Invariants and orbits of the standard $(\mathrm SL_4(\mathbb C)\times\mathrm SL_4(\mathbb C)\times\mathrm SL_2(\mathbb C))$-module

We consider the natural linear representation of the group $\mathrm SL_4(\mathbb C)\times\mathrm SL_4(\mathbb C)\times\mathrm SL_2(\mathbb C)$ on the space $\mathbb C^4\otimes\mathbb C^4\otimes\mathbb C^2$. Using the embedding of this representation in the adjoint representation of the Lie algebra $E_7$, we classify the orbits and find the generators of the algebra of invariants.