{'ambient': '1728.32842', 'aut_centralizer_order': 576, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1152, 'centralizer': '4.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '48.y1.a1', '48.bb1.a1', '72.s1.a1', '72.bc1.a1', '72.bc1.b1', '72.bo1.a1', '72.bu1.a1', '72.bu1.b1', '72.cc1.a1'], 'contains': ['288.c1.a1', '432.e1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1224, -1, 5025, -1, 3420, -1, 6804, -1], 'generators': [432, 624, 864], 'id': 91710290, 'label': '1728.32842.144.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '144.v1.a1', 'projective_image': '864.4263', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}