Eigenvalues · Hard problem

A $3\times3$ matrix $A$ has characteristic polynomial $\det(\lambda I - A) = \lambda^3 - 6\lambda^2 + 11\lambda - 6$. A control engineer calls any eigenvalue above the damping threshold $1.5$ an "unstable mode" and needs the product of the growth rates of all such modes to size a compensator. Find that product.