# 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;-)

• 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
• @Shamisen I appreciate your effort to help in correct tagging, but please note that it is agreed upon this should not be done in bursts. Please limit yourself to about three edits at a time (per day). – user9072 Feb 16 '16 at 0:15
• @quid Thanks for the advice, I was not aware of this rule – Shamisen Feb 16 '16 at 0:20

GAP has the following:

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.
• You answer is OK, Thank 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
• GAP3 is no longer maintained, please use GAP4 (the latest release of GAP 4.7.9 was made in November 2015). The overview of data libraries available there is here: gap-system.org/Datalib/datalib.html – Alexander Konovalov Feb 16 '16 at 9:51

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.

• This looks like a very useful site. – GMRA Feb 12 '10 at 14:41
• As I know the site You post I agree that it is very useful. As I am asking about presentations, it may looks like it is not the answer. But it has also informations about presentations as well. So it is definitely in scope of the question, not only related! Thanks! – kakaz Feb 12 '10 at 14:53

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.

• @Josh Perhaps you could say a bit more on your work. Is it available as a paper implemented in some system / package etc? This could be useful to others. – Tim Porter Aug 24 '10 at 6:11