Group cohomology of special linear group:SL(2,5)

This article describes the group cohomology of special linear group:SL(2,5).

Over the integers
The homology groups over the integers are as follows:

$$H_m(SL(2,5);\mathbb{Z}) = \left \lbrace \begin{array}{rl} \mathbb{Z}, & m = 0 \\ \mathbb{Z}/120\mathbb{Z}, & m \equiv 3 \pmod 4 \\ 0, & m \equiv 0,1,2 \pmod 4, m > 0 \\\end{array}\right.$$

The sequence of homology groups for positive degrees has a period of 4, which is in keeping with the fact that $$SL(2,5)$$ is a finite group with periodic cohomology, as are all special linear groups of degree two over a finite field.