I know that there exists a nice presentation (generators and relations) of the general linear group over a finite field (by Steinberg, I think). Is there also a nice presentation of $GL(n,\mathbb{Z}/m\mathbb{Z})$ for an arbitrary integer $m$? And perhaps also for the symplectic group over $\mathbb{Z}/m\mathbb{Z}$?

I want to do some calculations in these groups with a computer and my first problem was to determine these groups. One solution (my current) is of course to determine both by brute force. But already for small m,n this takes too much time.