{'ambient': '1728.33796', 'aut_centralizer_order': 24, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 48, 'centralizer': '72.d1.a1', 'complements': ['144.cc1.c1', '144.cc1.d1', '144.bx1.c1', '144.bx1.d1', '144.bz1.c1', '144.bz1.d1', '144.cb1.a1', '144.cb1.b1', '144.ce1.b1', '144.ce1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.b1', '6.a1.b1', '6.i1.a1', '6.m1.b1'], 'contains': ['24.b1.b1', '24.n1.b1', '24.p1.b1', '36.m1.b1', '36.v1.b1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3586, 3003, 6086, 4950, 6388, 984, 7961, 8782], 'generators': [1, 24, 4, 1086, 1296, 864], 'id': 92217525, 'label': '1728.33796.12.c1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.b1', 'normal_contained_in': ['4.g1.b1', '6.a1.b1'], 'normal_contains': ['24.b1.b1', '24.n1.b1', '24.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.b1', 'projective_image': '432.759', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}