  In a previous paper, the authors proved that the Prym variety of any
non-cyclic etale triple cover of a smooth curve of genus 2 is a Jacobian
variety of dimension 2. This gives a map from the moduli space of such covers
to the moduli space of Jacobian varieties of dimension 2. We extend this map to
a proper map of a certain moduli space of admissible $S_3$-covers of genus 7 to
the moduli space of principally polarized abelian surfaces. The main result is
that this map is finite surjective of degree 10.
