{'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], 'id': 30878506, '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'}