{'ambient': '1728.34645', 'aut_centralizer_order': None, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.e1.a1', '6.g1.a1', '6.i1.a1'], 'contains': ['24.d1.a1', '24.v1.a1', '24.bf1.a1', '24.cr1.a1', '24.cr1.b1', '36.h1.a1', '36.n1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 576, 72, 36, 864, 4], 'id': 93169092, 'label': '1728.34645.12.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}