Second cohomology group for trivial group action of V4 on V4

Description of the group
We consider here the second cohomology group for trivial group action of the specific information about::Klein four-group on the specific information about::Klein four-group, i.e.,

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

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

The cohomology group is isomorphic to elementary abelian group:E64.