Second cohomology group for trivial group action of V4 on E8

Description of the group
This is the second cohomology group for trivial group action where the acting group is Klein four-group and the group being acted upon is elementary abelian group:E8. In other words, it is the group:

$$\! H^2(G,A)$$

where $$G \cong V_4 \cong \mathbb{Z}_2 \times \mathbb{Z}_2$$ and $$A \cong E_8 \cong \mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2$$.

The group is isomorphic to elementary abelian group:E512, i.e., it is an elementary abelian group of order $$2^9 = 512$$.