ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 11 May 2016 07:49:13 -0500How to iterate over groups in increasing sizehttp://ask.sagemath.org/question/33358/how-to-iterate-over-groups-in-increasing-size/I would like some way to iterate over all finite groups in increasing size till I manually stop the program (preferably as permutation groups). Is there an easy command to do this? Tue, 10 May 2016 15:14:01 -0500http://ask.sagemath.org/question/33358/how-to-iterate-over-groups-in-increasing-size/Answer by vdelecroix for <p>I would like some way to iterate over all finite groups in increasing size till I manually stop the program (preferably as permutation groups). Is there an easy command to do this? </p>
http://ask.sagemath.org/question/33358/how-to-iterate-over-groups-in-increasing-size/?answer=33366#post-id-33366In [GAP](http://www.gap-system.org/) there are various databases available for groups, see http://www.gap-system.org/Datalib/datalib.html
Some of them are interfaced in Sage and available in the database_gap package. So first of all you have to install the package with the console command (needs internet connection)
$ sage -i database_gap
Then if you launch Sage you should be able to do
sage: for G in TransitiveGroups():
....: print G
....: print G.gens()
Transitive group number 1 of degree 0
[()]
Transitive group number 1 of degree 1
[()]
Transitive group number 1 of degree 2
[(1,2)]
Transitive group number 1 of degree 3
[(1,2,3)]
Transitive group number 2 of degree 3
[(1,2), (1,2,3)]
Transitive group number 1 of degree 4
[(1,2,3,4)]
...Wed, 11 May 2016 07:49:13 -0500http://ask.sagemath.org/question/33358/how-to-iterate-over-groups-in-increasing-size/?answer=33366#post-id-33366