Let VBn be the virtual braid group on n strands and let S-n be the symmetric group on n letters. Let n, m is an element of N such that n >= 5, m >= 2 and n >= m. We determine all possible homomorphisms from VBn to S-m from S-n to VBm and from VBn to VBm. As corollaries we get that Out(VBn) is isomorphic to Z/2Z x Z/2Z and that VBn is both, Hopfian and co-Hoan.