Second cohomology group for trivial group action of S3 on Z2

Description of the group
This article describes the second cohomology group for trivial group action:

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

where $$G$$ is symmetric group:S3 (i.e., the symmetric group on a set of size three) and $$A$$ is cyclic group:Z2.

The cohomology group is isomorphic to cyclic group:Z2.

Computation of cohomology group
The cohomology group can be computed directly from group cohomology of symmetric group:S3.