def METHOD_NAME(self):
    r"""
    Return the group of permutations whose action on this subset leave
    it fixed.
    EXAMPLES::
        sage: F = species.SubsetSpecies()
        sage: a = F.structures([1,2,3,4])[6]; a
        {1, 3}
        sage: a.automorphism_group()
        Permutation Group with generators [(2,4), (1,3)]
    ::
        sage: [a.transport(g) for g in a.automorphism_group()]
        [{1, 3}, {1, 3}, {1, 3}, {1, 3}]
    """
    from sage.groups.perm_gps.permgroup_named import SymmetricGroup
    from sage.groups.perm_gps.permgroup import PermutationGroup
    a = SymmetricGroup(self._list)
    b = SymmetricGroup(self.complement()._list)
    return PermutationGroup(a.gens() + b.gens())