  It has been proved by Adler that there exists a unique cubic hypersurface X
in P^8 which is invariant under the action of the simple group PSL(2,19). In
the present note we study the intermediate Jacobian of X and in particular we
prove that the subjacent 85-dimensional torus is an Abelian variety. The
symmetry group G=PSL(2,19) defines uniquely a G-invariant abelian 9-fold A(X),
which we study in detail and describe its period lattice.
