Database of finite presentations of used groups Do You know any kind of database of presentations of groups? 
It may be on-line or off-line in form of tables, ideally case would be integrated in some Computer Algebra System. I am interested the most in infinite group presentations, but feel free to put here also information about tables of presentations of finite groups. 
Maybe this thread should be wiki-type because probably there is many good answers to this question, and it is hard to compare for example software system with some kind of book or publication about this matter? I add biglist tag in a hope that it would appear;-)
 A: GAP has the following:


*

*Finitely Presented Groups

*Presentations and Tietze Transformations
An overview of all data libraries in GAP can be found here.
The following was a comment, but should be part of the answer:


*

*There was a lovely book that listed lots of this sort of material 
presentations, Group Tables by A. D. Thomas, G. V. Wood. It may not
answer your question but if you can get your hands on a copy is
an interesting  perspective.
It was published in the Shiva Mathematics series.

A: Related to your question, perhaps... there's the Atlas of finite group representations.  Although the atlas itself might not be what you're after, the above page contains links that might be more relevant.
A: In my dissertation I developed an algorithm for finding bounds on $H_2$ of a finitely presented group with finite field coefficients. I was motivated by a conjecture Quillen on the (co)homology of linear groups. As such, I included an appendix with presentations of several linear groups and the homology calculations using my algorithms. I didn't include the list of presentations for publication, but if these types of groups are of interest I could get it to you. 
