There is a map J from the Outer Space for a rank n free group to the homogeneous space of positive definite n-ary quadratic forms, equivariant with respect to the actions of Out(F_n) and GL_n(Z). I will show how this Jacobian map induces a cell structure on an Eilenberg-MacLane space for the kernel of the natural map from Out(F_3) to GL_3(Z) and discuss the group homology of this kernel.