Second cohomology group for trivial group action of Z2 on Z4

Description of the group
We consider here the second cohomology group for trivial group action of the specific information about::cyclic group:Z2 on the specific information about::cyclic group:Z4, i.e.,

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

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

The cohomology group is isomorphic to cyclic group:Z2.

Elements
We list here the elements, grouped by similarity under the action of the automorphism groups on both sides.