Orbits and invariants of cubic matrices of order three

Let $V_i$, $i=1, 2, 3$, be a three-dimensional complex vector space. For the natural linear representation of the group $\operatorname{SL}(V_1)\times\operatorname{SL}(V_2)\times \operatorname{SL}(V_3)$ in the space $V_1\otimes V_2\otimes V_3$ the orbits are classified and generators of the algebra of invariants are described.