1', '8.ha1.b1'], 'contains': ['32.fe1.b1', '32.ff1.a1', '32.fg1.b1', '32.fi1.d1', '32.fj1.b2', '32.fl1.a2', '32.fm1.b2', '32.hk1.j1', '32.hk1.p1', '32.hk1.z1', '32.hk1.bf1', '32.hk1.ch1', '32.hk1.cj1', '32.hk1.cx1', '32.hk1.cz1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 1979, -1, 9537, -1, 1977, -1], 'generators': [129, 2, 4, 168], 'label': '256.30836.16.ik1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879583
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.go1.b1', '8.ha1.b1'], 'contains': ['32.fe1.b1', '32.ff1.a2', '32.fg1.b1', '32.fi1.d1', '32.fj1.b1', '32.fl1.a1', '32.fm1.b1', '32.hk1.l1', '32.hk1.n1', '32.hk1.bb1', '32.hk1.bd1', '32.hk1.cf1', '32.hk1.cl1', '32.hk1.cv1', '32.hk1.db1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 1993, -1, 9537, -1, 1991, -1], 'generators': [129, 130, 4, 168], 'label': '256.30836.16.ik1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.d2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.d2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879598
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.in1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.hh1.c1', '8.hh1.d1'], 'contains': ['32.j1.b1', '32.ft1.a1', '32.fz1.a1', '32.gn1.b1', '32.gn1.c1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5802, -1, 4654, -1, 5805, -1, 4650, -1], 'generators': [81, 130, 160], 'label': '256.30836.16.in1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.in1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.in1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879584
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.go1.a1', '8.ha1.a1'], 'contains': ['32.fe1.c1', '32.ff1.b1', '32.fg1.c1', '32.fi1.a1', '32.fj1.a1', '32.fl1.a3', '32.fm1.a2', '32.hk1.bq1', '32.hk1.bs1', '32.hk1.bw1', '32.hk1.cc1', '32.hk1.dm1', '32.hk1.do1', '32.hk1.ei1', '32.hk1.eo1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 1701, -1, 9537, -1, 1700, -1], 'generators': [1, 34, 4, 168], 'label': '256.30836.16.ik1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.e1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879585
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.go1.a1', '8.ha1.a1'], 'contains': ['32.fe1.c1', '32.ff1.b2', '32.fg1.c1', '32.fi1.a1', '32.fj1.a2', '32.fl1.a4', '32.fm1.a1', '32.hk1.bo1', '32.hk1.bu1', '32.hk1.by1', '32.hk1.ca1', '32.hk1.dk1', '32.hk1.dq1', '32.hk1.ek1', '32.hk1.em1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 1687, -1, 9537, -1, 1686, -1], 'generators': [1, 162, 4, 168], 'label': '256.30836.16.ik1.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.e2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.e2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879586
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.go1.a1', '8.ha1.b1'], 'contains': ['32.fe1.c1', '32.ff1.b1', '32.fg1.d1', '32.fi1.b1', '32.fj1.a2', '32.fl1.a1', '32.fm1.b2', '32.hk1.br1', '32.hk1.bt1', '32.hk1.bx1', '32.hk1.cd1', '32.hk1.dn1', '32.hk1.dp1', '32.hk1.ej1', '32.hk1.ep1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 923, -1, 9537, -1, 922, -1], 'generators': [33, 34, 4, 168], 'label': '256.30836.16.ik1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.f1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879587
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.go1.a1', '8.ha1.b1'], 'contains': ['32.fe1.c1', '32.ff1.b2', '32.fg1.d1', '32.fi1.b1', '32.fj1.a1', '32.fl1.a2', '32.fm1.b1', '32.hk1.bp1', '32.hk1.bv1', '32.hk1.bz1', '32.hk1.cb1', '32.hk1.dl1', '32.hk1.dr1', '32.hk1.el1', '32.hk1.en1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 895, -1, 9537, -1, 894, -1], 'generators': [33, 162, 4, 168], 'label': '256.30836.16.ik1.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.f2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.f2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879588
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.go1.b1', '8.ha1.a1'], 'contains': ['32.fe1.d1', '32.ff1.b1', '32.fg1.c1', '32.fi1.c1', '32.fj1.b1', '32.fl1.a2', '32.fm1.a1', '32.hk1.de1', '32.hk1.dg1', '32.hk1.du1', '32.hk1.dw1', '32.hk1.ea1', '32.hk1.eg1', '32.hk1.eq1', '32.hk1.ew1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 2604, -1, 9537, -1, 2602, -1], 'generators': [161, 34, 4, 168], 'label': '256.30836.16.ik1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.g1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879589
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.go1.b1', '8.ha1.a1'], 'contains': ['32.fe1.d1', '32.ff1.b2', '32.fg1.c1', '32.fi1.c1', '32.fj1.b2', '32.fl1.a1', '32.fm1.a2', '32.hk1.dc1', '32.hk1.di1', '32.hk1.ds1', '32.hk1.dy1', '32.hk1.ec1', '32.hk1.ee1', '32.hk1.es1', '32.hk1.eu1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 2847, -1, 9537, -1, 2842, -1], 'generators': [161, 162, 4, 168], 'label': '256.30836.16.ik1.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.g2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.g2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879590
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.go1.b1', '8.ha1.b1'], 'contains': ['32.fe1.d1', '32.ff1.b1', '32.fg1.d1', '32.fi1.d1', '32.fj1.b2', '32.fl1.a4', '32.fm1.b1', '32.hk1.df1', '32.hk1.dh1', '32.hk1.dv1', '32.hk1.dx1', '32.hk1.eb1', '32.hk1.eh1', '32.hk1.er1', '32.hk1.ex1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 1660, -1, 9537, -1, 1658, -1], 'generators': [129, 34, 4, 168], 'label': '256.30836.16.ik1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.h1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879591
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.ik1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.go1.b1', '8.ha1.b1'], 'contains': ['32.fe1.d1', '32.ff1.b2', '32.fg1.d1', '32.fi1.d1', '32.fj1.b1', '32.fl1.a3', '32.fm1.b2', '32.hk1.dd1', '32.hk1.dj1', '32.hk1.dt1', '32.hk1.dz1', '32.hk1.ed1', '32.hk1.ef1', '32.hk1.et1', '32.hk1.ev1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9532, -1, 1673, -1, 9537, -1, 1672, -1], 'generators': [129, 162, 4, 168], 'label': '256.30836.16.ik1.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.ik1.h2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ik1.h2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879592
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.br1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.u1.a1', '2.v1.a1'], 'contains': ['8.q1.a1', '8.t1.a1', '8.v1.a1', '8.bt1.a1', '8.bw1.a1', '8.dd1.a1', '8.dg1.a1'], 'core': '4.br1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7830, 7536, 5558, 7395, 7834, 7533, 5553, 7412], 'generators': [1, 6, 16], 'label': '256.30836.4.br1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.br1.a1', 'normal_contained_in': ['2.c1.a1', '2.u1.a1', '2.v1.a1'], 'normal_contains': ['8.q1.a1', '8.t1.a1', '8.v1.a1', '8.bt1.a1', '8.bw1.a1', '8.dd1.a1', '8.dg1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.br1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.br1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879593
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.il1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.hg1.a1', '8.hg1.b1'], 'contains': ['32.j1.a1', '32.fp1.a1', '32.fq1.a1', '32.gc1.a1', '32.gc1.b1', '32.gl1.a1', '32.gl1.d1', '32.gu1.a1', '32.gu1.b1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9798, -1, 3675, -1, 9803, -1, 3671, -1], 'generators': [2, 4, 136, 160], 'label': '256.30836.16.il1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.il1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.il1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879594
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.il1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.hg1.c1', '8.hg1.d1'], 'contains': ['32.j1.b1', '32.fp1.a1', '32.fq1.a1', '32.gc1.c1', '32.gc1.d1', '32.gl1.b1', '32.gl1.c1', '32.gu1.c1', '32.gu1.d1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9798, -1, 3703, -1, 9803, -1, 3699, -1], 'generators': [130, 4, 136, 160], 'label': '256.30836.16.il1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.il1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.il1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879595
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.im1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.hg1.a1', '8.hg1.b1'], 'contains': ['32.j1.a1', '32.fr1.a1', '32.fs1.a1', '32.gd1.a1', '32.gd1.b1', '32.gm1.a1', '32.gm1.d1', '32.gv1.a1', '32.gv1.b1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9851, -1, 3445, -1, 9856, -1, 3446, -1], 'generators': [5, 2, 136, 160], 'label': '256.30836.16.im1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.im1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.im1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879596
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.im1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.hg1.c1', '8.hg1.d1'], 'contains': ['32.j1.b1', '32.fr1.a1', '32.fs1.a1', '32.gd1.c1', '32.gd1.d1', '32.gm1.b1', '32.gm1.c1', '32.gv1.c1', '32.gv1.d1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9851, -1, 3661, -1, 9856, -1, 3658, -1], 'generators': [5, 130, 136, 160], 'label': '256.30836.16.im1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.im1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.im1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879597
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.in1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.hh1.a1', '8.hh1.b1'], 'contains': ['32.j1.a1', '32.ft1.a1', '32.fz1.a1', '32.gn1.a1', '32.gn1.d1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5802, -1, 4573, -1, 5805, -1, 4570, -1], 'generators': [81, 2, 160], 'label': '256.30836.16.in1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.in1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.in1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879600
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.io1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.hi1.c1', '8.hi1.d1'], 'contains': ['32.j1.b1', '32.fu1.a1', '32.fx1.a1', '32.ge1.b1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8482, -1, 4744, -1, 8486, -1, 4740, -1], 'generators': [130, 20, 136], 'label': '256.30836.16.io1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.io1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.io1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879601
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ip1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.hi1.a1', '8.hi1.b1'], 'contains': ['32.j1.a1', '32.fv1.a1', '32.ga1.a1', '32.go1.a1', '32.go1.d1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6705, -1, 4809, -1, 6708, -1, 4805, -1], 'generators': [21, 2, 160], 'label': '256.30836.16.ip1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.ip1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ip1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879602
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ip1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.hi1.c1', '8.hi1.d1'], 'contains': ['32.j1.b1', '32.fv1.a1', '32.ga1.a1', '32.go1.b1', '32.go1.c1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6705, -1, 4836, -1, 6708, -1, 4831, -1], 'generators': [21, 130, 160], 'label': '256.30836.16.ip1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.ip1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ip1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879603
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bs1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.u1.a1', '2.w1.a1'], 'contains': ['8.q1.a1', '8.u1.a1', '8.x1.a1', '8.bu1.a1', '8.bx1.a1', '8.de1.a1', '8.dh1.a1', '8.gr1.a1', '8.gr1.b1'], 'core': '4.bs1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1159, 8323, 5705, 1822, 1159, 8319, 5700, 1826], 'generators': [1, 66, 68, 128], 'label': '256.30836.4.bs1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bs1.a1', 'normal_contained_in': ['2.b1.a1', '2.u1.a1', '2.w1.a1'], 'normal_contains': ['8.q1.a1', '8.u1.a1', '8.x1.a1', '8.bx1.a1', '8.bu1.a1', '8.dh1.a1', '8.de1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bs1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879604
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.hh1.a1', '8.hh1.b1'], 'contains': ['32.j1.a1', '32.fw1.a1', '32.fy1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7838, -1, 4345, -1, 7842, -1, 4341, -1], 'generators': [2, 80], 'label': '256.30836.16.iq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.iq1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879605
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.hh1.c1', '8.hh1.d1'], 'contains': ['32.j1.b1', '32.fw1.a1', '32.fy1.a1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7838, -1, 4383, -1, 7842, -1, 4379, -1], 'generators': [130, 80], 'label': '256.30836.16.iq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.iq1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iq1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879606
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ir1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.hg1.a1', '8.hg1.c1'], 'contains': ['32.k1.a1', '32.fp1.a1', '32.fr1.a1', '32.gf1.a1', '32.gf1.b1', '32.gf1.c1', '32.gf1.d1', '32.gp1.a1', '32.gp1.a2', '32.gw1.a1', '32.gw1.d1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9825, -1, 3841, -1, 9830, -1, 3838, -1], 'generators': [1, 4, 136, 160], 'label': '256.30836.16.ir1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.ir1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ir1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879607
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ir1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '8.hg1.b1', '8.hg1.d1'], 'contains': ['32.k1.b1', '32.fp1.a1', '32.fr1.a1', '32.gf1.e1', '32.gf1.f1', '32.gf1.g1', '32.gf1.h1', '32.gp1.b1', '32.gp1.b2', '32.gw1.b1', '32.gw1.c1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9825, -1, 3924, -1, 9830, -1, 3921, -1], 'generators': [129, 4, 136, 160], 'label': '256.30836.16.ir1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.ir1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ir1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879608
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.is1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.hg1.a1', '8.hg1.c1'], 'contains': ['32.k1.a1', '32.fq1.a1', '32.fs1.a1', '32.gg1.a1', '32.gg1.a2', '32.gq1.a1', '32.gq1.a2', '32.gx1.a1', '32.gx1.b1', '32.gx1.g1', '32.gx1.h1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9879, -1, 3869, -1, 9883, -1, 3866, -1], 'generators': [1, 6, 136, 160], 'label': '256.30836.16.is1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.is1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.is1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879609
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.is1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '8.hg1.b1', '8.hg1.d1'], 'contains': ['32.k1.b1', '32.fq1.a1', '32.fs1.a1', '32.gg1.b1', '32.gg1.b2', '32.gq1.b1', '32.gq1.b2', '32.gx1.c1', '32.gx1.d1', '32.gx1.e1', '32.gx1.f1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9879, -1, 4009, -1, 9883, -1, 4005, -1], 'generators': [129, 6, 136, 160], 'label': '256.30836.16.is1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.is1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.is1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879610
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.it1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.hh1.a1', '8.hh1.c1'], 'contains': ['32.k1.a1', '32.ft1.a1', '32.fy1.a1', '32.gy1.a1', '32.gy1.d1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5890, -1, 4485, -1, 5893, -1, 4481, -1], 'generators': [1, 82, 160], 'label': '256.30836.16.it1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.it1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.it1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879611
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.it1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.r1.a1', '8.hh1.b1', '8.hh1.d1'], 'contains': ['32.k1.b1', '32.ft1.a1', '32.fy1.a1', '32.gy1.b1', '32.gy1.c1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5890, -1, 4531, -1, 5893, -1, 4527, -1], 'generators': [129, 82, 160], 'label': '256.30836.16.it1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.it1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.it1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879612
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '8.hi1.a1', '8.hi1.c1'], 'contains': ['32.k1.a1', '32.fu1.a1', '32.fv1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8439, -1, 4614, -1, 8443, -1, 4610, -1], 'generators': [1, 22], 'label': '256.30836.16.iu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.iu1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iu1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879613
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '8.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.v1.a1', '8.hi1.b1', '8.hi1.d1'], 'contains': ['32.k1.b1', '32.fu1.a1', '32.fv1.a1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8439, -1, 4721, -1, 8443, -1, 4717, -1], 'generators': [129, 22], 'label': '256.30836.16.iu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.iu1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iu1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879614
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bt1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.v1.a1', '2.w1.a1'], 'contains': ['8.q1.a1', '8.w1.a1', '8.bc1.a1', '8.by1.a1', '8.cb1.a1', '8.di1.a1', '8.dm1.a1'], 'core': '4.bt1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7556, 2045, 5677, 8281, 7559, 2044, 5673, 8299], 'generators': [1, 6, 80], 'label': '256.30836.4.bt1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bt1.a1', 'normal_contained_in': ['2.a1.a1', '2.w1.a1', '2.v1.a1'], 'normal_contains': ['8.q1.a1', '8.bc1.a1', '8.w1.a1', '8.by1.a1', '8.cb1.a1', '8.dm1.a1', '8.di1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bt1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879615
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '8.hh1.a1', '8.hh1.c1'], 'contains': ['32.k1.a1', '32.fw1.a1', '32.fz1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7875, -1, 4364, -1, 7878, -1, 4360, -1], 'generators': [1, 80], 'label': '256.30836.16.iv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.iv1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iv1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879616
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.w1.a1', '8.hh1.b1', '8.hh1.d1'], 'contains': ['32.k1.b1', '32.fw1.a1', '32.fz1.a1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7875, -1, 4421, -1, 7878, -1, 4417, -1], 'generators': [129, 80], 'label': '256.30836.16.iv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.iv1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iv1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879619
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ix1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.hg1.a1', '8.hg1.d1'], 'contains': ['32.l1.a1', '32.fp1.a1', '32.fs1.a1', '32.gh1.a1', '32.gh1.c1', '32.gr1.a1', '32.gr1.a2', '32.gz1.a1', '32.gz1.b1'], 'core': '32.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9932, -1, 3855, -1, 9936, -1, 3852, -1], 'generators': [3, 4, 136, 160], 'label': '256.30836.16.ix1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.ix1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ix1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879620
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ix1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bd1.a1', '8.hg1.b1', '8.hg1.c1'], 'contains': ['32.l1.b1', '32.fp1.a1', '32.fs1.a1', '32.gh1.b1', '32.gh1.d1', '32.gr1.b1', '32.gr1.b2', '32.gz1.c1', '32.gz1.d1'], 'core': '32.l1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9932, -1, 2215, -1, 9936, -1, 2213, -1], 'generators': [131, 4, 136, 160], 'label': '256.30836.16.ix1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.ix1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ix1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879621
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bq1.a1', '8.hg1.a1', '8.hg1.d1'], 'contains': ['32.l1.a1', '32.fq1.a1', '32.fr1.a1', '32.gi1.a1', '32.gi1.c1', '32.gs1.a1', '32.gs1.a2', '32.ha1.a1', '32.ha1.c1'], 'core': '32.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9772, -1, 3800, -1, 9777, -1, 3796, -1], 'generators': [5, 6, 136, 160], 'label': '256.30836.16.iy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.iy1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iy1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879622
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iy1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.bq1.a1', '8.hg1.b1', '8.hg1.c1'], 'contains': ['32.l1.b1', '32.fq1.a1', '32.fr1.a1', '32.gi1.b1', '32.gi1.d1', '32.gs1.b1', '32.gs1.b2', '32.ha1.b1', '32.ha1.d1'], 'core': '32.l1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9772, -1, 2201, -1, 9777, -1, 2200, -1], 'generators': [133, 6, 136, 160], 'label': '256.30836.16.iy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.iy1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iy1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879623
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cp1.a1', '8.hh1.a1', '8.hh1.d1'], 'contains': ['32.l1.a1', '32.ft1.a1', '32.fw1.a1', '32.gj1.a1'], 'core': '32.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6657, -1, 4508, -1, 6660, -1, 4504, -1], 'generators': [3, 80, 136], 'label': '256.30836.16.iz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.iz1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iz1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879624
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.iz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cp1.a1', '8.hh1.b1', '8.hh1.c1'], 'contains': ['32.l1.b1', '32.ft1.a1', '32.fw1.a1', '32.gj1.b1'], 'core': '32.l1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6657, -1, 4442, -1, 6660, -1, 4438, -1], 'generators': [131, 80, 136], 'label': '256.30836.16.iz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cp1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.iz1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.iz1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879625
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bu1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.t1.a1', '2.w1.a1'], 'contains': ['8.q1.a1', '8.y1.a1', '8.z1.a1', '8.bz1.a1', '8.cc1.a1', '8.dj1.a1', '8.dk1.a1'], 'core': '4.bu1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7592, 9084, 5869, 8497, 7596, 9081, 5864, 8516], 'generators': [1, 18, 20], 'label': '256.30836.4.bu1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bu1.a1', 'normal_contained_in': ['2.c1.a1', '2.t1.a1', '2.w1.a1'], 'normal_contains': ['8.q1.a1', '8.y1.a1', '8.z1.a1', '8.cc1.a1', '8.bz1.a1', '8.dk1.a1', '8.dj1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bu1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879626
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ja1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cu1.a1', '8.hi1.a1', '8.hi1.d1'], 'contains': ['32.l1.a1', '32.fu1.a1', '32.ga1.a1'], 'core': '32.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8365, -1, 4702, -1, 8369, -1, 4698, -1], 'generators': [21, 22], 'label': '256.30836.16.ja1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cu1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.ja1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ja1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879627
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.ja1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cu1.a1', '8.hi1.b1', '8.hi1.c1'], 'contains': ['32.l1.b1', '32.fu1.a1', '32.ga1.a1'], 'core': '32.l1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8365, -1, 4552, -1, 8369, -1, 4548, -1], 'generators': [149, 22], 'label': '256.30836.16.ja1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cu1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.ja1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.ja1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879628
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.jb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cv1.a1', '8.hi1.a1', '8.hi1.d1'], 'contains': ['32.l1.a1', '32.fv1.a1', '32.fx1.a1'], 'core': '32.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8328, -1, 4786, -1, 8333, -1, 4782, -1], 'generators': [3, 20], 'label': '256.30836.16.jb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cv1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.jb1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879629
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.jb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cv1.a1', '8.hi1.b1', '8.hi1.c1'], 'contains': ['32.l1.b1', '32.fv1.a1', '32.fx1.a1'], 'core': '32.l1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8328, -1, 4594, -1, 8333, -1, 4591, -1], 'generators': [131, 20], 'label': '256.30836.16.jb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cv1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.jb1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jb1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 30879630
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.jc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cy1.a1', '8.hh1.a1', '8.hh1.d1'], 'contains': ['32.l1.a1', '32.fy1.a1', '32.fz1.a1'], 'core': '32.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7181, -1, 4464, -1, 7184, -1, 4460, -1], 'generators': [81, 82], 'label': '256.30836.16.jc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cy1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.jc1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879631
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '16.jc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2048, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.cy1.a1', '8.hh1.b1', '8.hh1.c1'], 'contains': ['32.l1.b1', '32.fy1.a1', '32.fz1.a1'], 'core': '32.l1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7181, -1, 4402, -1, 7184, -1, 4398, -1], 'generators': [209, 82], 'label': '256.30836.16.jc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.cy1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.jc1.b1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jc1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879632
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.ha1.a1', '8.hg1.a1'], 'contains': ['32.gb1.a1', '32.gc1.a1', '32.gd1.a1', '32.gf1.a1', '32.gg1.a1', '32.gh1.a1', '32.gi1.a1', '32.hk1.a1', '32.hk1.c1', '32.hk1.y1', '32.hk1.ba1', '32.hk1.bw1', '32.hk1.by1', '32.hk1.eq1', '32.hk1.es1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 2906, -1, 9963, -1, 2901, -1], 'generators': [1, 2, 4, 160], 'label': '256.30836.16.jd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879633
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.ha1.b1', '8.hg1.a1'], 'contains': ['32.gb1.a1', '32.gc1.a1', '32.gd1.b1', '32.gf1.b1', '32.gg1.a2', '32.gh1.a1', '32.gi1.c1', '32.hk1.b1', '32.hk1.d1', '32.hk1.z1', '32.hk1.bb1', '32.hk1.bx1', '32.hk1.bz1', '32.hk1.er1', '32.hk1.et1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 1826, -1, 9963, -1, 1825, -1], 'generators': [137, 2, 4, 160], 'label': '256.30836.16.jd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879634
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.ha1.a1', '8.hg1.a1'], 'contains': ['32.gb1.a1', '32.gc1.b1', '32.gd1.a1', '32.gf1.c1', '32.gg1.a2', '32.gh1.c1', '32.gi1.a1', '32.hk1.e1', '32.hk1.g1', '32.hk1.bc1', '32.hk1.be1', '32.hk1.ca1', '32.hk1.cc1', '32.hk1.eu1', '32.hk1.ew1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 3338, -1, 9963, -1, 3331, -1], 'generators': [137, 2, 140, 160], 'label': '256.30836.16.jd1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879635
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.ha1.b1', '8.hg1.a1'], 'contains': ['32.gb1.a1', '32.gc1.b1', '32.gd1.b1', '32.gf1.d1', '32.gg1.a1', '32.gh1.c1', '32.gi1.c1', '32.hk1.f1', '32.hk1.h1', '32.hk1.bd1', '32.hk1.bf1', '32.hk1.cb1', '32.hk1.cd1', '32.hk1.ev1', '32.hk1.ex1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 2892, -1, 9963, -1, 2887, -1], 'generators': [1, 2, 140, 160], 'label': '256.30836.16.jd1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879636
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.j1.a1', '128.j1.b1', '128.l1.a1', '128.l1.b1', '128.k1.a1', '128.k1.b1', '128.n1.a1', '128.n1.b1', '128.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.f1.a1', '4.g1.a1', '4.ba1.a1', '4.bb1.a1', '4.bf1.a1', '4.bg1.a1', '4.cc1.a1', '4.cd1.a1', '4.cj1.a1', '4.ck1.a1', '4.fb1.a1', '4.fc1.a1', '4.ff1.a1', '4.fg1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3214, 8103, 7209, 7545, 3215, 8051, 7202, 7561], 'generators': [1, 2, 68, 16], 'label': '256.30836.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.f1.a1', '4.g1.a1', '4.cc1.a1', '4.cd1.a1', '4.cj1.a1', '4.ck1.a1', '4.bb1.a1', '4.ba1.a1', '4.bg1.a1', '4.bf1.a1', '4.fc1.a1', '4.fb1.a1', '4.fg1.a1', '4.ff1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879637
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bv1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.d1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.m1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.j1', '64.dk1.l1', '64.dk1.k1', '64.dk1.i1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.e1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.f2', '64.do1.h2', '64.do1.g1', '64.do1.e1', '64.do1.g2', '64.do1.e2', '64.do1.f1', '64.do1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.p1.a1', '2.t1.a1'], 'contains': ['8.r1.a1', '8.s1.a1', '8.z1.a1', '8.dn1.a1', '8.dq1.a1', '8.ea1.a1', '8.et1.a1'], 'core': '4.bv1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1935, 8733, 7587, 7351, 1936, 8730, 7581, 7367], 'generators': [1, 18, 64], 'label': '256.30836.4.bv1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bv1.a1', 'normal_contained_in': ['2.d1.a1', '2.p1.a1', '2.t1.a1'], 'normal_contains': ['8.r1.a1', '8.s1.a1', '8.z1.a1', '8.dq1.a1', '8.dn1.a1', '8.et1.a1', '8.ea1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bv1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879638
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.ha1.a1', '8.hg1.b1'], 'contains': ['32.gb1.b1', '32.gc1.a1', '32.gd1.a1', '32.gf1.e1', '32.gg1.b1', '32.gh1.b1', '32.gi1.b1', '32.hk1.i1', '32.hk1.k1', '32.hk1.q1', '32.hk1.s1', '32.hk1.ea1', '32.hk1.ec1', '32.hk1.ei1', '32.hk1.ek1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 1798, -1, 9963, -1, 1797, -1], 'generators': [9, 2, 4, 160], 'label': '256.30836.16.jd1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.e1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879639
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.ha1.b1', '8.hg1.b1'], 'contains': ['32.gb1.b1', '32.gc1.a1', '32.gd1.b1', '32.gf1.f1', '32.gg1.b2', '32.gh1.b1', '32.gi1.d1', '32.hk1.j1', '32.hk1.l1', '32.hk1.r1', '32.hk1.t1', '32.hk1.eb1', '32.hk1.ed1', '32.hk1.ej1', '32.hk1.el1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 937, -1, 9963, -1, 936, -1], 'generators': [129, 2, 4, 160], 'label': '256.30836.16.jd1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.f1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879640
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.ha1.a1', '8.hg1.b1'], 'contains': ['32.gb1.b1', '32.gc1.b1', '32.gd1.a1', '32.gf1.g1', '32.gg1.b2', '32.gh1.d1', '32.gi1.b1', '32.hk1.m1', '32.hk1.o1', '32.hk1.u1', '32.hk1.w1', '32.hk1.ee1', '32.hk1.eg1', '32.hk1.em1', '32.hk1.eo1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 2879, -1, 9963, -1, 2873, -1], 'generators': [129, 2, 140, 160], 'label': '256.30836.16.jd1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.g1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879641
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.ha1.b1', '8.hg1.b1'], 'contains': ['32.gb1.b1', '32.gc1.b1', '32.gd1.b1', '32.gf1.h1', '32.gg1.b1', '32.gh1.d1', '32.gi1.d1', '32.hk1.n1', '32.hk1.p1', '32.hk1.v1', '32.hk1.x1', '32.hk1.ef1', '32.hk1.eh1', '32.hk1.en1', '32.hk1.ep1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 1784, -1, 9963, -1, 1783, -1], 'generators': [9, 2, 140, 160], 'label': '256.30836.16.jd1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.h1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879642
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.ha1.a1', '8.hg1.c1'], 'contains': ['32.gb1.c1', '32.gc1.c1', '32.gd1.c1', '32.gf1.a1', '32.gg1.a2', '32.gh1.b1', '32.gi1.b1', '32.hk1.bg1', '32.hk1.bi1', '32.hk1.bo1', '32.hk1.bq1', '32.hk1.cu1', '32.hk1.cw1', '32.hk1.ds1', '32.hk1.du1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 1743, -1, 9963, -1, 1741, -1], 'generators': [1, 130, 4, 160], 'label': '256.30836.16.jd1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.i1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879643
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.ha1.b1', '8.hg1.c1'], 'contains': ['32.gb1.c1', '32.gc1.c1', '32.gd1.d1', '32.gf1.b1', '32.gg1.a1', '32.gh1.b1', '32.gi1.d1', '32.hk1.bh1', '32.hk1.bj1', '32.hk1.bp1', '32.hk1.br1', '32.hk1.cv1', '32.hk1.cx1', '32.hk1.dt1', '32.hk1.dv1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 909, -1, 9963, -1, 908, -1], 'generators': [137, 130, 4, 160], 'label': '256.30836.16.jd1.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.j1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879644
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.ha1.a1', '8.hg1.c1'], 'contains': ['32.gb1.c1', '32.gc1.d1', '32.gd1.c1', '32.gf1.c1', '32.gg1.a1', '32.gh1.d1', '32.gi1.b1', '32.hk1.bk1', '32.hk1.bm1', '32.hk1.bs1', '32.hk1.bu1', '32.hk1.cy1', '32.hk1.da1', '32.hk1.dw1', '32.hk1.dy1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 2949, -1, 9963, -1, 2942, -1], 'generators': [137, 130, 140, 160], 'label': '256.30836.16.jd1.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.k1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879645
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.ha1.b1', '8.hg1.c1'], 'contains': ['32.gb1.c1', '32.gc1.d1', '32.gd1.d1', '32.gf1.d1', '32.gg1.a2', '32.gh1.d1', '32.gi1.d1', '32.hk1.bl1', '32.hk1.bn1', '32.hk1.bt1', '32.hk1.bv1', '32.hk1.cz1', '32.hk1.db1', '32.hk1.dx1', '32.hk1.dz1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 1757, -1, 9963, -1, 1755, -1], 'generators': [1, 130, 140, 160], 'label': '256.30836.16.jd1.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.l1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879646
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.ha1.a1', '8.hg1.d1'], 'contains': ['32.gb1.d1', '32.gc1.c1', '32.gd1.c1', '32.gf1.e1', '32.gg1.b2', '32.gh1.a1', '32.gi1.a1', '32.hk1.ce1', '32.hk1.cg1', '32.hk1.cm1', '32.hk1.co1', '32.hk1.dc1', '32.hk1.de1', '32.hk1.dk1', '32.hk1.dm1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 2977, -1, 9963, -1, 2970, -1], 'generators': [9, 130, 4, 160], 'label': '256.30836.16.jd1.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.m1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879647
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.a1', '8.ha1.b1', '8.hg1.d1'], 'contains': ['32.gb1.d1', '32.gc1.c1', '32.gd1.d1', '32.gf1.f1', '32.gg1.b1', '32.gh1.a1', '32.gi1.c1', '32.hk1.cf1', '32.hk1.ch1', '32.hk1.cn1', '32.hk1.cp1', '32.hk1.dd1', '32.hk1.df1', '32.hk1.dl1', '32.hk1.dn1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 1881, -1, 9963, -1, 1880, -1], 'generators': [129, 130, 4, 160], 'label': '256.30836.16.jd1.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.n1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879648
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bw1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.k1.a1', 'complements': ['64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.h1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.f1', '64.dk1.e1', '64.dk1.g1', '64.dk1.h1', '64.dk1.j1', '64.dk1.i1', '64.dk1.k1', '64.dk1.l1', '64.dk1.m1', '64.dk1.n1', '64.dk1.p1', '64.dk1.o1', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.f1', '64.dn1.h2', '64.dn1.e1', '64.dn1.e2', '64.dn1.h1', '64.do1.a1', '64.do1.b2', '64.do1.d2', '64.do1.c1', '64.do1.d1', '64.do1.c2', '64.do1.a2', '64.do1.b1', '64.do1.f1', '64.do1.e2', '64.do1.g2', '64.do1.h1', '64.do1.g1', '64.do1.h2', '64.do1.f2', '64.do1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.q1.a1', '2.u1.a1'], 'contains': ['8.r1.a1', '8.t1.a1', '8.u1.a1', '8.do1.a1', '8.dp1.a1', '8.ec1.a1', '8.eu1.a1', '8.gs1.a1', '8.gs1.b1'], 'core': '4.bw1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [930, 5858, 8884, 3021, 931, 5856, 8876, 3027], 'generators': [1, 66, 16, 128], 'label': '256.30836.4.bw1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bw1.a1', 'normal_contained_in': ['2.d1.a1', '2.q1.a1', '2.u1.a1'], 'normal_contains': ['8.r1.a1', '8.u1.a1', '8.t1.a1', '8.do1.a1', '8.dp1.a1', '8.eu1.a1', '8.ec1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bw1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879649
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.ha1.a1', '8.hg1.d1'], 'contains': ['32.gb1.d1', '32.gc1.d1', '32.gd1.c1', '32.gf1.g1', '32.gg1.b1', '32.gh1.c1', '32.gi1.a1', '32.hk1.ci1', '32.hk1.ck1', '32.hk1.cq1', '32.hk1.cs1', '32.hk1.dg1', '32.hk1.di1', '32.hk1.do1', '32.hk1.dq1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 3366, -1, 9963, -1, 3359, -1], 'generators': [129, 130, 140, 160], 'label': '256.30836.16.jd1.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.o1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879650
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jd1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.fz1.b1', '8.ha1.b1', '8.hg1.d1'], 'contains': ['32.gb1.d1', '32.gc1.d1', '32.gd1.d1', '32.gf1.h1', '32.gg1.b2', '32.gh1.c1', '32.gi1.c1', '32.hk1.cj1', '32.hk1.cl1', '32.hk1.cr1', '32.hk1.ct1', '32.hk1.dh1', '32.hk1.dj1', '32.hk1.dp1', '32.hk1.dr1'], 'core': '128.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9958, -1, 3171, -1, 9963, -1, 3165, -1], 'generators': [9, 130, 140, 160], 'label': '256.30836.16.jd1.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jd1.p1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jd1.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879651
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.gu1.a1', '8.hg1.a1'], 'contains': ['32.gk1.a1', '32.gl1.a1', '32.gm1.a1', '32.gp1.a1', '32.gq1.a1', '32.gr1.a1', '32.gs1.a1', '32.hk1.a1', '32.hk1.c1', '32.hk1.f1', '32.hk1.h1', '32.hk1.z1', '32.hk1.bb1', '32.hk1.bc1', '32.hk1.be1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 2090, -1, 9750, -1, 2088, -1], 'generators': [1, 2, 4, 40], 'label': '256.30836.16.je1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.a1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879652
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.gu1.a1', '8.hg1.a1'], 'contains': ['32.gk1.a1', '32.gl1.a1', '32.gm1.a1', '32.gp1.a2', '32.gq1.a2', '32.gr1.a2', '32.gs1.a2', '32.hk1.b1', '32.hk1.d1', '32.hk1.e1', '32.hk1.g1', '32.hk1.y1', '32.hk1.ba1', '32.hk1.bd1', '32.hk1.bf1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 2146, -1, 9750, -1, 2144, -1], 'generators': [161, 2, 4, 40], 'label': '256.30836.16.je1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.a2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879653
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.gu1.a1', '8.hg1.b1'], 'contains': ['32.gk1.b1', '32.gl1.a1', '32.gm1.a1', '32.gp1.b1', '32.gq1.b1', '32.gr1.b1', '32.gs1.b1', '32.hk1.j1', '32.hk1.l1', '32.hk1.m1', '32.hk1.o1', '32.hk1.q1', '32.hk1.s1', '32.hk1.v1', '32.hk1.x1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 1409, -1, 9750, -1, 1408, -1], 'generators': [129, 2, 4, 40], 'label': '256.30836.16.je1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.b1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879654
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.gu1.a1', '8.hg1.b1'], 'contains': ['32.gk1.b1', '32.gl1.a1', '32.gm1.a1', '32.gp1.b2', '32.gq1.b2', '32.gr1.b2', '32.gs1.b2', '32.hk1.i1', '32.hk1.k1', '32.hk1.n1', '32.hk1.p1', '32.hk1.r1', '32.hk1.t1', '32.hk1.u1', '32.hk1.w1'], 'core': '64.h1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 1520, -1, 9750, -1, 1519, -1], 'generators': [33, 2, 4, 40], 'label': '256.30836.16.je1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.b2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879655
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.gu1.b1', '8.hg1.c1'], 'contains': ['32.gk1.c1', '32.gl1.b1', '32.gm1.b1', '32.gp1.a1', '32.gq1.a2', '32.gr1.b1', '32.gs1.b2', '32.hk1.bg1', '32.hk1.bi1', '32.hk1.bl1', '32.hk1.bn1', '32.hk1.cv1', '32.hk1.cx1', '32.hk1.cy1', '32.hk1.da1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 1437, -1, 9750, -1, 1436, -1], 'generators': [1, 130, 4, 40], 'label': '256.30836.16.je1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.c1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879656
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.gu1.b1', '8.hg1.c1'], 'contains': ['32.gk1.c1', '32.gl1.b1', '32.gm1.b1', '32.gp1.a2', '32.gq1.a1', '32.gr1.b2', '32.gs1.b1', '32.hk1.bh1', '32.hk1.bj1', '32.hk1.bk1', '32.hk1.bm1', '32.hk1.cu1', '32.hk1.cw1', '32.hk1.cz1', '32.hk1.db1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 1576, -1, 9750, -1, 1575, -1], 'generators': [161, 130, 4, 40], 'label': '256.30836.16.je1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.c2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879657
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.gu1.a1', '8.hg1.c1'], 'contains': ['32.gk1.d1', '32.gl1.c1', '32.gm1.c1', '32.gp1.a1', '32.gq1.a2', '32.gr1.b2', '32.gs1.b1', '32.hk1.bo1', '32.hk1.bq1', '32.hk1.bt1', '32.hk1.bv1', '32.hk1.dt1', '32.hk1.dv1', '32.hk1.dw1', '32.hk1.dy1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 1326, -1, 9750, -1, 1325, -1], 'generators': [1, 34, 4, 40], 'label': '256.30836.16.je1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.d1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879733
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.bh1.a1', '16.bq1.a1', '16.bq1.b1', '16.bx1.a1', '16.cc1.a1', '16.cd1.a1'], 'contains': ['64.a1.a1', '64.o1.a1', '64.z1.a1', '64.bz1.a1', '64.bz1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7290, -1, 5079, -1, 7293, -1, 5074, -1], 'generators': [3, 32, 128], 'label': '256.30836.32.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.q1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879658
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.gu1.a1', '8.hg1.c1'], 'contains': ['32.gk1.d1', '32.gl1.c1', '32.gm1.c1', '32.gp1.a2', '32.gq1.a1', '32.gr1.b1', '32.gs1.b2', '32.hk1.bp1', '32.hk1.br1', '32.hk1.bs1', '32.hk1.bu1', '32.hk1.ds1', '32.hk1.du1', '32.hk1.dx1', '32.hk1.dz1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 1340, -1, 9750, -1, 1339, -1], 'generators': [161, 34, 4, 40], 'label': '256.30836.16.je1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.d2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.d2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879659
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bx1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.o1', '64.dj1.c1', '64.dj1.h1', '64.dj1.l1', '64.dj1.k1', '64.dj1.g1', '64.dj1.d1', '64.dj1.p1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e1', '64.dn1.e2', '64.dn1.h1', '64.dn1.h2', '64.dn1.g1', '64.dn1.g2', '64.dn1.f1', '64.dn1.f2', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.f2', '64.do1.h2', '64.do1.g1', '64.do1.e1', '64.do1.g2', '64.do1.e2', '64.do1.f1', '64.do1.h1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.o1', '64.dk1.m1', '64.dk1.n1', '64.dk1.p1', '64.dk1.k1', '64.dk1.i1', '64.dk1.j1', '64.dk1.l1', '64.dk1.e1', '64.dk1.g1', '64.dk1.h1', '64.dk1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.p1.a1', '2.u1.a1'], 'contains': ['8.r1.a1', '8.v1.a1', '8.x1.a1', '8.dr1.a1', '8.ds1.a1', '8.fb1.a1', '8.fj1.a1'], 'core': '4.bx1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2036, 7170, 5372, 2711, 2037, 7168, 5366, 2716], 'generators': [1, 82, 68], 'label': '256.30836.4.bx1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bx1.a1', 'normal_contained_in': ['2.e1.a1', '2.p1.a1', '2.u1.a1'], 'normal_contains': ['8.r1.a1', '8.v1.a1', '8.x1.a1', '8.ds1.a1', '8.dr1.a1', '8.fj1.a1', '8.fb1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bx1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879660
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.gu1.b1', '8.hg1.a1'], 'contains': ['32.gk1.e1', '32.gl1.d1', '32.gm1.d1', '32.gp1.a1', '32.gq1.a1', '32.gr1.a2', '32.gs1.a2', '32.hk1.bw1', '32.hk1.by1', '32.hk1.cb1', '32.hk1.cd1', '32.hk1.er1', '32.hk1.et1', '32.hk1.eu1', '32.hk1.ew1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 1910, -1, 9750, -1, 1908, -1], 'generators': [1, 162, 4, 40], 'label': '256.30836.16.je1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.e1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879661
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.gu1.b1', '8.hg1.a1'], 'contains': ['32.gk1.e1', '32.gl1.d1', '32.gm1.d1', '32.gp1.a2', '32.gq1.a2', '32.gr1.a1', '32.gs1.a1', '32.hk1.bx1', '32.hk1.bz1', '32.hk1.ca1', '32.hk1.cc1', '32.hk1.eq1', '32.hk1.es1', '32.hk1.ev1', '32.hk1.ex1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 2118, -1, 9750, -1, 2116, -1], 'generators': [161, 162, 4, 40], 'label': '256.30836.16.je1.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.e2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.e2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879662
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.gu1.b1', '8.hg1.d1'], 'contains': ['32.gk1.f1', '32.gl1.b1', '32.gm1.b1', '32.gp1.b1', '32.gq1.b2', '32.gr1.a1', '32.gs1.a2', '32.hk1.cf1', '32.hk1.ch1', '32.hk1.ci1', '32.hk1.ck1', '32.hk1.cm1', '32.hk1.co1', '32.hk1.cr1', '32.hk1.ct1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 2104, -1, 9750, -1, 2102, -1], 'generators': [129, 130, 4, 40], 'label': '256.30836.16.je1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.f1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879663
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.a1', '8.gu1.b1', '8.hg1.d1'], 'contains': ['32.gk1.f1', '32.gl1.b1', '32.gm1.b1', '32.gp1.b2', '32.gq1.b1', '32.gr1.a2', '32.gs1.a1', '32.hk1.ce1', '32.hk1.cg1', '32.hk1.cj1', '32.hk1.cl1', '32.hk1.cn1', '32.hk1.cp1', '32.hk1.cq1', '32.hk1.cs1'], 'core': '64.h1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 2173, -1, 9750, -1, 2172, -1], 'generators': [33, 130, 4, 40], 'label': '256.30836.16.je1.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.f2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.f2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879664
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.gu1.a1', '8.hg1.d1'], 'contains': ['32.gk1.g1', '32.gl1.c1', '32.gm1.c1', '32.gp1.b1', '32.gq1.b2', '32.gr1.a2', '32.gs1.a1', '32.hk1.dd1', '32.hk1.df1', '32.hk1.dg1', '32.hk1.di1', '32.hk1.dk1', '32.hk1.dm1', '32.hk1.dp1', '32.hk1.dr1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 1924, -1, 9750, -1, 1922, -1], 'generators': [129, 34, 4, 40], 'label': '256.30836.16.je1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.g1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879665
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.gu1.a1', '8.hg1.d1'], 'contains': ['32.gk1.g1', '32.gl1.c1', '32.gm1.c1', '32.gp1.b2', '32.gq1.b1', '32.gr1.a1', '32.gs1.a2', '32.hk1.dc1', '32.hk1.de1', '32.hk1.dh1', '32.hk1.dj1', '32.hk1.dl1', '32.hk1.dn1', '32.hk1.do1', '32.hk1.dq1'], 'core': '64.h1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 2132, -1, 9750, -1, 2130, -1], 'generators': [33, 34, 4, 40], 'label': '256.30836.16.je1.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.g2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.g2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879666
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.gu1.b1', '8.hg1.b1'], 'contains': ['32.gk1.h1', '32.gl1.d1', '32.gm1.d1', '32.gp1.b1', '32.gq1.b1', '32.gr1.b2', '32.gs1.b2', '32.hk1.eb1', '32.hk1.ed1', '32.hk1.ee1', '32.hk1.eg1', '32.hk1.ei1', '32.hk1.ek1', '32.hk1.en1', '32.hk1.ep1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 1395, -1, 9750, -1, 1394, -1], 'generators': [129, 162, 4, 40], 'label': '256.30836.16.je1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.h1', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879667
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.je1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gf1.b1', '8.gu1.b1', '8.hg1.b1'], 'contains': ['32.gk1.h1', '32.gl1.d1', '32.gm1.d1', '32.gp1.b2', '32.gq1.b2', '32.gr1.b1', '32.gs1.b1', '32.hk1.ea1', '32.hk1.ec1', '32.hk1.ef1', '32.hk1.eh1', '32.hk1.ej1', '32.hk1.el1', '32.hk1.em1', '32.hk1.eo1'], 'core': '64.h1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9745, -1, 1354, -1, 9750, -1, 1352, -1], 'generators': [33, 162, 4, 40], 'label': '256.30836.16.je1.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.je1.h2', 'projective_image': '128.2182', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.je1.h2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879668
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.a1', '8.go1.a1', '8.hg1.a1'], 'contains': ['32.gt1.a1', '32.gu1.a1', '32.gv1.a1', '32.gw1.a1', '32.gx1.a1', '32.gz1.a1', '32.ha1.a1', '32.hk1.a1', '32.hk1.b1', '32.hk1.e1', '32.hk1.f1', '32.hk1.bw1', '32.hk1.bx1', '32.hk1.ca1', '32.hk1.cb1'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 3074, -1, 9990, -1, 3067, -1], 'generators': [1, 2, 4, 136], 'label': '256.30836.16.jf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.a1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879734
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.bj1.a1', '16.bn1.a1', '16.bq1.a1', '16.bq1.b1', '16.ce1.a1', '16.cf1.a1'], 'contains': ['64.a1.a1', '64.p1.a1', '64.p1.b1', '64.ba1.a1', '64.ca1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8042, -1, 5093, -1, 8046, -1, 5088, -1], 'generators': [7, 32, 128], 'label': '256.30836.32.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.r1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879669
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.b1', '8.go1.a1', '8.hg1.a1'], 'contains': ['32.gt1.a1', '32.gu1.b1', '32.gv1.b1', '32.gw1.a1', '32.gx1.b1', '32.gz1.b1', '32.ha1.c1', '32.hk1.c1', '32.hk1.d1', '32.hk1.g1', '32.hk1.h1', '32.hk1.by1', '32.hk1.bz1', '32.hk1.cc1', '32.hk1.cd1'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 2187, -1, 9990, -1, 2186, -1], 'generators': [1, 162, 4, 136], 'label': '256.30836.16.jf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.b1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879670
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.by1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.o1', '64.dj1.c1', '64.dj1.h1', '64.dj1.l1', '64.dj1.k1', '64.dj1.g1', '64.dj1.d1', '64.dj1.p1', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.f2', '64.do1.h2', '64.do1.g1', '64.do1.e1', '64.do1.g2', '64.do1.e2', '64.do1.f1', '64.do1.h1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e1', '64.dn1.e2', '64.dn1.h1', '64.dn1.h2', '64.dn1.g1', '64.dn1.g2', '64.dn1.f1', '64.dn1.f2', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.m1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.j1', '64.dk1.l1', '64.dk1.k1', '64.dk1.i1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.q1.a1', '2.t1.a1'], 'contains': ['8.r1.a1', '8.y1.a1', '8.bb1.a1', '8.dt1.a1', '8.du1.a1', '8.fq1.a1', '8.fw1.a1'], 'core': '4.by1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7282, 5501, 7606, 9415, 7285, 5499, 7600, 9436], 'generators': [1, 82, 20], 'label': '256.30836.4.by1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.by1.a1', 'normal_contained_in': ['2.e1.a1', '2.q1.a1', '2.t1.a1'], 'normal_contains': ['8.r1.a1', '8.y1.a1', '8.bb1.a1', '8.du1.a1', '8.dt1.a1', '8.fw1.a1', '8.fq1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.by1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.by1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879671
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.a1', '8.go1.b1', '8.hg1.b1'], 'contains': ['32.gt1.b1', '32.gu1.a1', '32.gv1.a1', '32.gw1.b1', '32.gx1.c1', '32.gz1.c1', '32.ha1.b1', '32.hk1.i1', '32.hk1.j1', '32.hk1.m1', '32.hk1.n1', '32.hk1.ea1', '32.hk1.eb1', '32.hk1.ee1', '32.hk1.ef1'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 2500, -1, 9990, -1, 2499, -1], 'generators': [129, 2, 4, 136], 'label': '256.30836.16.jf1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.c1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879672
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.b1', '8.go1.b1', '8.hg1.b1'], 'contains': ['32.gt1.b1', '32.gu1.b1', '32.gv1.b1', '32.gw1.b1', '32.gx1.d1', '32.gz1.d1', '32.ha1.d1', '32.hk1.k1', '32.hk1.l1', '32.hk1.o1', '32.hk1.p1', '32.hk1.ec1', '32.hk1.ed1', '32.hk1.eg1', '32.hk1.eh1'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 2076, -1, 9990, -1, 2075, -1], 'generators': [129, 162, 4, 136], 'label': '256.30836.16.jf1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.d1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879673
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.c1', '8.go1.a1', '8.hg1.b1'], 'contains': ['32.gt1.c1', '32.gu1.a1', '32.gv1.b1', '32.gw1.c1', '32.gx1.e1', '32.gz1.d1', '32.ha1.b1', '32.hk1.q1', '32.hk1.r1', '32.hk1.u1', '32.hk1.v1', '32.hk1.ei1', '32.hk1.ej1', '32.hk1.em1', '32.hk1.en1'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 1534, -1, 9990, -1, 1533, -1], 'generators': [33, 2, 4, 136], 'label': '256.30836.16.jf1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.e1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879674
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.d1', '8.go1.a1', '8.hg1.b1'], 'contains': ['32.gt1.c1', '32.gu1.b1', '32.gv1.a1', '32.gw1.c1', '32.gx1.f1', '32.gz1.c1', '32.ha1.d1', '32.hk1.s1', '32.hk1.t1', '32.hk1.w1', '32.hk1.x1', '32.hk1.ek1', '32.hk1.el1', '32.hk1.eo1', '32.hk1.ep1'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 1812, -1, 9990, -1, 1811, -1], 'generators': [33, 162, 4, 136], 'label': '256.30836.16.jf1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.f1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879675
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.c1', '8.go1.b1', '8.hg1.a1'], 'contains': ['32.gt1.d1', '32.gu1.a1', '32.gv1.b1', '32.gw1.d1', '32.gx1.g1', '32.gz1.b1', '32.ha1.a1', '32.hk1.y1', '32.hk1.z1', '32.hk1.bc1', '32.hk1.bd1', '32.hk1.eq1', '32.hk1.er1', '32.hk1.eu1', '32.hk1.ev1'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 2935, -1, 9990, -1, 2929, -1], 'generators': [161, 2, 4, 136], 'label': '256.30836.16.jf1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.g1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879676
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.d1', '8.go1.b1', '8.hg1.a1'], 'contains': ['32.gt1.d1', '32.gu1.b1', '32.gv1.a1', '32.gw1.d1', '32.gx1.h1', '32.gz1.a1', '32.ha1.c1', '32.hk1.ba1', '32.hk1.bb1', '32.hk1.be1', '32.hk1.bf1', '32.hk1.es1', '32.hk1.et1', '32.hk1.ew1', '32.hk1.ex1'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 3254, -1, 9990, -1, 3248, -1], 'generators': [161, 162, 4, 136], 'label': '256.30836.16.jf1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.h1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879677
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.a1', '8.go1.a1', '8.hg1.c1'], 'contains': ['32.gt1.e1', '32.gu1.c1', '32.gv1.c1', '32.gw1.a1', '32.gx1.a1', '32.gz1.c1', '32.ha1.b1', '32.hk1.bg1', '32.hk1.bh1', '32.hk1.bk1', '32.hk1.bl1', '32.hk1.bo1', '32.hk1.bp1', '32.hk1.bs1', '32.hk1.bt1'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 1770, -1, 9990, -1, 1769, -1], 'generators': [1, 130, 4, 136], 'label': '256.30836.16.jf1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.i1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879678
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.b1', '8.go1.a1', '8.hg1.c1'], 'contains': ['32.gt1.e1', '32.gu1.d1', '32.gv1.d1', '32.gw1.a1', '32.gx1.b1', '32.gz1.d1', '32.ha1.d1', '32.hk1.bi1', '32.hk1.bj1', '32.hk1.bm1', '32.hk1.bn1', '32.hk1.bq1', '32.hk1.br1', '32.hk1.bu1', '32.hk1.bv1'], 'core': '64.i1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 1381, -1, 9990, -1, 1380, -1], 'generators': [1, 34, 4, 136], 'label': '256.30836.16.jf1.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.j1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879679
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.a1', '8.go1.b1', '8.hg1.d1'], 'contains': ['32.gt1.f1', '32.gu1.c1', '32.gv1.c1', '32.gw1.b1', '32.gx1.c1', '32.gz1.a1', '32.ha1.a1', '32.hk1.ce1', '32.hk1.cf1', '32.hk1.ci1', '32.hk1.cj1', '32.hk1.dc1', '32.hk1.dd1', '32.hk1.dg1', '32.hk1.dh1'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 3296, -1, 9990, -1, 3290, -1], 'generators': [129, 130, 4, 136], 'label': '256.30836.16.jf1.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.k1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879735
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.br1.a1', '16.br1.b1', '16.cc1.a1', '16.ce1.a1', '16.cg1.a1', '16.ch1.a1'], 'contains': ['64.a1.a1', '64.q1.a1', '64.bb1.a1', '64.cb1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3360, -1, 6210, -1, 3362, -1, 6204, -1], 'generators': [83, 32, 128], 'label': '256.30836.32.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.y1.a1', 'old_label': '32.s1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879680
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.b1', '8.go1.b1', '8.hg1.d1'], 'contains': ['32.gt1.f1', '32.gu1.d1', '32.gv1.d1', '32.gw1.b1', '32.gx1.d1', '32.gz1.b1', '32.ha1.c1', '32.hk1.cg1', '32.hk1.ch1', '32.hk1.ck1', '32.hk1.cl1', '32.hk1.de1', '32.hk1.df1', '32.hk1.di1', '32.hk1.dj1'], 'core': '64.i1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 2920, -1, 9990, -1, 2915, -1], 'generators': [129, 34, 4, 136], 'label': '256.30836.16.jf1.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.l1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879681
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.bz1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.i1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.d1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.m1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.j1', '64.dk1.l1', '64.dk1.k1', '64.dk1.i1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.e1', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.g1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.r1.a1', '2.v1.a1'], 'contains': ['8.s1.a1', '8.t1.a1', '8.w1.a1', '8.dv1.a1', '8.dw1.a1', '8.ed1.a1', '8.eo1.a1'], 'core': '4.bz1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6284, 3236, 7725, 7246, 6288, 3235, 7719, 7262], 'generators': [1, 16, 64], 'label': '256.30836.4.bz1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bz1.a1', 'normal_contained_in': ['2.d1.a1', '2.r1.a1', '2.v1.a1'], 'normal_contains': ['8.t1.a1', '8.s1.a1', '8.w1.a1', '8.ed1.a1', '8.dv1.a1', '8.eo1.a1', '8.dw1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bz1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879682
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.c1', '8.go1.a1', '8.hg1.d1'], 'contains': ['32.gt1.g1', '32.gu1.c1', '32.gv1.d1', '32.gw1.c1', '32.gx1.e1', '32.gz1.b1', '32.ha1.a1', '32.hk1.cm1', '32.hk1.cn1', '32.hk1.cq1', '32.hk1.cr1', '32.hk1.dk1', '32.hk1.dl1', '32.hk1.do1', '32.hk1.dp1'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 2431, -1, 9990, -1, 2429, -1], 'generators': [33, 130, 4, 136], 'label': '256.30836.16.jf1.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.m1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879683
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.d1', '8.go1.a1', '8.hg1.d1'], 'contains': ['32.gt1.g1', '32.gu1.d1', '32.gv1.c1', '32.gw1.c1', '32.gx1.f1', '32.gz1.a1', '32.ha1.c1', '32.hk1.co1', '32.hk1.cp1', '32.hk1.cs1', '32.hk1.ct1', '32.hk1.dm1', '32.hk1.dn1', '32.hk1.dq1', '32.hk1.dr1'], 'core': '64.i1.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 3115, -1, 9990, -1, 3109, -1], 'generators': [33, 34, 4, 136], 'label': '256.30836.16.jf1.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.n1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879684
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.c1', '8.go1.b1', '8.hg1.c1'], 'contains': ['32.gt1.h1', '32.gu1.c1', '32.gv1.d1', '32.gw1.d1', '32.gx1.g1', '32.gz1.d1', '32.ha1.b1', '32.hk1.cu1', '32.hk1.cv1', '32.hk1.cy1', '32.hk1.cz1', '32.hk1.ds1', '32.hk1.dt1', '32.hk1.dw1', '32.hk1.dx1'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 2159, -1, 9990, -1, 2158, -1], 'generators': [161, 130, 4, 136], 'label': '256.30836.16.jf1.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.o1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879685
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jf1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.d1', '8.go1.b1', '8.hg1.c1'], 'contains': ['32.gt1.h1', '32.gu1.d1', '32.gv1.c1', '32.gw1.d1', '32.gx1.h1', '32.gz1.c1', '32.ha1.d1', '32.hk1.cw1', '32.hk1.cx1', '32.hk1.da1', '32.hk1.db1', '32.hk1.du1', '32.hk1.dv1', '32.hk1.dy1', '32.hk1.dz1'], 'core': '64.i1.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [9985, -1, 2486, -1, 9990, -1, 2485, -1], 'generators': [161, 34, 4, 136], 'label': '256.30836.16.jf1.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jf1.p1', 'projective_image': '128.2201', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jf1.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879686
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.a1', '8.gu1.a1', '8.ha1.a1'], 'contains': ['32.hb1.a1', '32.hc1.a1', '32.hd1.a1', '32.he1.a1', '32.hf1.a1', '32.hh1.a1', '32.hi1.a1', '32.hk1.a1', '32.hk1.e1', '32.hk1.i1', '32.hk1.m1', '32.hk1.bo1', '32.hk1.bs1', '32.hk1.dc1', '32.hk1.dg1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 3032, -1, 9910, -1, 3026, -1], 'generators': [1, 2, 4, 8], 'label': '256.30836.16.jg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879687
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.a1', '8.gu1.a1', '8.ha1.b1'], 'contains': ['32.hb1.a1', '32.hc1.a1', '32.hd1.c1', '32.he1.b1', '32.hf1.a1', '32.hh1.a2', '32.hi1.b1', '32.hk1.b1', '32.hk1.f1', '32.hk1.j1', '32.hk1.n1', '32.hk1.bp1', '32.hk1.bt1', '32.hk1.dd1', '32.hk1.dh1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 1840, -1, 9910, -1, 1838, -1], 'generators': [129, 2, 4, 8], 'label': '256.30836.16.jg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879688
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.b1', '8.gu1.a1', '8.ha1.a1'], 'contains': ['32.hb1.a1', '32.hc1.b1', '32.hd1.b1', '32.he1.a1', '32.hf1.b1', '32.hh1.b1', '32.hi1.c1', '32.hk1.c1', '32.hk1.g1', '32.hk1.k1', '32.hk1.o1', '32.hk1.bq1', '32.hk1.bu1', '32.hk1.de1', '32.hk1.di1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 2285, -1, 9910, -1, 2283, -1], 'generators': [1, 34, 4, 8], 'label': '256.30836.16.jg1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879689
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.b1', '8.gu1.a1', '8.ha1.b1'], 'contains': ['32.hb1.a1', '32.hc1.b1', '32.hd1.d1', '32.he1.b1', '32.hf1.b1', '32.hh1.b2', '32.hi1.d1', '32.hk1.d1', '32.hk1.h1', '32.hk1.l1', '32.hk1.p1', '32.hk1.br1', '32.hk1.bv1', '32.hk1.df1', '32.hk1.dj1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 1368, -1, 9910, -1, 1366, -1], 'generators': [129, 34, 4, 8], 'label': '256.30836.16.jg1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879690
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.c1', '8.gu1.a1', '8.ha1.a1'], 'contains': ['32.hb1.b1', '32.hc1.a1', '32.hd1.b1', '32.he1.c1', '32.hf1.c1', '32.hh1.b2', '32.hi1.a1', '32.hk1.q1', '32.hk1.u1', '32.hk1.y1', '32.hk1.bc1', '32.hk1.dk1', '32.hk1.do1', '32.hk1.ds1', '32.hk1.dw1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 2299, -1, 9910, -1, 2297, -1], 'generators': [161, 2, 4, 8], 'label': '256.30836.16.jg1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.e1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879771
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.dw1.a1', '16.dw1.b1', '16.dy1.a1', '16.dy1.b1', '16.ed1.a1', '16.ed1.b1'], 'contains': ['64.c1.a1', '64.l1.a1', '64.l1.b1', '64.cq1.a1', '64.cz1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9080, -1, 4787, -1, 9084, -1, 4782, -1], 'generators': [4, 136, 128], 'label': '256.30836.32.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bx1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879691
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.c1', '8.gu1.a1', '8.ha1.b1'], 'contains': ['32.hb1.b1', '32.hc1.a1', '32.hd1.d1', '32.he1.d1', '32.hf1.c1', '32.hh1.b1', '32.hi1.b1', '32.hk1.r1', '32.hk1.v1', '32.hk1.z1', '32.hk1.bd1', '32.hk1.dl1', '32.hk1.dp1', '32.hk1.dt1', '32.hk1.dx1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 1478, -1, 9910, -1, 1477, -1], 'generators': [33, 2, 4, 8], 'label': '256.30836.16.jg1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.f1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879692
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ca1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.l1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.n1', '64.dj1.b1', '64.dj1.e1', '64.dj1.i1', '64.dj1.j1', '64.dj1.f1', '64.dj1.o1', '64.dj1.c1', '64.dj1.d1', '64.dj1.p1', '64.dj1.k1', '64.dj1.g1', '64.dj1.h1', '64.dj1.l1', '64.do1.a1', '64.do1.c1', '64.do1.a2', '64.do1.c2', '64.do1.d1', '64.do1.b1', '64.do1.d2', '64.do1.b2', '64.do1.e2', '64.do1.g2', '64.do1.e1', '64.do1.g1', '64.do1.h2', '64.do1.f2', '64.do1.h1', '64.do1.f1', '64.dn1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.b2', '64.dn1.c1', '64.dn1.c2', '64.dn1.d1', '64.dn1.d2', '64.dn1.e1', '64.dn1.e2', '64.dn1.f1', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.h1', '64.dn1.h2', '64.dk1.a1', '64.dk1.c1', '64.dk1.b1', '64.dk1.d1', '64.dk1.m1', '64.dk1.o1', '64.dk1.n1', '64.dk1.p1', '64.dk1.e1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.i1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.p1.a1', '2.v1.a1'], 'contains': ['8.s1.a1', '8.v1.a1', '8.bc1.a1', '8.dx1.a1', '8.dy1.a1', '8.ep1.a1', '8.eq1.a1'], 'core': '4.ca1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5824, 6197, 7856, 4169, 5827, 6195, 7849, 4178], 'generators': [1, 22, 64], 'label': '256.30836.4.ca1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ca1.a1', 'normal_contained_in': ['2.f1.a1', '2.p1.a1', '2.v1.a1'], 'normal_contains': ['8.v1.a1', '8.s1.a1', '8.bc1.a1', '8.eq1.a1', '8.dy1.a1', '8.ep1.a1', '8.dx1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ca1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879693
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.d1', '8.gu1.a1', '8.ha1.a1'], 'contains': ['32.hb1.b1', '32.hc1.b1', '32.hd1.a1', '32.he1.c1', '32.hf1.d1', '32.hh1.a2', '32.hi1.c1', '32.hk1.s1', '32.hk1.w1', '32.hk1.ba1', '32.hk1.be1', '32.hk1.dm1', '32.hk1.dq1', '32.hk1.du1', '32.hk1.dy1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 2963, -1, 9910, -1, 2956, -1], 'generators': [161, 34, 4, 8], 'label': '256.30836.16.jg1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.g1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879694
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.d1', '8.gu1.a1', '8.ha1.b1'], 'contains': ['32.hb1.b1', '32.hc1.b1', '32.hd1.c1', '32.he1.d1', '32.hf1.d1', '32.hh1.a1', '32.hi1.d1', '32.hk1.t1', '32.hk1.x1', '32.hk1.bb1', '32.hk1.bf1', '32.hk1.dn1', '32.hk1.dr1', '32.hk1.dv1', '32.hk1.dz1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 1729, -1, 9910, -1, 1727, -1], 'generators': [33, 34, 4, 8], 'label': '256.30836.16.jg1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.h1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879695
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.a1', '8.gu1.b1', '8.ha1.a1'], 'contains': ['32.hb1.c1', '32.hc1.c1', '32.hd1.e1', '32.he1.a1', '32.hf1.a1', '32.hh1.a2', '32.hi1.a1', '32.hk1.bg1', '32.hk1.bk1', '32.hk1.bw1', '32.hk1.ca1', '32.hk1.ce1', '32.hk1.ci1', '32.hk1.ea1', '32.hk1.ee1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 3018, -1, 9910, -1, 3012, -1], 'generators': [1, 130, 4, 8], 'label': '256.30836.16.jg1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.i1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879696
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.a1', '8.gu1.b1', '8.ha1.b1'], 'contains': ['32.hb1.c1', '32.hc1.c1', '32.hd1.g1', '32.he1.b1', '32.hf1.a1', '32.hh1.a1', '32.hi1.b1', '32.hk1.bh1', '32.hk1.bl1', '32.hk1.bx1', '32.hk1.cb1', '32.hk1.cf1', '32.hk1.cj1', '32.hk1.eb1', '32.hk1.ef1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 1867, -1, 9910, -1, 1866, -1], 'generators': [129, 130, 4, 8], 'label': '256.30836.16.jg1.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.j1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879697
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.b1', '8.gu1.b1', '8.ha1.a1'], 'contains': ['32.hb1.c1', '32.hc1.d1', '32.hd1.f1', '32.he1.a1', '32.hf1.b1', '32.hh1.b2', '32.hi1.c1', '32.hk1.bi1', '32.hk1.bm1', '32.hk1.by1', '32.hk1.cc1', '32.hk1.cg1', '32.hk1.ck1', '32.hk1.ec1', '32.hk1.eg1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 2271, -1, 9910, -1, 2269, -1], 'generators': [1, 162, 4, 8], 'label': '256.30836.16.jg1.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.k1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879698
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.b1', '8.gu1.b1', '8.ha1.b1'], 'contains': ['32.hb1.c1', '32.hc1.d1', '32.hd1.h1', '32.he1.b1', '32.hf1.b1', '32.hh1.b1', '32.hi1.d1', '32.hk1.bj1', '32.hk1.bn1', '32.hk1.bz1', '32.hk1.cd1', '32.hk1.ch1', '32.hk1.cl1', '32.hk1.ed1', '32.hk1.eh1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 1423, -1, 9910, -1, 1422, -1], 'generators': [129, 162, 4, 8], 'label': '256.30836.16.jg1.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.l1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879699
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.c1', '8.gu1.b1', '8.ha1.a1'], 'contains': ['32.hb1.d1', '32.hc1.c1', '32.hd1.f1', '32.he1.c1', '32.hf1.c1', '32.hh1.b1', '32.hi1.a1', '32.hk1.cm1', '32.hk1.cq1', '32.hk1.cu1', '32.hk1.cy1', '32.hk1.ei1', '32.hk1.em1', '32.hk1.eq1', '32.hk1.eu1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 2459, -1, 9910, -1, 2457, -1], 'generators': [161, 130, 4, 8], 'label': '256.30836.16.jg1.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.m1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879700
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.c1', '8.gu1.b1', '8.ha1.b1'], 'contains': ['32.hb1.d1', '32.hc1.c1', '32.hd1.h1', '32.he1.d1', '32.hf1.c1', '32.hh1.b2', '32.hi1.b1', '32.hk1.cn1', '32.hk1.cr1', '32.hk1.cv1', '32.hk1.cz1', '32.hk1.ej1', '32.hk1.en1', '32.hk1.er1', '32.hk1.ev1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 1632, -1, 9910, -1, 1630, -1], 'generators': [33, 130, 4, 8], 'label': '256.30836.16.jg1.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.n1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879701
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.d1', '8.gu1.b1', '8.ha1.a1'], 'contains': ['32.hb1.d1', '32.hc1.d1', '32.hd1.e1', '32.he1.c1', '32.hf1.d1', '32.hh1.a1', '32.hi1.c1', '32.hk1.co1', '32.hk1.cs1', '32.hk1.cw1', '32.hk1.da1', '32.hk1.ek1', '32.hk1.eo1', '32.hk1.es1', '32.hk1.ew1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 3004, -1, 9910, -1, 2998, -1], 'generators': [161, 162, 4, 8], 'label': '256.30836.16.jg1.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.o1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879772
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.by1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.dx1.a1', '16.dx1.b1', '16.dy1.a1', '16.dy1.b1', '16.ee1.a1', '16.ee1.b1'], 'contains': ['64.c1.a1', '64.n1.a1', '64.cs1.a1', '64.db1.a1', '64.db1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9054, -1, 4536, -1, 9058, -1, 4532, -1], 'generators': [5, 136, 128], 'label': '256.30836.32.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.by1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.by1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879702
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '16.jg1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4096, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.gl1.d1', '8.gu1.b1', '8.ha1.b1'], 'contains': ['32.hb1.d1', '32.hc1.d1', '32.hd1.g1', '32.he1.d1', '32.hf1.d1', '32.hh1.a2', '32.hi1.d1', '32.hk1.cp1', '32.hk1.ct1', '32.hk1.cx1', '32.hk1.db1', '32.hk1.el1', '32.hk1.ep1', '32.hk1.et1', '32.hk1.ex1'], 'core': '128.g1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9905, -1, 1854, -1, 9910, -1, 1852, -1], 'generators': [33, 162, 4, 8], 'label': '256.30836.16.jg1.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.jg1.p1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.jg1.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879703
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cb1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.n1', '64.dj1.b1', '64.dj1.e1', '64.dj1.i1', '64.dj1.j1', '64.dj1.f1', '64.dj1.c1', '64.dj1.o1', '64.dj1.p1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.l1', '64.dj1.h1', '64.dn1.a1', '64.dn1.a2', '64.dn1.b1', '64.dn1.b2', '64.dn1.c1', '64.dn1.c2', '64.dn1.d1', '64.dn1.d2', '64.dn1.e2', '64.dn1.e1', '64.dn1.f2', '64.dn1.f1', '64.dn1.g2', '64.dn1.g1', '64.dn1.h2', '64.dn1.h1', '64.dk1.a1', '64.dk1.c1', '64.dk1.b1', '64.dk1.d1', '64.dk1.m1', '64.dk1.o1', '64.dk1.n1', '64.dk1.p1', '64.dk1.e1', '64.dk1.g1', '64.dk1.f1', '64.dk1.h1', '64.dk1.i1', '64.dk1.k1', '64.dk1.j1', '64.dk1.l1', '64.do1.a1', '64.do1.c1', '64.do1.a2', '64.do1.c2', '64.do1.d1', '64.do1.b1', '64.do1.d2', '64.do1.b2', '64.do1.e1', '64.do1.g1', '64.do1.e2', '64.do1.g2', '64.do1.h1', '64.do1.f1', '64.do1.h2', '64.do1.f2'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.r1.a1', '2.t1.a1'], 'contains': ['8.s1.a1', '8.y1.a1', '8.ba1.a1', '8.dz1.a1', '8.eb1.a1', '8.er1.a1', '8.es1.a1'], 'core': '4.cb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7718, 5929, 7774, 5831, 7722, 5927, 7767, 5844], 'generators': [1, 20, 64], 'label': '256.30836.4.cb1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cb1.a1', 'normal_contained_in': ['2.f1.a1', '2.r1.a1', '2.t1.a1'], 'normal_contains': ['8.s1.a1', '8.y1.a1', '8.ba1.a1', '8.es1.a1', '8.er1.a1', '8.eb1.a1', '8.dz1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cb1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879704
{'ambient': '256.30836', 'aut_centralizer_order': 32768, 'aut_label': '32.a1', 'aut_quo_index': 9999360, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.i1.a1', '16.j1.a1', '16.k1.a1', '16.l1.a1', '16.m1.a1', '16.n1.a1', '16.o1.a1', '16.p1.a1', '16.q1.a1', '16.r1.a1', '16.s1.a1', '16.t1.a1', '16.u1.a1', '16.v1.a1', '16.w1.a1', '16.x1.a1', '16.y1.a1', '16.z1.a1', '16.ba1.a1', '16.bb1.a1', '16.bc1.a1', '16.bd1.a1', '16.be1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1', '64.d1.a1', '64.e1.a1', '64.f1.a1', '64.g1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5647, 4614, 7034, 5963, 5639, 4598, 7029, 5975], 'generators': [136, 32, 128], 'label': '256.30836.32.a1.a1', 'mobius_quo': -8, 'mobius_sub': -1024, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.b1.a1', '16.a1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1', '16.o1.a1', '16.j1.a1', '16.p1.a1', '16.l1.a1', '16.m1.a1', '16.k1.a1', '16.i1.a1', '16.n1.a1', '16.y1.a1', '16.z1.a1', '16.bc1.a1', '16.s1.a1', '16.w1.a1', '16.ba1.a1', '16.u1.a1', '16.bb1.a1', '16.bd1.a1', '16.q1.a1', '16.be1.a1', '16.r1.a1', '16.t1.a1', '16.x1.a1', '16.v1.a1'], 'normal_contains': ['64.g1.a1', '64.e1.a1', '64.b1.a1', '64.a1.a1', '64.f1.a1', '64.d1.a1', '64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.51', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879705
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.b1', 'aut_quo_index': 72, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.bi1.a1', '16.bm1.a1', '16.bq1.a1', '16.br1.a1', '16.bs1.a1', '16.bt1.a1', '16.bu1.a1', '16.bv1.a1', '16.bw1.a1'], 'contains': ['64.a1.a1', '64.l1.a1', '64.w1.a1', '64.bw1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7317, 3756, 5435, 2590, 7320, 3801, 5430, 2534], 'generators': [4, 32, 128], 'label': '256.30836.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.c1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '64.264', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879706
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.b1', 'aut_quo_index': 72, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.bi1.b1', '16.bm1.b1', '16.bq1.b1', '16.br1.b1', '16.bs1.b1', '16.bt1.b1', '16.bu1.b1', '16.bv1.b1', '16.bw1.b1'], 'contains': ['64.a1.a1', '64.l1.b1', '64.w1.b1', '64.bw1.b1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7317, 3756, 5656, 2908, 7320, 3801, 5652, 2823], 'generators': [140, 32, 128], 'label': '256.30836.32.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.b1', 'normal_contained_in': ['16.c1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.b1', 'projective_image': '64.264', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879707
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.c1', 'aut_quo_index': 72, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.co1.a1', '16.cp1.a1', '16.cq1.a1', '16.cr1.a1', '16.cs1.a1', '16.ct1.a1', '16.cu1.a1', '16.cv1.a1', '16.cw1.a1'], 'contains': ['64.b1.a1', '64.h1.a1', '64.h1.b1', '64.j1.a1', '64.bh1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4982, 5238, 8547, 6258, 4980, 5232, 8539, 6272], 'generators': [2, 168, 128], 'label': '256.30836.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.b1.a1', '64.h1.a1', '64.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '64.264', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879708
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.c1', 'aut_quo_index': 72, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.co1.b1', '16.cp1.b1', '16.cq1.b1', '16.cr1.b1', '16.cs1.b1', '16.ct1.b1', '16.cu1.b1', '16.cv1.b1', '16.cw1.b1'], 'contains': ['64.b1.a1', '64.h1.c1', '64.h1.d1', '64.j1.b1', '64.bh1.b1'], 'core': '32.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4982, 5238, 8357, 6160, 4980, 5232, 8350, 6174], 'generators': [34, 168, 128], 'label': '256.30836.32.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.b1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.b1.a1', '64.h1.c1', '64.h1.d1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.b1', 'projective_image': '64.264', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879709
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.d1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.bf1.a1', '16.bf1.b1', '16.dv1.a1', '16.dy1.a1', '16.dz1.a1', '16.ea1.a1', '16.eb1.a1', '16.ec1.a1'], 'contains': ['64.c1.a1', '64.i1.a1', '64.i1.b1', '64.k1.a1', '64.cy1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8282, 7009, 5796, 7340, 8286, 7007, 5790, 7356], 'generators': [1, 136, 128], 'label': '256.30836.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.b1.a1', '16.bf1.a1', '16.bf1.b1'], 'normal_contains': ['64.c1.a1', '64.i1.b1', '64.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '64.263', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879710
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.d1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.bf1.c1', '16.bf1.d1', '16.dv1.b1', '16.dy1.b1', '16.dz1.b1', '16.ea1.b1', '16.eb1.b1', '16.ec1.b1'], 'contains': ['64.c1.a1', '64.i1.c1', '64.i1.d1', '64.k1.b1', '64.cy1.b1'], 'core': '32.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8282, 7009, 5782, 7373, 8286, 7007, 5777, 7389], 'generators': [33, 136, 128], 'label': '256.30836.32.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.b1', 'normal_contained_in': ['16.b1.a1', '16.bf1.c1', '16.bf1.d1'], 'normal_contains': ['64.c1.a1', '64.i1.c1', '64.i1.d1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.b1', 'projective_image': '64.263', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879773
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.dv1.a1', '16.dv1.b1', '16.ed1.a1', '16.ed1.b1', '16.ee1.a1', '16.ee1.b1'], 'contains': ['64.c1.a1', '64.o1.a1', '64.ct1.a1', '64.ct1.b1', '64.dc1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9027, -1, 4828, -1, 9031, -1, 4824, -1], 'generators': [3, 136, 128], 'label': '256.30836.32.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bz1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879711
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.e1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.bf1.a1', '16.bf1.c1', '16.dw1.a1', '16.ee1.a1', '16.ef1.a1', '16.eg1.a1', '16.eh1.a1', '16.ei1.a1'], 'contains': ['64.c1.a1', '64.m1.a1', '64.cr1.a1', '64.da1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8255, 4875, 5740, 7146, 8259, 4873, 5735, 7161], 'generators': [6, 136, 128], 'label': '256.30836.32.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': ['16.d1.a1', '16.bf1.a1', '16.bf1.c1'], 'normal_contains': ['64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.e1.a1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879712
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.e1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.bf1.b1', '16.bf1.d1', '16.dw1.b1', '16.ee1.b1', '16.ef1.b1', '16.eg1.b1', '16.eh1.b1', '16.ei1.b1'], 'contains': ['64.c1.a1', '64.m1.b1', '64.cr1.b1', '64.da1.b1'], 'core': '32.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8255, 4875, 5573, 7210, 8259, 4873, 5569, 7226], 'generators': [38, 136, 128], 'label': '256.30836.32.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.b1', 'normal_contained_in': ['16.d1.a1', '16.bf1.b1', '16.bf1.d1'], 'normal_contains': ['64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.e1.b1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879713
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.f1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.bf1.a1', '16.bf1.d1', '16.dx1.a1', '16.ed1.a1', '16.ej1.a1', '16.ek1.a1', '16.el1.a1', '16.em1.a1'], 'contains': ['64.c1.a1', '64.p1.a1', '64.cu1.a1', '64.dd1.a1'], 'core': '32.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8308, 4747, 5726, 7178, 8312, 4727, 5721, 7193], 'generators': [7, 136, 128], 'label': '256.30836.32.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1.a1', 'normal_contained_in': ['16.g1.a1', '16.bf1.a1', '16.bf1.d1'], 'normal_contains': ['64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.f1.a1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879714
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cc1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.d1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.m1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.j1', '64.dk1.l1', '64.dk1.k1', '64.dk1.i1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.e1', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.g1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.r1.a1', '2.u1.a1'], 'contains': ['8.t1.a1', '8.x1.a1', '8.ba1.a1', '8.ee1.a1', '8.eg1.a1', '8.ev1.a1', '8.ew1.a1'], 'core': '4.cc1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1718, 7587, 6142, 6471, 1719, 7584, 6137, 6485], 'generators': [1, 68, 16], 'label': '256.30836.4.cc1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cc1.a1', 'normal_contained_in': ['2.g1.a1', '2.r1.a1', '2.u1.a1'], 'normal_contains': ['8.t1.a1', '8.x1.a1', '8.ba1.a1', '8.eg1.a1', '8.ee1.a1', '8.ew1.a1', '8.ev1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cc1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879715
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.f1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.bf1.b1', '16.bf1.c1', '16.dx1.b1', '16.ed1.b1', '16.ej1.b1', '16.ek1.b1', '16.el1.b1', '16.em1.b1'], 'contains': ['64.c1.a1', '64.p1.b1', '64.cu1.b1', '64.dd1.b1'], 'core': '32.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8308, 4747, 5490, 7112, 8312, 4727, 5485, 7128], 'generators': [39, 136, 128], 'label': '256.30836.32.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.f1.b1', 'normal_contained_in': ['16.g1.a1', '16.bf1.b1', '16.bf1.c1'], 'normal_contains': ['64.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.f1.b1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879716
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.g1', 'aut_quo_index': 72, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.eo1.a1', '16.et1.a1', '16.eu1.a1', '16.ev1.a1', '16.ew1.a1', '16.ex1.a1', '16.ey1.a1', '16.ez1.a1', '16.fa1.a1'], 'contains': ['64.d1.a1', '64.i1.a1', '64.i1.c1', '64.v1.a1', '64.bi1.a1'], 'core': '32.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3141, 6946, 6259, 7308, 3142, 6943, 6253, 7324], 'generators': [1, 136, 32], 'label': '256.30836.32.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1.a1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.d1.a1', '64.i1.c1', '64.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.g1.a1', 'projective_image': '64.264', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879717
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.g1', 'aut_quo_index': 72, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.eo1.b1', '16.et1.b1', '16.eu1.b1', '16.ev1.b1', '16.ew1.b1', '16.ex1.b1', '16.ey1.b1', '16.ez1.b1', '16.fa1.b1'], 'contains': ['64.d1.a1', '64.i1.b1', '64.i1.d1', '64.v1.b1', '64.bi1.b1'], 'core': '32.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3141, 6946, 6296, 7405, 3142, 6943, 6290, 7422], 'generators': [129, 136, 32], 'label': '256.30836.32.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.g1.b1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.d1.a1', '64.i1.b1', '64.i1.d1'], 'normalizer': '1.a1.a1', 'old_label': '32.g1.b1', 'projective_image': '64.264', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879718
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.h1', 'aut_quo_index': 72, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.fv1.a1', '16.fw1.a1', '16.fx1.a1', '16.fy1.a1', '16.fz1.a1', '16.ga1.a1', '16.gb1.a1', '16.gc1.a1', '16.gd1.a1'], 'contains': ['64.e1.a1', '64.h1.a1', '64.h1.c1', '64.u1.a1', '64.cx1.a1'], 'core': '32.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6074, 5206, 6686, 6193, 6077, 5200, 6680, 6206], 'generators': [2, 8, 32], 'label': '256.30836.32.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.h1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.e1.a1', '64.h1.a1', '64.h1.c1'], 'normalizer': '1.a1.a1', 'old_label': '32.h1.a1', 'projective_image': '64.264', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879719
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.h1', 'aut_quo_index': 72, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.fv1.b1', '16.fw1.b1', '16.fx1.b1', '16.fy1.b1', '16.fz1.b1', '16.ga1.b1', '16.gb1.b1', '16.gc1.b1', '16.gd1.b1'], 'contains': ['64.e1.a1', '64.h1.b1', '64.h1.d1', '64.u1.b1', '64.cx1.b1'], 'core': '32.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6074, 5206, 6699, 6225, 6077, 5200, 6694, 6239], 'generators': [130, 8, 32], 'label': '256.30836.32.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.h1.b1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.e1.a1', '64.h1.b1', '64.h1.d1'], 'normalizer': '1.a1.a1', 'old_label': '32.h1.b1', 'projective_image': '64.264', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879720
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.i1', 'aut_quo_index': 72, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.hf1.a1', '16.hi1.a1', '16.hp1.a1', '16.hs1.a1', '16.ht1.a1', '16.hu1.a1', '16.hv1.a1', '16.hw1.a1', '16.hx1.a1'], 'contains': ['64.f1.a1', '64.bl1.a1', '64.by1.a1', '64.db1.a1'], 'core': '32.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7343, 4515, 6737, 4570, 7347, 4529, 6731, 5252], 'generators': [5, 8, 160], 'label': '256.30836.32.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.i1.a1', 'normal_contained_in': ['16.e1.a1'], 'normal_contains': ['64.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.i1.a1', 'projective_image': '64.264', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879721
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.i1', 'aut_quo_index': 72, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.hf1.b1', '16.hi1.b1', '16.hp1.b1', '16.hs1.b1', '16.ht1.b1', '16.hu1.b1', '16.hv1.b1', '16.hw1.b1', '16.hx1.b1'], 'contains': ['64.f1.a1', '64.bl1.b1', '64.by1.b1', '64.db1.b1'], 'core': '32.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7343, 4515, 6672, 3851, 7347, 4529, 6666, 3796], 'generators': [133, 8, 160], 'label': '256.30836.32.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.i1.b1', 'normal_contained_in': ['16.e1.a1'], 'normal_contains': ['64.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.i1.b1', 'projective_image': '64.264', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.i1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879722
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.j1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.bg1.a1', '16.bg1.b1', '16.il1.a1', '16.im1.a1', '16.in1.a1', '16.io1.a1', '16.ip1.a1', '16.iq1.a1'], 'contains': ['64.g1.a1', '64.h1.a1', '64.h1.d1', '64.bu1.a1', '64.cp1.a1'], 'core': '32.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8228, 5566, 5203, 7243, 8232, 5561, 5199, 7258], 'generators': [2, 136, 160], 'label': '256.30836.32.j1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.j1.a1', 'normal_contained_in': ['16.a1.a1', '16.bg1.b1', '16.bg1.a1'], 'normal_contains': ['64.g1.a1', '64.h1.a1', '64.h1.d1'], 'normalizer': '1.a1.a1', 'old_label': '32.j1.a1', 'projective_image': '64.263', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879723
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.j1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.bg1.c1', '16.bg1.d1', '16.il1.b1', '16.im1.b1', '16.in1.b1', '16.io1.b1', '16.ip1.b1', '16.iq1.b1'], 'contains': ['64.g1.a1', '64.h1.b1', '64.h1.c1', '64.bu1.b1', '64.cp1.b1'], 'core': '32.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8228, 5566, 5245, 7275, 8232, 5561, 5241, 7291], 'generators': [130, 136, 160], 'label': '256.30836.32.j1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.j1.b1', 'normal_contained_in': ['16.a1.a1', '16.bg1.d1', '16.bg1.c1'], 'normal_contains': ['64.g1.a1', '64.h1.b1', '64.h1.c1'], 'normalizer': '1.a1.a1', 'old_label': '32.j1.b1', 'projective_image': '64.263', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879724
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.k1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.bg1.a1', '16.bg1.c1', '16.ir1.a1', '16.is1.a1', '16.it1.a1', '16.iu1.a1', '16.iv1.a1', '16.iw1.a1'], 'contains': ['64.g1.a1', '64.i1.a1', '64.i1.d1', '64.bv1.a1', '64.cf1.a1'], 'core': '32.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8361, 6977, 5190, 7438, 8365, 6975, 5185, 7454], 'generators': [1, 136, 160], 'label': '256.30836.32.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.k1.a1', 'normal_contained_in': ['16.b1.a1', '16.bg1.a1', '16.bg1.c1'], 'normal_contains': ['64.g1.a1', '64.i1.d1', '64.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.k1.a1', 'projective_image': '64.263', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879725
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cd1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.i1', '64.dj1.j1', '64.dj1.b1', '64.dj1.e1', '64.dj1.m1', '64.dj1.n1', '64.dj1.f1', '64.dj1.k1', '64.dj1.c1', '64.dj1.d1', '64.dj1.l1', '64.dj1.o1', '64.dj1.g1', '64.dj1.h1', '64.dj1.p1', '64.do1.a1', '64.do1.b1', '64.do1.d2', '64.do1.c2', '64.do1.d1', '64.do1.c1', '64.do1.a2', '64.do1.b2', '64.do1.f2', '64.do1.e2', '64.do1.g1', '64.do1.h1', '64.do1.g2', '64.do1.h2', '64.do1.f1', '64.do1.e1', '64.dn1.a1', '64.dn1.c2', '64.dn1.d1', '64.dn1.b2', '64.dn1.c1', '64.dn1.a2', '64.dn1.b1', '64.dn1.d2', '64.dn1.g2', '64.dn1.e1', '64.dn1.f2', '64.dn1.h1', '64.dn1.e2', '64.dn1.g1', '64.dn1.h2', '64.dn1.f1', '64.dk1.a1', '64.dk1.d1', '64.dk1.c1', '64.dk1.b1', '64.dk1.i1', '64.dk1.l1', '64.dk1.k1', '64.dk1.j1', '64.dk1.e1', '64.dk1.h1', '64.dk1.g1', '64.dk1.f1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.n1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.q1.a1', '2.v1.a1'], 'contains': ['8.t1.a1', '8.bb1.a1', '8.bc1.a1', '8.ef1.a1', '8.eh1.a1', '8.ex1.a1', '8.ey1.a1'], 'core': '4.cd1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2407, 5385, 8302, 7457, 2409, 5383, 8295, 7474], 'generators': [1, 70, 16], 'label': '256.30836.4.cd1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cd1.a1', 'normal_contained_in': ['2.g1.a1', '2.q1.a1', '2.v1.a1'], 'normal_contains': ['8.t1.a1', '8.bb1.a1', '8.bc1.a1', '8.ef1.a1', '8.eh1.a1', '8.ex1.a1', '8.ey1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cd1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879726
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.k1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.bg1.b1', '16.bg1.d1', '16.ir1.b1', '16.is1.b1', '16.it1.b1', '16.iu1.b1', '16.iv1.b1', '16.iw1.b1'], 'contains': ['64.g1.a1', '64.i1.b1', '64.i1.c1', '64.bv1.b1', '64.cf1.b1'], 'core': '32.k1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8361, 6977, 5231, 7536, 8365, 6975, 5227, 7552], 'generators': [129, 136, 160], 'label': '256.30836.32.k1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.k1.b1', 'normal_contained_in': ['16.b1.a1', '16.bg1.b1', '16.bg1.d1'], 'normal_contains': ['64.g1.a1', '64.i1.b1', '64.i1.c1'], 'normalizer': '1.a1.a1', 'old_label': '32.k1.b1', 'projective_image': '64.263', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879727
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.l1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.bg1.a1', '16.bg1.d1', '16.ix1.a1', '16.iy1.a1', '16.iz1.a1', '16.ja1.a1', '16.jb1.a1', '16.jc1.a1'], 'contains': ['64.g1.a1', '64.bz1.a1', '64.cj1.a1', '64.ct1.a1'], 'core': '32.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8335, 4842, 5217, 7470, 8339, 4822, 5213, 7487], 'generators': [3, 136, 160], 'label': '256.30836.32.l1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.l1.a1', 'normal_contained_in': ['16.f1.a1', '16.bg1.d1', '16.bg1.a1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.l1.a1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879728
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.l1', 'aut_quo_index': 48, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.bg1.b1', '16.bg1.c1', '16.ix1.b1', '16.iy1.b1', '16.iz1.b1', '16.ja1.b1', '16.jb1.b1', '16.jc1.b1'], 'contains': ['64.g1.a1', '64.bz1.b1', '64.cj1.b1', '64.ct1.b1'], 'core': '32.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8335, 4842, 5176, 7503, 8339, 4822, 5171, 7519], 'generators': [131, 136, 160], 'label': '256.30836.32.l1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.l1.b1', 'normal_contained_in': ['16.f1.a1', '16.bg1.b1', '16.bg1.c1'], 'normal_contains': ['64.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.l1.b1', 'projective_image': '64.263', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.l1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879729
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.bh1.a1', '16.bi1.a1', '16.bi1.b1', '16.bj1.a1', '16.bk1.a1', '16.bl1.a1'], 'contains': ['64.a1.a1', '64.j1.a1', '64.j1.b1', '64.u1.a1', '64.u1.b1', '64.bu1.a1', '64.bu1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8015, -1, 5162, -1, 8019, -1, 5157, -1], 'generators': [2, 32, 128], 'label': '256.30836.32.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.m1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879730
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.bh1.a1', '16.bm1.a1', '16.bm1.b1', '16.bn1.a1', '16.bo1.a1', '16.bp1.a1'], 'contains': ['64.a1.a1', '64.k1.a1', '64.k1.b1', '64.v1.a1', '64.v1.b1', '64.bv1.a1', '64.bv1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7989, -1, 5120, -1, 7993, -1, 5116, -1], 'generators': [1, 32, 128], 'label': '256.30836.32.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.n1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879731
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.bi1.a1', '16.bi1.b1', '16.bn1.a1', '16.bx1.a1', '16.by1.a1', '16.bz1.a1'], 'contains': ['64.a1.a1', '64.m1.a1', '64.m1.b1', '64.x1.a1', '64.bx1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8068, -1, 5051, -1, 8073, -1, 5046, -1], 'generators': [6, 32, 128], 'label': '256.30836.32.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.o1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879732
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.bj1.a1', '16.bm1.a1', '16.bm1.b1', '16.bx1.a1', '16.ca1.a1', '16.cb1.a1'], 'contains': ['64.a1.a1', '64.n1.a1', '64.y1.a1', '64.by1.a1', '64.by1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7962, -1, 5065, -1, 7966, -1, 5060, -1], 'generators': [5, 32, 128], 'label': '256.30836.32.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.p1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879779
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1', '16.ec1.a1', '16.ec1.b1', '16.eg1.a1', '16.eg1.b1', '16.el1.a1', '16.el1.b1'], 'contains': ['64.c1.a1', '64.df1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7555, -1, 7948, -1, 7559, -1, 7941, -1], 'generators': [70, 128], 'label': '256.30836.32.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '32.cf1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879736
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ce1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.o1.a1', 'complements': ['64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.g1', '64.dj1.d1', '64.dj1.p1', '64.dj1.k1', '64.dj1.c1', '64.dj1.h1', '64.dj1.l1', '64.dj1.o1', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.e1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.k1', '64.dk1.l1', '64.dk1.j1', '64.dk1.i1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.m1', '64.do1.a1', '64.do1.b2', '64.do1.d2', '64.do1.c1', '64.do1.d1', '64.do1.c2', '64.do1.a2', '64.do1.b1', '64.do1.e2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.h2', '64.do1.g1', '64.do1.e1', '64.do1.f2', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.dn1.g2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.s1.a1', '2.u1.a1'], 'contains': ['8.u1.a1', '8.v1.a1', '8.ba1.a1', '8.ei1.a1', '8.ej1.a1', '8.ez1.a1', '8.fd1.a1'], 'core': '4.ce1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5885, 6394, 8068, 961, 5888, 6392, 8061, 963], 'generators': [1, 66, 84], 'label': '256.30836.4.ce1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ce1.a1', 'normal_contained_in': ['2.f1.a1', '2.s1.a1', '2.u1.a1'], 'normal_contains': ['8.u1.a1', '8.v1.a1', '8.ba1.a1', '8.fd1.a1', '8.ez1.a1', '8.ej1.a1', '8.ei1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ce1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879737
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.bo1.a1', '16.bs1.a1', '16.bs1.b1', '16.ca1.a1', '16.ci1.a1', '16.cj1.a1'], 'contains': ['64.a1.a1', '64.r1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6308, -1, 5909, -1, 6312, -1, 5904, -1], 'generators': [64, 32], 'label': '256.30836.32.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.r1.a1', 'old_label': '32.t1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879738
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.bk1.a1', '16.bt1.a1', '16.bt1.b1', '16.by1.a1', '16.ci1.a1', '16.ck1.a1'], 'contains': ['64.a1.a1', '64.bc1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6109, -1, 5814, -1, 6112, -1, 5809, -1], 'generators': [16, 128], 'label': '256.30836.32.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.j1.a1', 'old_label': '32.u1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.u1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879739
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.bo1.a1', '16.bu1.a1', '16.bu1.b1', '16.cb1.a1', '16.cg1.a1', '16.cl1.a1'], 'contains': ['64.a1.a1', '64.s1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5567, -1, 6191, -1, 5560, -1, 6186, -1], 'generators': [65, 32], 'label': '256.30836.32.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.p1.a1', 'old_label': '32.v1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879740
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '16.bl1.a1', '16.bv1.a1', '16.bv1.b1', '16.by1.a1', '16.ch1.a1', '16.cl1.a1'], 'contains': ['64.a1.a1', '64.cc1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6706, -1, 6086, -1, 6709, -1, 6080, -1], 'generators': [22, 128], 'label': '256.30836.32.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '32.w1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879741
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dv1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.q1.a1', '16.bw1.a1', '16.bw1.b1', '16.cc1.a1', '16.cf1.a1', '16.ci1.a1', '16.cm1.a1'], 'contains': ['64.a1.a1', '64.cd1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6220, -1, 6001, -1, 6224, -1, 5996, -1], 'generators': [80, 128], 'label': '256.30836.32.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.x1.a1', 'old_label': '32.x1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879742
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.bp1.a1', '16.bs1.a1', '16.bs1.b1', '16.cb1.a1', '16.ck1.a1', '16.cm1.a1'], 'contains': ['64.a1.a1', '64.bd1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5743, -1, 5886, -1, 5826, -1, 5881, -1], 'generators': [68, 128], 'label': '256.30836.32.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.r1.a1', 'old_label': '32.y1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879743
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.s1.a1', '16.bl1.a1', '16.bt1.a1', '16.bt1.b1', '16.bz1.a1', '16.cj1.a1', '16.cm1.a1'], 'contains': ['64.a1.a1', '64.ce1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6662, -1, 5638, -1, 6665, -1, 5633, -1], 'generators': [20, 128], 'label': '256.30836.32.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.j1.a1', 'old_label': '32.z1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879744
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1.a1', '16.bk1.a1', '16.bv1.a1', '16.bv1.b1', '16.bz1.a1', '16.cg1.a1', '16.cn1.a1'], 'contains': ['64.a1.a1', '64.be1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5105, -1, 6109, -1, 5103, -1, 6103, -1], 'generators': [18, 128], 'label': '256.30836.32.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.i1.a1', 'old_label': '32.ba1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879745
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.fd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.u1.a1', '16.bw1.a1', '16.bw1.b1', '16.cd1.a1', '16.ce1.a1', '16.cj1.a1', '16.ck1.a1'], 'contains': ['64.a1.a1', '64.t1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5682, -1, 6049, -1, 5675, -1, 6043, -1], 'generators': [84, 32], 'label': '256.30836.32.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.x1.a1', 'old_label': '32.bb1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879746
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1', '16.bp1.a1', '16.bu1.a1', '16.bu1.b1', '16.ca1.a1', '16.ch1.a1', '16.cn1.a1'], 'contains': ['64.a1.a1', '64.bf1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3760, -1, 6156, -1, 3879, -1, 6151, -1], 'generators': [69, 128], 'label': '256.30836.32.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.p1.a1', 'old_label': '32.bc1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879747
{'ambient': '256.30836', 'aut_centralizer_order': 8, 'aut_label': '2.h1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': ['128.i1.a1', '128.i1.c1', '128.i1.d1', '128.i1.b1', '128.m1.a1', '128.m1.b1', '128.l1.a1', '128.l1.b1', '128.n1.a1', '128.n1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.i1.a1', '4.l1.a1', '4.t1.a1', '4.w1.a1', '4.z1.a1', '4.bf1.a1', '4.cr1.a1', '4.ct1.a1', '4.cw1.a1', '4.db1.a1', '4.dn1.a1', '4.dp1.a1', '4.ds1.a1', '4.dx1.a1'], 'core': '2.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3127, 6709, 8205, 7014, 3128, 6706, 8197, 7029], 'generators': [17, 2, 4, 64], 'label': '256.30836.2.h1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.l1.a1', '4.i1.a1', '4.w1.a1', '4.t1.a1', '4.z1.a1', '4.bf1.a1', '4.cr1.a1', '4.ct1.a1', '4.db1.a1', '4.cw1.a1', '4.dp1.a1', '4.dn1.a1', '4.ds1.a1', '4.dx1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.h1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879774
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ca1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.dz1.a1', '16.dz1.b1', '16.ef1.a1', '16.ef1.b1', '16.ej1.a1', '16.ej1.b1'], 'contains': ['64.c1.a1', '64.q1.a1', '64.cv1.a1', '64.de1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5393, -1, 6067, -1, 5386, -1, 6062, -1], 'generators': [83, 136, 128], 'label': '256.30836.32.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '32.ca1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879775
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.ea1.a1', '16.ea1.b1', '16.eg1.a1', '16.eg1.b1', '16.ek1.a1', '16.ek1.b1'], 'contains': ['64.c1.a1', '64.r1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7511, -1, 8045, -1, 7515, -1, 8038, -1], 'generators': [64, 136], 'label': '256.30836.32.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '32.cb1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879748
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cf1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.h1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.f1', '64.dk1.e1', '64.dk1.g1', '64.dk1.h1', '64.dk1.j1', '64.dk1.i1', '64.dk1.k1', '64.dk1.l1', '64.dk1.m1', '64.dk1.n1', '64.dk1.p1', '64.dk1.o1', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.f1', '64.dn1.h2', '64.dn1.e1', '64.dn1.e2', '64.dn1.h1', '64.do1.a1', '64.do1.b2', '64.do1.d2', '64.do1.c1', '64.do1.d1', '64.do1.c2', '64.do1.a2', '64.do1.b1', '64.do1.f1', '64.do1.e2', '64.do1.g2', '64.do1.h1', '64.do1.g1', '64.do1.h2', '64.do1.f2', '64.do1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.s1.a1', '2.w1.a1'], 'contains': ['8.u1.a1', '8.w1.a1', '8.z1.a1', '8.ek1.a1', '8.em1.a1', '8.fe1.a1', '8.fg1.a1'], 'core': '4.cf1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1625, 3413, 8366, 4762, 1625, 3412, 8359, 4773], 'generators': [1, 66, 80], 'label': '256.30836.4.cf1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cf1.a1', 'normal_contained_in': ['2.d1.a1', '2.s1.a1', '2.w1.a1'], 'normal_contains': ['8.u1.a1', '8.z1.a1', '8.w1.a1', '8.fe1.a1', '8.fg1.a1', '8.em1.a1', '8.ek1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cf1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879749
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.ep1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.br1.a1', '16.br1.b1', '16.cd1.a1', '16.cf1.a1', '16.cl1.a1', '16.cn1.a1'], 'contains': ['64.a1.a1', '64.bg1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4421, -1, 6240, -1, 4418, -1, 6235, -1], 'generators': [87, 128], 'label': '256.30836.32.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.y1.a1', 'old_label': '32.bd1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879750
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.co1.a1', '16.co1.b1', '16.cx1.a1', '16.cy1.a1', '16.cz1.a1', '16.da1.a1'], 'contains': ['64.b1.a1', '64.k1.a1', '64.k1.b1', '64.bi1.a1', '64.bi1.b1', '64.cf1.a1', '64.cf1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7732, -1, 5754, -1, 7736, -1, 5749, -1], 'generators': [1, 168, 128], 'label': '256.30836.32.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.be1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.be1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879751
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.cp1.a1', '16.cp1.b1', '16.cx1.a1', '16.db1.a1', '16.dc1.a1', '16.dd1.a1'], 'contains': ['64.b1.a1', '64.l1.a1', '64.l1.b1', '64.bj1.a1', '64.cg1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7758, -1, 5462, -1, 7762, -1, 5457, -1], 'generators': [4, 168, 128], 'label': '256.30836.32.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bf1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879752
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.cp1.a1', '16.cp1.b1', '16.cy1.a1', '16.de1.a1', '16.df1.a1', '16.dg1.a1'], 'contains': ['64.b1.a1', '64.m1.a1', '64.m1.b1', '64.bk1.a1', '64.ch1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7157, -1, 5546, -1, 7160, -1, 5541, -1], 'generators': [6, 168, 128], 'label': '256.30836.32.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bg1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879753
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.cq1.a1', '16.cq1.b1', '16.cx1.a1', '16.de1.a1', '16.dh1.a1', '16.di1.a1'], 'contains': ['64.b1.a1', '64.n1.a1', '64.bl1.a1', '64.bl1.b1', '64.ci1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7183, -1, 5023, -1, 7187, -1, 5018, -1], 'generators': [5, 168, 128], 'label': '256.30836.32.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.bh1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879754
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.co1.a1', '16.co1.b1', '16.db1.a1', '16.de1.a1', '16.dj1.a1', '16.dk1.a1'], 'contains': ['64.b1.a1', '64.o1.a1', '64.bm1.a1', '64.cj1.a1', '64.cj1.b1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7211, -1, 5768, -1, 7214, -1, 5763, -1], 'generators': [3, 168, 128], 'label': '256.30836.32.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.bi1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879755
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.cq1.a1', '16.cq1.b1', '16.cy1.a1', '16.db1.a1', '16.dl1.a1', '16.dm1.a1'], 'contains': ['64.b1.a1', '64.p1.a1', '64.p1.b1', '64.bn1.a1', '64.ck1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7785, -1, 5037, -1, 7789, -1, 5032, -1], 'generators': [7, 168, 128], 'label': '256.30836.32.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.bj1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879756
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.cr1.a1', '16.cr1.b1', '16.dh1.a1', '16.dl1.a1', '16.dn1.a1', '16.do1.a1'], 'contains': ['64.b1.a1', '64.q1.a1', '64.bo1.a1', '64.cl1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3167, -1, 9004, -1, 3169, -1, 8996, -1], 'generators': [83, 168, 128], 'label': '256.30836.32.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.l1.a1', 'old_label': '32.bk1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879757
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '16.cs1.a1', '16.cs1.b1', '16.cz1.a1', '16.dj1.a1', '16.dn1.a1', '16.dp1.a1'], 'contains': ['64.b1.a1', '64.r1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5479, -1, 8682, -1, 5472, -1, 8674, -1], 'generators': [64, 168], 'label': '256.30836.32.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.bl1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879758
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.bw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.cs1.a1', '16.cs1.b1', '16.da1.a1', '16.dk1.a1', '16.do1.a1', '16.dq1.a1'], 'contains': ['64.b1.a1', '64.bp1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4178, -1, 8659, -1, 4179, -1, 8651, -1], 'generators': [66, 128], 'label': '256.30836.32.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.bm1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879776
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.ea1.a1', '16.ea1.b1', '16.eh1.a1', '16.eh1.b1', '16.el1.a1', '16.el1.b1'], 'contains': ['64.c1.a1', '64.s1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6882, -1, 8022, -1, 6886, -1, 8016, -1], 'generators': [65, 136], 'label': '256.30836.32.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '32.cc1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879777
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.fd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.u1.a1', '16.eb1.a1', '16.eb1.b1', '16.ei1.a1', '16.ei1.b1', '16.ej1.a1', '16.ej1.b1'], 'contains': ['64.c1.a1', '64.t1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6397, -1, 5955, -1, 6400, -1, 5950, -1], 'generators': [84, 136], 'label': '256.30836.32.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '32.cd1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879778
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ce1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.ec1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.dz1.a1', '16.dz1.b1', '16.ei1.a1', '16.ei1.b1', '16.em1.a1', '16.em1.b1'], 'contains': ['64.c1.a1', '64.cw1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6441, -1, 5932, -1, 6444, -1, 5927, -1], 'generators': [82, 128], 'label': '256.30836.32.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '32.ce1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879759
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cg1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.f1', '64.dj1.j1', '64.dj1.m1', '64.dj1.e1', '64.dj1.b1', '64.dj1.n1', '64.dj1.i1', '64.dj1.d1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.h1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dk1.a1', '64.dk1.b1', '64.dk1.d1', '64.dk1.c1', '64.dk1.f1', '64.dk1.e1', '64.dk1.g1', '64.dk1.h1', '64.dk1.j1', '64.dk1.i1', '64.dk1.k1', '64.dk1.l1', '64.dk1.m1', '64.dk1.n1', '64.dk1.p1', '64.dk1.o1', '64.dn1.a1', '64.dn1.d2', '64.dn1.d1', '64.dn1.a2', '64.dn1.c1', '64.dn1.b2', '64.dn1.b1', '64.dn1.c2', '64.dn1.f2', '64.dn1.g1', '64.dn1.g2', '64.dn1.f1', '64.dn1.h2', '64.dn1.e1', '64.dn1.e2', '64.dn1.h1', '64.do1.a1', '64.do1.b2', '64.do1.d2', '64.do1.c1', '64.do1.d1', '64.do1.c2', '64.do1.a2', '64.do1.b1', '64.do1.f1', '64.do1.e2', '64.do1.g2', '64.do1.h1', '64.do1.g1', '64.do1.h2', '64.do1.f2', '64.do1.e1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.q1.a1', '2.w1.a1'], 'contains': ['8.u1.a1', '8.y1.a1', '8.bc1.a1', '8.el1.a1', '8.en1.a1', '8.ff1.a1', '8.fh1.a1'], 'core': '4.cg1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1574, 5553, 8145, 3379, 1575, 5551, 8137, 3386], 'generators': [1, 66, 20], 'label': '256.30836.4.cg1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cg1.a1', 'normal_contained_in': ['2.f1.a1', '2.q1.a1', '2.w1.a1'], 'normal_contains': ['8.u1.a1', '8.y1.a1', '8.bc1.a1', '8.fh1.a1', '8.ff1.a1', '8.en1.a1', '8.el1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cg1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879760
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.ca1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '16.ct1.a1', '16.ct1.b1', '16.cz1.a1', '16.dk1.a1', '16.dr1.a1', '16.ds1.a1'], 'contains': ['64.b1.a1', '64.s1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4835, -1, 8705, -1, 4833, -1, 8697, -1], 'generators': [65, 168], 'label': '256.30836.32.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '32.bn1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879761
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '16.cu1.a1', '16.cu1.b1', '16.dc1.a1', '16.df1.a1', '16.do1.a1', '16.dp1.a1'], 'contains': ['64.b1.a1', '64.bq1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3203, -1, 8986, -1, 3204, -1, 8978, -1], 'generators': [17, 128], 'label': '256.30836.32.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.bo1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879762
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.ce1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.ct1.a1', '16.ct1.b1', '16.da1.a1', '16.dj1.a1', '16.dt1.a1', '16.du1.a1'], 'contains': ['64.b1.a1', '64.br1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3703, -1, 8728, -1, 3718, -1, 8720, -1], 'generators': [67, 128], 'label': '256.30836.32.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '32.bp1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879763
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.cv1.a1', '16.cv1.b1', '16.dd1.a1', '16.df1.a1', '16.dr1.a1', '16.dt1.a1'], 'contains': ['64.b1.a1', '64.cm1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3528, -1, 8963, -1, 3530, -1, 8955, -1], 'generators': [23, 128], 'label': '256.30836.32.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.a1', 'old_label': '32.bq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879764
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.br1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.fd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.u1.a1', '16.cw1.a1', '16.cw1.b1', '16.di1.a1', '16.dl1.a1', '16.ds1.a1', '16.dt1.a1'], 'contains': ['64.b1.a1', '64.t1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4090, -1, 9228, -1, 4091, -1, 9220, -1], 'generators': [84, 168], 'label': '256.30836.32.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '32.br1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.br1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879765
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1', '16.cr1.a1', '16.cr1.b1', '16.di1.a1', '16.dm1.a1', '16.dp1.a1', '16.dq1.a1'], 'contains': ['64.b1.a1', '64.cn1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3484, -1, 9160, -1, 3486, -1, 9152, -1], 'generators': [81, 128], 'label': '256.30836.32.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.l1.a1', 'old_label': '32.bs1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879766
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.cv1.a1', '16.cv1.b1', '16.dc1.a1', '16.dg1.a1', '16.ds1.a1', '16.du1.a1'], 'contains': ['64.b1.a1', '64.co1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3572, -1, 8940, -1, 3574, -1, 8932, -1], 'generators': [21, 128], 'label': '256.30836.32.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.a1', 'old_label': '32.bt1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879767
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ba1.a1', '16.cu1.a1', '16.cu1.b1', '16.dd1.a1', '16.dg1.a1', '16.dn1.a1', '16.dq1.a1'], 'contains': ['64.b1.a1', '64.bs1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3247, -1, 8917, -1, 3248, -1, 8909, -1], 'generators': [19, 128], 'label': '256.30836.32.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.ba1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.bu1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879768
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.eq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bb1.a1', '16.cw1.a1', '16.cw1.b1', '16.dh1.a1', '16.dm1.a1', '16.dr1.a1', '16.du1.a1'], 'contains': ['64.b1.a1', '64.bt1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3396, -1, 9251, -1, 3398, -1, 9243, -1], 'generators': [86, 128], 'label': '256.30836.32.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '32.bv1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879769
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.bw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.dv1.a1', '16.dv1.b1', '16.dw1.a1', '16.dw1.b1', '16.dx1.a1', '16.dx1.b1'], 'contains': ['64.c1.a1', '64.j1.a1', '64.j1.b1', '64.cp1.a1', '64.cp1.b1', '64.cx1.a1', '64.cx1.b1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8974, -1, 4842, -1, 8978, -1, 4838, -1], 'generators': [2, 136, 128], 'label': '256.30836.32.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.bw1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879770
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ch1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.i1', '64.dj1.n1', '64.dj1.f1', '64.dj1.e1', '64.dj1.m1', '64.dj1.j1', '64.dj1.b1', '64.dj1.k1', '64.dj1.c1', '64.dj1.h1', '64.dj1.p1', '64.dj1.o1', '64.dj1.g1', '64.dj1.d1', '64.dj1.l1', '64.do1.a1', '64.do1.b1', '64.do1.a2', '64.do1.b2', '64.do1.d1', '64.do1.c1', '64.do1.d2', '64.do1.c2', '64.do1.e2', '64.do1.f2', '64.do1.e1', '64.do1.f1', '64.do1.h2', '64.do1.g2', '64.do1.h1', '64.do1.g1', '64.dn1.a1', '64.dn1.c2', '64.dn1.b1', '64.dn1.d2', '64.dn1.c1', '64.dn1.a2', '64.dn1.d1', '64.dn1.b2', '64.dn1.g2', '64.dn1.e1', '64.dn1.h2', '64.dn1.f1', '64.dn1.e2', '64.dn1.g1', '64.dn1.f2', '64.dn1.h1', '64.dk1.a1', '64.dk1.b1', '64.dk1.c1', '64.dk1.d1', '64.dk1.i1', '64.dk1.j1', '64.dk1.k1', '64.dk1.l1', '64.dk1.n1', '64.dk1.m1', '64.dk1.p1', '64.dk1.o1', '64.dk1.f1', '64.dk1.e1', '64.dk1.h1', '64.dk1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.s1.a1', '2.v1.a1'], 'contains': ['8.v1.a1', '8.w1.a1', '8.bb1.a1', '8.fa1.a1', '8.fc1.a1', '8.fi1.a1', '8.fk1.a1'], 'core': '4.ch1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8491, 2182, 7823, 7086, 8495, 2181, 7816, 7102], 'generators': [1, 70, 80], 'label': '256.30836.4.ch1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ch1.a1', 'normal_contained_in': ['2.e1.a1', '2.s1.a1', '2.v1.a1'], 'normal_contains': ['8.v1.a1', '8.bb1.a1', '8.w1.a1', '8.fk1.a1', '8.fi1.a1', '8.fa1.a1', '8.fc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ch1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879780
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.ez1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bc1.a1', '16.eb1.a1', '16.eb1.b1', '16.ef1.a1', '16.ef1.b1', '16.em1.a1', '16.em1.b1'], 'contains': ['64.c1.a1', '64.dg1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6750, -1, 5978, -1, 6754, -1, 5973, -1], 'generators': [85, 128], 'label': '256.30836.32.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '32.cg1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879781
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ci1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.d1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.m1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.j1', '64.dk1.l1', '64.dk1.k1', '64.dk1.i1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.e1', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.g1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.r1.a1', '2.w1.a1'], 'contains': ['8.w1.a1', '8.x1.a1', '8.y1.a1', '8.fl1.a1', '8.fm1.a1', '8.fo1.a1', '8.fr1.a1'], 'core': '4.ci1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6222, 2772, 5493, 5901, 6225, 2771, 5489, 5914], 'generators': [1, 68, 80], 'label': '256.30836.4.ci1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ci1.a1', 'normal_contained_in': ['2.e1.a1', '2.r1.a1', '2.w1.a1'], 'normal_contains': ['8.x1.a1', '8.y1.a1', '8.w1.a1', '8.fm1.a1', '8.fr1.a1', '8.fo1.a1', '8.fl1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ci1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879782
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ch1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bd1.a1', '16.ec1.a1', '16.ec1.b1', '16.eh1.a1', '16.eh1.b1', '16.ek1.a1', '16.ek1.b1'], 'contains': ['64.c1.a1', '64.dh1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6927, -1, 7971, -1, 6930, -1, 7964, -1], 'generators': [71, 128], 'label': '256.30836.32.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.v1.a1', 'old_label': '32.ch1.a1', 'projective_image': '64.263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879783
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ci1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.co1.a1', '16.dv1.a1', '16.en1.a1', '16.en1.b1', '16.en1.c1', '16.en1.d1'], 'contains': ['64.j1.a1', '64.k1.a1', '64.o1.a1', '64.di1.a1', '64.di1.b1', '64.di1.e1', '64.di1.h1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8840, -1, 3981, -1, 8845, -1, 3977, -1], 'generators': [1, 2, 128], 'label': '256.30836.32.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ci1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879784
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ci1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.co1.a1', '16.dv1.b1', '16.en1.e1', '16.en1.f1', '16.en1.g1', '16.en1.h1'], 'contains': ['64.j1.a1', '64.k1.b1', '64.o1.a1', '64.di1.c1', '64.di1.d1', '64.di1.i1', '64.di1.j1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8840, -1, 3952, -1, 8845, -1, 3949, -1], 'generators': [33, 2, 128], 'label': '256.30836.32.ci1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ci1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ci1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879785
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ci1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.co1.b1', '16.dv1.a1', '16.en1.i1', '16.en1.j1', '16.en1.k1', '16.en1.l1'], 'contains': ['64.j1.b1', '64.k1.a1', '64.o1.a1', '64.di1.f1', '64.di1.g1', '64.di1.k1', '64.di1.n1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8840, -1, 3911, -1, 8845, -1, 3908, -1], 'generators': [1, 138, 128], 'label': '256.30836.32.ci1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ci1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ci1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879786
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ci1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bh1.a1', '16.co1.b1', '16.dv1.b1', '16.en1.m1', '16.en1.n1', '16.en1.o1', '16.en1.p1'], 'contains': ['64.j1.b1', '64.k1.b1', '64.o1.a1', '64.di1.l1', '64.di1.m1', '64.di1.o1', '64.di1.p1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8840, -1, 3786, -1, 8845, -1, 3783, -1], 'generators': [33, 138, 128], 'label': '256.30836.32.ci1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ci1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ci1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879787
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.cp1.a1', '16.dw1.a1', '16.en1.a1', '16.en1.e1'], 'contains': ['64.j1.a1', '64.l1.a1', '64.m1.a1', '64.dj1.a1', '64.dj1.e1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8893, -1, 4315, -1, 8898, -1, 4310, -1], 'generators': [2, 4, 128], 'label': '256.30836.32.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cj1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879788
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.cp1.a1', '16.dw1.b1', '16.en1.b1', '16.en1.f1'], 'contains': ['64.j1.a1', '64.l1.a1', '64.m1.b1', '64.dj1.b1', '64.dj1.f1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8893, -1, 4286, -1, 8898, -1, 4282, -1], 'generators': [170, 4, 128], 'label': '256.30836.32.cj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cj1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879789
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.b1', '16.cp1.a1', '16.dw1.a1', '16.en1.c1', '16.en1.g1'], 'contains': ['64.j1.a1', '64.l1.b1', '64.m1.a1', '64.dj1.c1', '64.dj1.g1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8893, -1, 4508, -1, 8898, -1, 4505, -1], 'generators': [2, 140, 128], 'label': '256.30836.32.cj1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cj1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879790
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.b1', '16.cp1.a1', '16.dw1.b1', '16.en1.d1', '16.en1.h1'], 'contains': ['64.j1.a1', '64.l1.b1', '64.m1.b1', '64.dj1.d1', '64.dj1.h1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8893, -1, 4495, -1, 8898, -1, 4491, -1], 'generators': [170, 140, 128], 'label': '256.30836.32.cj1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cj1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879791
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.cp1.b1', '16.dw1.a1', '16.en1.i1', '16.en1.m1'], 'contains': ['64.j1.b1', '64.l1.a1', '64.m1.a1', '64.dj1.i1', '64.dj1.m1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8893, -1, 4272, -1, 8898, -1, 4269, -1], 'generators': [138, 4, 128], 'label': '256.30836.32.cj1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cj1.e1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879816
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.de1.a1', '16.ee1.a1', '16.en1.a1', '16.en1.g1', '16.en1.k1', '16.en1.m1'], 'contains': ['64.m1.a1', '64.n1.a1', '64.o1.a1', '64.do1.a1', '64.do1.b1', '64.do1.c1', '64.do1.d1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8867, -1, 2757, -1, 8871, -1, 2755, -1], 'generators': [5, 6, 128], 'label': '256.30836.32.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cp1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879817
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.de1.a1', '16.ee1.a1', '16.en1.c1', '16.en1.e1', '16.en1.i1', '16.en1.o1'], 'contains': ['64.m1.a1', '64.n1.a1', '64.o1.a1', '64.do1.a2', '64.do1.b2', '64.do1.c2', '64.do1.d2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8867, -1, 2744, -1, 8871, -1, 2741, -1], 'generators': [37, 6, 128], 'label': '256.30836.32.cp1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cp1.a2', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cp1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879792
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cj1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.d1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.m1', '64.dk1.o1', '64.dk1.p1', '64.dk1.n1', '64.dk1.j1', '64.dk1.l1', '64.dk1.k1', '64.dk1.i1', '64.dk1.f1', '64.dk1.h1', '64.dk1.g1', '64.dk1.e1', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.g1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.e2'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.p1.a1', '2.w1.a1'], 'contains': ['8.x1.a1', '8.z1.a1', '8.bc1.a1', '8.fn1.a1', '8.fp1.a1', '8.ft1.a1', '8.fy1.a1', '8.gt1.a1', '8.gt1.b1'], 'core': '4.cj1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [866, 8674, 5894, 4695, 866, 8671, 5889, 4705], 'generators': [1, 18, 68, 128], 'label': '256.30836.4.cj1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cj1.a1', 'normal_contained_in': ['2.g1.a1', '2.p1.a1', '2.w1.a1'], 'normal_contains': ['8.x1.a1', '8.z1.a1', '8.bc1.a1', '8.fy1.a1', '8.ft1.a1', '8.fp1.a1', '8.fn1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cj1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879793
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.a1', '16.cp1.b1', '16.dw1.b1', '16.en1.j1', '16.en1.n1'], 'contains': ['64.j1.b1', '64.l1.a1', '64.m1.b1', '64.dj1.j1', '64.dj1.n1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8893, -1, 4230, -1, 8898, -1, 4227, -1], 'generators': [34, 4, 128], 'label': '256.30836.32.cj1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cj1.f1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879794
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.b1', '16.cp1.b1', '16.dw1.a1', '16.en1.k1', '16.en1.o1'], 'contains': ['64.j1.b1', '64.l1.b1', '64.m1.a1', '64.dj1.k1', '64.dj1.o1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8893, -1, 4481, -1, 8898, -1, 4477, -1], 'generators': [138, 140, 128], 'label': '256.30836.32.cj1.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cj1.g1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879795
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cj1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bi1.b1', '16.cp1.b1', '16.dw1.b1', '16.en1.l1', '16.en1.p1'], 'contains': ['64.j1.b1', '64.l1.b1', '64.m1.b1', '64.dj1.l1', '64.dj1.p1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8893, -1, 4467, -1, 8898, -1, 4463, -1], 'generators': [34, 140, 128], 'label': '256.30836.32.cj1.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cj1.h1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cj1.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879796
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ck1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.cq1.a1', '16.dx1.a1', '16.en1.a1', '16.en1.c1', '16.en1.f1', '16.en1.h1'], 'contains': ['64.j1.a1', '64.n1.a1', '64.p1.a1', '64.dk1.a1', '64.dk1.c1', '64.dk1.e1', '64.dk1.g1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8920, -1, 3967, -1, 8925, -1, 3963, -1], 'generators': [5, 2, 128], 'label': '256.30836.32.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ck1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879797
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ck1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.cq1.a1', '16.dx1.b1', '16.en1.b1', '16.en1.d1', '16.en1.e1', '16.en1.g1'], 'contains': ['64.j1.a1', '64.n1.a1', '64.p1.b1', '64.dk1.b1', '64.dk1.d1', '64.dk1.f1', '64.dk1.h1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8920, -1, 2910, -1, 8925, -1, 2908, -1], 'generators': [37, 2, 128], 'label': '256.30836.32.ck1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ck1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ck1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879798
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ck1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.cq1.b1', '16.dx1.a1', '16.en1.i1', '16.en1.k1', '16.en1.n1', '16.en1.p1'], 'contains': ['64.j1.b1', '64.n1.a1', '64.p1.a1', '64.dk1.i1', '64.dk1.k1', '64.dk1.m1', '64.dk1.o1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8920, -1, 3897, -1, 8925, -1, 3894, -1], 'generators': [5, 138, 128], 'label': '256.30836.32.ck1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ck1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ck1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879799
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.ck1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bj1.a1', '16.cq1.b1', '16.dx1.b1', '16.en1.j1', '16.en1.l1', '16.en1.m1', '16.en1.o1'], 'contains': ['64.j1.b1', '64.n1.a1', '64.p1.b1', '64.dk1.j1', '64.dk1.l1', '64.dk1.n1', '64.dk1.p1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8920, -1, 2619, -1, 8925, -1, 2616, -1], 'generators': [37, 138, 128], 'label': '256.30836.32.ck1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.ck1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ck1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879800
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1', '16.cx1.a1', '16.dy1.a1', '16.en1.a1', '16.en1.b1', '16.en1.i1', '16.en1.j1'], 'contains': ['64.k1.a1', '64.l1.a1', '64.n1.a1', '64.dl1.a1', '64.dl1.b1', '64.dl1.e1', '64.dl1.f1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8946, -1, 1867, -1, 8951, -1, 1866, -1], 'generators': [1, 4, 128], 'label': '256.30836.32.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cl1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879801
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.b1', '16.cx1.a1', '16.dy1.a1', '16.en1.c1', '16.en1.d1', '16.en1.k1', '16.en1.l1'], 'contains': ['64.k1.a1', '64.l1.b1', '64.n1.a1', '64.dl1.c1', '64.dl1.d1', '64.dl1.g1', '64.dl1.h1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8946, -1, 3800, -1, 8951, -1, 3796, -1], 'generators': [1, 140, 128], 'label': '256.30836.32.cl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cl1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cl1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879802
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.a1', '16.cx1.a1', '16.dy1.b1', '16.en1.e1', '16.en1.f1', '16.en1.m1', '16.en1.n1'], 'contains': ['64.k1.b1', '64.l1.a1', '64.n1.a1', '64.dl1.i1', '64.dl1.j1', '64.dl1.m1', '64.dl1.n1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8946, -1, 1881, -1, 8951, -1, 1880, -1], 'generators': [33, 4, 128], 'label': '256.30836.32.cl1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cl1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cl1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879818
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.de1.a1', '16.ee1.b1', '16.en1.b1', '16.en1.h1', '16.en1.l1', '16.en1.n1'], 'contains': ['64.m1.b1', '64.n1.a1', '64.o1.a1', '64.do1.e1', '64.do1.f1', '64.do1.g1', '64.do1.h1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8867, -1, 2452, -1, 8871, -1, 2449, -1], 'generators': [37, 38, 128], 'label': '256.30836.32.cp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cp1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cp1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879819
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bx1.a1', '16.de1.a1', '16.ee1.b1', '16.en1.d1', '16.en1.f1', '16.en1.j1', '16.en1.p1'], 'contains': ['64.m1.b1', '64.n1.a1', '64.o1.a1', '64.do1.e2', '64.do1.f2', '64.do1.g2', '64.do1.h2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8867, -1, 2465, -1, 8871, -1, 2463, -1], 'generators': [5, 38, 128], 'label': '256.30836.32.cp1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bq1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cp1.b2', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cp1.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879803
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.ck1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': ['64.dj1.a1', '64.dj1.m1', '64.dj1.j1', '64.dj1.f1', '64.dj1.e1', '64.dj1.i1', '64.dj1.n1', '64.dj1.b1', '64.dj1.c1', '64.dj1.o1', '64.dj1.l1', '64.dj1.h1', '64.dj1.g1', '64.dj1.k1', '64.dj1.p1', '64.dj1.d1', '64.do1.a1', '64.do1.c1', '64.do1.d2', '64.do1.b2', '64.do1.d1', '64.do1.b1', '64.do1.a2', '64.do1.c2', '64.do1.g1', '64.do1.e1', '64.do1.f2', '64.do1.h2', '64.do1.f1', '64.do1.h1', '64.do1.g2', '64.do1.e2', '64.dk1.a1', '64.dk1.c1', '64.dk1.d1', '64.dk1.b1', '64.dk1.o1', '64.dk1.m1', '64.dk1.n1', '64.dk1.p1', '64.dk1.k1', '64.dk1.i1', '64.dk1.j1', '64.dk1.l1', '64.dk1.e1', '64.dk1.g1', '64.dk1.h1', '64.dk1.f1', '64.dn1.a1', '64.dn1.a2', '64.dn1.d1', '64.dn1.d2', '64.dn1.c1', '64.dn1.c2', '64.dn1.b1', '64.dn1.b2', '64.dn1.e2', '64.dn1.e1', '64.dn1.h2', '64.dn1.h1', '64.dn1.g2', '64.dn1.g1', '64.dn1.f2', '64.dn1.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.s1.a1', '2.t1.a1'], 'contains': ['8.z1.a1', '8.ba1.a1', '8.bb1.a1', '8.fs1.a1', '8.fu1.a1', '8.fv1.a1', '8.fx1.a1'], 'core': '4.ck1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6340, 9337, 8212, 8743, 6343, 9333, 8205, 8762], 'generators': [1, 18, 84], 'label': '256.30836.4.ck1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.ck1.a1', 'normal_contained_in': ['2.g1.a1', '2.s1.a1', '2.t1.a1'], 'normal_contains': ['8.ba1.a1', '8.bb1.a1', '8.z1.a1', '8.fx1.a1', '8.fu1.a1', '8.fs1.a1', '8.fv1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.ck1.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879804
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cl1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bm1.b1', '16.cx1.a1', '16.dy1.b1', '16.en1.g1', '16.en1.h1', '16.en1.o1', '16.en1.p1'], 'contains': ['64.k1.b1', '64.l1.b1', '64.n1.a1', '64.dl1.k1', '64.dl1.l1', '64.dl1.o1', '64.dl1.p1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8946, -1, 3814, -1, 8951, -1, 3810, -1], 'generators': [33, 140, 128], 'label': '256.30836.32.cl1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cl1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cl1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879805
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.a1', '16.bn1.a1', '16.cy1.a1', '16.en1.a1', '16.en1.c1', '16.en1.i1', '16.en1.k1'], 'contains': ['64.k1.a1', '64.m1.a1', '64.p1.a1', '64.dm1.a1', '64.dm1.a2', '64.dm1.c1', '64.dm1.c2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8814, -1, 3828, -1, 8818, -1, 3824, -1], 'generators': [1, 6, 128], 'label': '256.30836.32.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cm1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879806
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.b1', '16.bn1.a1', '16.cy1.a1', '16.en1.b1', '16.en1.d1', '16.en1.j1', '16.en1.l1'], 'contains': ['64.k1.a1', '64.m1.b1', '64.p1.b1', '64.dm1.b1', '64.dm1.b2', '64.dm1.d1', '64.dm1.d2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8814, -1, 2605, -1, 8818, -1, 2602, -1], 'generators': [1, 38, 128], 'label': '256.30836.32.cm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cm1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cm1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879807
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.c1', '16.bn1.a1', '16.cy1.a1', '16.en1.e1', '16.en1.g1', '16.en1.m1', '16.en1.o1'], 'contains': ['64.k1.b1', '64.m1.a1', '64.p1.b1', '64.dm1.e1', '64.dm1.e2', '64.dm1.g1', '64.dm1.g2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8814, -1, 2827, -1, 8818, -1, 2824, -1], 'generators': [33, 6, 128], 'label': '256.30836.32.cm1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cm1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cm1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879808
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cm1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bf1.d1', '16.bn1.a1', '16.cy1.a1', '16.en1.f1', '16.en1.h1', '16.en1.n1', '16.en1.p1'], 'contains': ['64.k1.b1', '64.m1.b1', '64.p1.a1', '64.dm1.f1', '64.dm1.f2', '64.dm1.h1', '64.dm1.h2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8814, -1, 3772, -1, 8818, -1, 3769, -1], 'generators': [33, 38, 128], 'label': '256.30836.32.cm1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bf1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.cm1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cm1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879809
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bo1.a1', '16.cz1.a1', '16.ea1.a1'], 'contains': ['64.k1.a1', '64.r1.a1', '64.s1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6838, -1, 8091, -1, 6842, -1, 8085, -1], 'generators': [1, 64], 'label': '256.30836.32.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.a1', 'old_label': '32.cn1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879810
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cn1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bo1.a1', '16.cz1.a1', '16.ea1.b1'], 'contains': ['64.k1.b1', '64.r1.a1', '64.s1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6838, -1, 8068, -1, 6842, -1, 8062, -1], 'generators': [33, 64], 'label': '256.30836.32.cn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.s1.a1', 'old_label': '32.cn1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cn1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879811
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.co1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.a1', '16.db1.a1', '16.ed1.a1', '16.en1.a1', '16.en1.f1', '16.en1.i1', '16.en1.n1'], 'contains': ['64.l1.a1', '64.o1.a1', '64.p1.a1', '64.dn1.a1', '64.dn1.a2', '64.dn1.c1', '64.dn1.c2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9001, -1, 2090, -1, 9005, -1, 2088, -1], 'generators': [3, 4, 128], 'label': '256.30836.32.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.co1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.co1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879812
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.co1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.a1', '16.db1.a1', '16.ed1.b1', '16.en1.b1', '16.en1.e1', '16.en1.j1', '16.en1.m1'], 'contains': ['64.l1.a1', '64.o1.a1', '64.p1.b1', '64.dn1.b1', '64.dn1.b2', '64.dn1.d1', '64.dn1.d2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9001, -1, 1687, -1, 9005, -1, 1686, -1], 'generators': [35, 4, 128], 'label': '256.30836.32.co1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.co1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.co1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879813
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.co1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.b1', '16.db1.a1', '16.ed1.a1', '16.en1.c1', '16.en1.h1', '16.en1.k1', '16.en1.p1'], 'contains': ['64.l1.b1', '64.o1.a1', '64.p1.a1', '64.dn1.e1', '64.dn1.e2', '64.dn1.g1', '64.dn1.g2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9001, -1, 4050, -1, 9005, -1, 4046, -1], 'generators': [3, 140, 128], 'label': '256.30836.32.co1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.co1.c1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.co1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879814
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cl1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.x1.a1', '2.y1.a1'], 'contains': ['8.bd1.a1', '8.be1.a1', '8.bn1.a1', '8.cp1.a1', '8.cx1.a1', '8.db1.a1', '8.di1.a1', '8.gc1.a1', '8.gc1.b1'], 'core': '4.cl1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5024, 1169, 5217, 6759, 5027, 1168, 5213, 6774], 'generators': [3, 4, 80, 136], 'label': '256.30836.4.cl1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cl1.a1', 'normal_contained_in': ['2.a1.a1', '2.x1.a1', '2.y1.a1'], 'normal_contains': ['8.bd1.a1', '8.be1.a1', '8.bn1.a1', '8.cp1.a1', '8.cx1.a1', '8.db1.a1', '8.di1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cl1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 30879815
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.co1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bq1.b1', '16.db1.a1', '16.ed1.b1', '16.en1.d1', '16.en1.g1', '16.en1.l1', '16.en1.o1'], 'contains': ['64.l1.b1', '64.o1.a1', '64.p1.b1', '64.dn1.f1', '64.dn1.f2', '64.dn1.h1', '64.dn1.h2'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9001, -1, 2813, -1, 9005, -1, 2811, -1], 'generators': [35, 140, 128], 'label': '256.30836.32.co1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '32.co1.d1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.co1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879820
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cq1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ce1.a1', '16.dl1.a1', '16.ej1.a1'], 'contains': ['64.p1.a1', '64.q1.a1', '64.t1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4957, -1, 6139, -1, 4955, -1, 6133, -1], 'generators': [83, 84], 'label': '256.30836.32.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.db1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.db1.a1', 'old_label': '32.cq1.a1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879821
{'ambient': '256.30836', 'aut_centralizer_order': 512, 'aut_label': '32.cq1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ce1.a1', '16.dl1.a1', '16.ej1.b1'], 'contains': ['64.p1.b1', '64.q1.a1', '64.t1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4957, -1, 6126, -1, 4955, -1, 6121, -1], 'generators': [115, 84], 'label': '256.30836.32.cq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.db1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.db1.a1', 'old_label': '32.cq1.b1', 'projective_image': '128.2222', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cq1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879822
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cr1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.eo1.a1', '16.eo1.b1', '16.ep1.a1', '16.eq1.a1', '16.er1.a1', '16.es1.a1'], 'contains': ['64.d1.a1', '64.u1.a1', '64.u1.b1', '64.bh1.a1', '64.bh1.b1', '64.cp1.a1', '64.cp1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7050, -1, 5699, -1, 7054, -1, 5693, -1], 'generators': [2, 136, 32], 'label': '256.30836.32.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cr1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879823
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cs1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.ep1.a1', '16.et1.a1', '16.et1.b1', '16.fb1.a1', '16.fc1.a1', '16.fd1.a1'], 'contains': ['64.d1.a1', '64.w1.a1', '64.w1.b1', '64.bj1.a1', '64.cq1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7679, -1, 4773, -1, 7682, -1, 4769, -1], 'generators': [4, 136, 32], 'label': '256.30836.32.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cs1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879824
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ct1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.ep1.a1', '16.eu1.a1', '16.eu1.b1', '16.fe1.a1', '16.ff1.a1', '16.fg1.a1'], 'contains': ['64.d1.a1', '64.x1.a1', '64.bk1.a1', '64.cr1.a1', '64.cr1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7103, -1, 5518, -1, 7107, -1, 5513, -1], 'generators': [6, 136, 32], 'label': '256.30836.32.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.ct1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879825
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cm1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.x1.a1', '2.z1.a1'], 'contains': ['8.bd1.a1', '8.bf1.a1', '8.bl1.a1', '8.cq1.a1', '8.cw1.a1', '8.dc1.a1', '8.dh1.a1'], 'core': '4.cm1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6977, 7772, 7797, 4229, 6980, 7769, 7790, 4238], 'generators': [3, 4, 64], 'label': '256.30836.4.cm1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cm1.a1', 'normal_contained_in': ['2.b1.a1', '2.x1.a1', '2.z1.a1'], 'normal_contains': ['8.bd1.a1', '8.bl1.a1', '8.bf1.a1', '8.cq1.a1', '8.cw1.a1', '8.dh1.a1', '8.dc1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cm1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879826
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.eq1.a1', '16.et1.a1', '16.et1.b1', '16.fe1.a1', '16.fh1.a1', '16.fi1.a1'], 'contains': ['64.d1.a1', '64.y1.a1', '64.bl1.a1', '64.bl1.b1', '64.cs1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7130, -1, 4759, -1, 7134, -1, 4755, -1], 'generators': [5, 136, 32], 'label': '256.30836.32.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.cu1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879827
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.eo1.a1', '16.eo1.b1', '16.fb1.a1', '16.fe1.a1', '16.fj1.a1', '16.fk1.a1'], 'contains': ['64.d1.a1', '64.z1.a1', '64.bm1.a1', '64.ct1.a1', '64.ct1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7077, -1, 5684, -1, 7080, -1, 5679, -1], 'generators': [3, 136, 32], 'label': '256.30836.32.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.cv1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879828
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.eq1.a1', '16.eu1.a1', '16.eu1.b1', '16.fb1.a1', '16.fl1.a1', '16.fm1.a1'], 'contains': ['64.d1.a1', '64.ba1.a1', '64.bn1.a1', '64.cu1.a1', '64.cu1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7705, -1, 5476, -1, 7709, -1, 5471, -1], 'generators': [7, 136, 32], 'label': '256.30836.32.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.cw1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879829
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.ev1.a1', '16.ev1.b1', '16.fc1.a1', '16.fh1.a1', '16.fn1.a1', '16.fo1.a1'], 'contains': ['64.d1.a1', '64.bb1.a1', '64.bo1.a1', '64.cv1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2000, -1, 6378, -1, 2001, -1, 6373, -1], 'generators': [83, 136, 32], 'label': '256.30836.32.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.q1.a1', 'old_label': '32.cx1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879830
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cy1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.er1.a1', '16.ew1.a1', '16.ew1.b1', '16.fj1.a1', '16.fn1.a1', '16.fp1.a1'], 'contains': ['64.d1.a1', '64.bc1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2167, -1, 7508, -1, 2168, -1, 7501, -1], 'generators': [16, 136], 'label': '256.30836.32.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.cy1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879831
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.cz1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.bw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '16.ex1.a1', '16.ex1.b1', '16.ff1.a1', '16.fl1.a1', '16.fo1.a1', '16.fp1.a1'], 'contains': ['64.d1.a1', '64.bp1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2123, -1, 8201, -1, 2124, -1, 8194, -1], 'generators': [66, 32], 'label': '256.30836.32.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '32.cz1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879832
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.da1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '16.es1.a1', '16.ew1.a1', '16.ew1.b1', '16.fk1.a1', '16.fo1.a1', '16.fq1.a1'], 'contains': ['64.d1.a1', '64.bq1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1832, -1, 7708, -1, 1833, -1, 7701, -1], 'generators': [17, 32], 'label': '256.30836.32.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '32.da1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.da1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879833
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.db1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.ce1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.o1.a1', '16.ex1.a1', '16.ex1.b1', '16.fg1.a1', '16.fm1.a1', '16.fn1.a1', '16.fq1.a1'], 'contains': ['64.d1.a1', '64.br1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2079, -1, 8178, -1, 2080, -1, 8171, -1], 'generators': [67, 32], 'label': '256.30836.32.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.u1.a1', 'old_label': '32.db1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.db1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879834
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.ey1.a1', '16.ey1.b1', '16.ff1.a1', '16.fm1.a1', '16.fr1.a1', '16.fs1.a1'], 'contains': ['64.d1.a1', '64.bd1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1921, -1, 6445, -1, 1921, -1, 6439, -1], 'generators': [68, 136], 'label': '256.30836.32.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.w1.a1', 'old_label': '32.dc1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879835
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1.a1', '16.er1.a1', '16.ez1.a1', '16.ez1.b1', '16.fk1.a1', '16.fr1.a1', '16.ft1.a1'], 'contains': ['64.d1.a1', '64.be1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1700, -1, 6970, -1, 1700, -1, 6964, -1], 'generators': [18, 136], 'label': '256.30836.32.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '32.dd1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879852
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.ds1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.r1.a1', '16.gb1.a1', '16.gb1.b1', '16.gg1.a1', '16.gq1.a1', '16.gu1.a1', '16.gz1.a1'], 'contains': ['64.e1.a1', '64.bd1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5061, -1, 7315, -1, 5059, -1, 7309, -1], 'generators': [68, 8], 'label': '256.30836.32.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.ds1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879836
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.cn1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.x1.a1', '2.ba1.a1'], 'contains': ['8.bd1.a1', '8.bg1.a1', '8.bm1.a1', '8.cr1.a1', '8.cv1.a1', '8.dd1.a1', '8.dj1.a1'], 'core': '4.cn1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6695, 2426, 6254, 3584, 6698, 2425, 6249, 3593], 'generators': [3, 4, 16], 'label': '256.30836.4.cn1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.cn1.a1', 'normal_contained_in': ['2.c1.a1', '2.x1.a1', '2.ba1.a1'], 'normal_contains': ['8.bd1.a1', '8.bg1.a1', '8.bm1.a1', '8.cr1.a1', '8.cv1.a1', '8.dd1.a1', '8.dj1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.cn1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 30879837
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.de1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.ec1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.v1.a1', '16.ev1.a1', '16.ev1.b1', '16.fd1.a1', '16.fi1.a1', '16.fp1.a1', '16.fq1.a1'], 'contains': ['64.d1.a1', '64.cw1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2212, -1, 6360, -1, 2213, -1, 6355, -1], 'generators': [82, 32], 'label': '256.30836.32.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.q1.a1', 'old_label': '32.de1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.de1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879838
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.df1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1', '16.ey1.a1', '16.ey1.b1', '16.fg1.a1', '16.fl1.a1', '16.ft1.a1', '16.fu1.a1'], 'contains': ['64.d1.a1', '64.bf1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1744, -1, 6422, -1, 1744, -1, 6416, -1], 'generators': [69, 136], 'label': '256.30836.32.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.w1.a1', 'old_label': '32.df1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.df1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879839
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.ba1.a1', '16.es1.a1', '16.ez1.a1', '16.ez1.b1', '16.fj1.a1', '16.fs1.a1', '16.fu1.a1'], 'contains': ['64.d1.a1', '64.bs1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1788, -1, 7016, -1, 1789, -1, 7010, -1], 'generators': [19, 32], 'label': '256.30836.32.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.ba1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '32.dg1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879840
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.eq1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.bb1.a1', '16.fa1.a1', '16.fa1.b1', '16.fd1.a1', '16.fh1.a1', '16.fr1.a1', '16.fu1.a1'], 'contains': ['64.d1.a1', '64.bt1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2035, -1, 6468, -1, 2036, -1, 6462, -1], 'generators': [86, 32], 'label': '256.30836.32.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.p1.a1', 'old_label': '32.dh1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879841
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.di1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.ep1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.be1.a1', '16.fa1.a1', '16.fa1.b1', '16.fc1.a1', '16.fi1.a1', '16.fs1.a1', '16.ft1.a1'], 'contains': ['64.d1.a1', '64.bg1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1876, -1, 6337, -1, 1877, -1, 6332, -1], 'generators': [87, 136], 'label': '256.30836.32.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.p1.a1', 'old_label': '32.di1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.di1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879842
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '2.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.fv1.a1', '16.fv1.b1', '16.ge1.a1', '16.gf1.a1', '16.gg1.a1', '16.gh1.a1'], 'contains': ['64.e1.a1', '64.v1.a1', '64.v1.b1', '64.cf1.a1', '64.cf1.b1', '64.cy1.a1', '64.cy1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7839, -1, 5713, -1, 7842, -1, 5707, -1], 'generators': [1, 8, 32], 'label': '256.30836.32.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.dj1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 30879843
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.fw1.a1', '16.fw1.b1', '16.ge1.a1', '16.gi1.a1', '16.gj1.a1', '16.gk1.a1'], 'contains': ['64.e1.a1', '64.w1.a1', '64.w1.b1', '64.cg1.a1', '64.cz1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7909, -1, 4981, -1, 7913, -1, 4977, -1], 'generators': [4, 8, 32], 'label': '256.30836.32.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.dk1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30879844
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.fw1.a1', '16.fw1.b1', '16.gf1.a1', '16.gl1.a1', '16.gm1.a1', '16.gn1.a1'], 'contains': ['64.e1.a1', '64.x1.a1', '64.ch1.a1', '64.da1.a1', '64.da1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7237, -1, 5448, -1, 7240, -1, 5444, -1], 'generators': [6, 8, 32], 'label': '256.30836.32.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.dl1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30879845
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.fx1.a1', '16.fx1.b1', '16.ge1.a1', '16.gl1.a1', '16.go1.a1', '16.gp1.a1'], 'contains': ['64.e1.a1', '64.y1.a1', '64.ci1.a1', '64.db1.a1', '64.db1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7263, -1, 4925, -1, 7267, -1, 4921, -1], 'generators': [5, 8, 32], 'label': '256.30836.32.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.dm1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30879846
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.fv1.a1', '16.fv1.b1', '16.gi1.a1', '16.gl1.a1', '16.gq1.a1', '16.gr1.a1'], 'contains': ['64.e1.a1', '64.z1.a1', '64.cj1.a1', '64.cj1.b1', '64.dc1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7812, -1, 5670, -1, 7816, -1, 5665, -1], 'generators': [3, 8, 32], 'label': '256.30836.32.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '32.dn1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30879847
{'ambient': '256.30836', 'aut_centralizer_order': 64, 'aut_label': '4.co1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 64, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.y1.a1', '2.ba1.a1'], 'contains': ['8.bd1.a1', '8.bh1.a1', '8.bi1.a1', '8.cs1.a1', '8.cz1.a1', '8.de1.a1', '8.df1.a1'], 'core': '4.co1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7319, 926, 6451, 1759, 7322, 926, 6445, 1762], 'generators': [65, 66, 4], 'label': '256.30836.4.co1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.co1.a1', 'normal_contained_in': ['2.b1.a1', '2.y1.a1', '2.ba1.a1'], 'normal_contains': ['8.bd1.a1', '8.bi1.a1', '8.bh1.a1', '8.cs1.a1', '8.cz1.a1', '8.df1.a1', '8.de1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.co1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.co1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 30879848
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.do1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '16.fx1.a1', '16.fx1.b1', '16.gf1.a1', '16.gi1.a1', '16.gs1.a1', '16.gt1.a1'], 'contains': ['64.e1.a1', '64.ba1.a1', '64.ck1.a1', '64.dd1.a1', '64.dd1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7936, -1, 4967, -1, 7940, -1, 4963, -1], 'generators': [7, 8, 32], 'label': '256.30836.32.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.do1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.do1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30879849
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dp1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.fy1.a1', '16.fy1.b1', '16.gj1.a1', '16.gm1.a1', '16.gu1.a1', '16.gv1.a1'], 'contains': ['64.e1.a1', '64.bb1.a1', '64.cl1.a1', '64.de1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3282, -1, 8510, -1, 3284, -1, 8502, -1], 'generators': [83, 8, 32], 'label': '256.30836.32.dp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.dp1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 30879850
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '16.fz1.a1', '16.fz1.b1', '16.go1.a1', '16.gs1.a1', '16.gw1.a1', '16.gx1.a1'], 'contains': ['64.e1.a1', '64.bc1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4365, -1, 6560, -1, 4363, -1, 6554, -1], 'generators': [16, 8], 'label': '256.30836.32.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '32.dq1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 30879851
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dr1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '4.be1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.p1.a1', '16.ga1.a1', '16.ga1.b1', '16.gp1.a1', '16.gs1.a1', '16.gu1.a1', '16.gy1.a1'], 'contains': ['64.e1.a1', '64.cm1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4315, -1, 8339, -1, 4315, -1, 8332, -1], 'generators': [23, 32], 'label': '256.30836.32.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '32.dr1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 30879853
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dt1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.t1.a1', '16.fz1.a1', '16.fz1.b1', '16.gp1.a1', '16.gt1.a1', '16.ha1.a1', '16.hb1.a1'], 'contains': ['64.e1.a1', '64.be1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4134, -1, 6537, -1, 4135, -1, 6531, -1], 'generators': [18, 8], 'label': '256.30836.32.dt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.n1.a1', 'old_label': '32.dt1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879854
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.du1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.w1.a1', '16.gb1.a1', '16.gb1.b1', '16.gh1.a1', '16.gr1.a1', '16.gv1.a1', '16.gy1.a1'], 'contains': ['64.e1.a1', '64.df1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6176, -1, 7554, -1, 6179, -1, 7547, -1], 'generators': [70, 32], 'label': '256.30836.32.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.du1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.du1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879855
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.dw1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.x1.a1', '16.fy1.a1', '16.fy1.b1', '16.gk1.a1', '16.gn1.a1', '16.gy1.a1', '16.gz1.a1'], 'contains': ['64.e1.a1', '64.cn1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4791, -1, 8529, -1, 4788, -1, 8521, -1], 'generators': [81, 32], 'label': '256.30836.32.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '32.dv1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879856
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.y1.a1', '16.gc1.a1', '16.gc1.b1', '16.gg1.a1', '16.gr1.a1', '16.gw1.a1', '16.ha1.a1'], 'contains': ['64.e1.a1', '64.bf1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4267, -1, 6718, -1, 4268, -1, 6712, -1], 'generators': [69, 8], 'label': '256.30836.32.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.y1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '32.dw1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 30879857
{'ambient': '256.30836', 'aut_centralizer_order': 4096, 'aut_label': '32.dx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8192, 'centralizer': '8.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.z1.a1', '16.ga1.a1', '16.ga1.b1', '16.go1.a1', '16.gt1.a1', '16.gv1.a1', '16.gz1.a1'], 'contains': ['64.e1.a1', '64.co1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4576, -1, 8316, -1, 4594, -1, 8309, -1], 'generators': [21, 32], 'label': '256.30836.32.dx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '32.dx1.a1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.dx1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
