{'ambient': '1728.33796', 'aut_centralizer_order': 4, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 24, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.b1.b1'], 'contains': ['12.c1.a1', '12.u1.b1', '12.bc1.a1', '12.bi1.b1', '12.bk1.b1', '12.cn1.b1', '12.co1.b1', '18.b1.b1', '18.j1.b1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3345, -1, 7221, -1, 7036, -1, 6238, -1], 'generators': [1, 4, 864, 6, 576, 108, 432], 'id': 92218184, 'label': '1728.33796.6.i1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.b1', 'old_label': '6.i1.b1', 'projective_image': '432.759', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.b1', 'subgroup_fusion': None, 'weyl_group': '144.192'}