Group cohomology of projective special linear group of degree two over a finite field

This article describes the group cohomology of the projective special linear group of degree two over a finite field. The order (size) of the field is $$q$$, and the characteristic prime is $$p$$. $$q$$ is a power of $$p$$. We denote the group as $$PSL(2,q)$$ or $$PSL_2(q)$$.