Second cohomology group for trivial group action of Z4 on Z4

Description of the group
We consider here the second cohomology group for trivial group action of specific information about::cyclic group:Z4 on the specific information about::cyclic group:Z4, i.e.,

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

where $$G \cong \mathbb{Z}_4$$ and $$A \cong \mathbb{Z}_4$$.

The cohomology group is isomorphic to cyclic group:Z4.

Note that since cyclic over central implies abelian, the fact that the top group is cyclic forces all the corresponding group extensions to be abelian. In particular, all the 2-cocycles are symmetric 2-cocycles.