# 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;-)

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If you want community wiki, there is a checkmark for that when you edit it. Bottom right, just below the main text input field. –  Harald Hanche-Olsen Feb 12 '10 at 12:25
Harald: Thank You for pointing! –  kakaz Feb 12 '10 at 13:21

GAP has the following: http://www.gap-system.org/Gap3/Manual3/C023S010.htm

(But note GAP4 exists now I think.)

(i) There is on the GAP site, the following: ftp.gap-system.org/pub/gap/…

(ii) 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.

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You answer is OK, Yhank You! This is what I am looking for, but maybe someone give us also another references, maybe on off-line tables? –  kakaz Feb 12 '10 at 12:08
There is on the GAP site the following: ftp.gap-system.org/pub/gap/gap-3.4.4/deposit/gap/gpl.ps.gz –  Tim Porter Feb 12 '10 at 12:14
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. –  Tim Porter Feb 12 '10 at 12:21
Definitely it is interesting, so Probably You should place it as an answer not a comment! –  kakaz Feb 12 '10 at 13:21
It's worth mentioning that one of the things that GAP bundles - as well as several other software packages - is the Small Groups Database; based on some enumeration of groups, it gives you a (size,index number) indexing to all finite groups of size at most some upper bound. And this works perfectly fine offline. –  Mikael Vejdemo-Johansson Feb 12 '10 at 18:14
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.