Second cohomology group for trivial group action of Q8 on Z4

Description of the group
This article describes the second cohomology group for trivial group action of quaternion group on cyclic group:Z4, i.e., the group:

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

where $$G$$ is the quaternion group and $$A$$ is cyclic group:Z4.

The cohomology group itself is isomorphic to the Klein four-group.

Computation of cohomology group
The cohomology group can be computed abstractly as the group cohomology of quaternion group.