[GAP Forum] bicyclic extensions of simple groups

[Dmitrii Pasechnik]

Dear Nick,
On Thu, Feb 26, 2015 at 10:35:52AM +0000, Nicholas Gill wrote:
> Hi GAP-folk,
> 
> I would like to construct a bunch of bicyclic extensions of some finite simple groups. Here "bicyclic" is in the sense of the ATLAS. I'm thinking of things like
> 3.A6.2, 6.A6.2, 12.A6.2, (2x2).Sz(8).3
> I realise the definition of these things is a little icky. In fact I only need an example of each such group up to isoclinism - this is what the ATLAS provides and that's good enough for me... But to start any example of such a group would be handy.

you can find presentations and representations in Atlas of Finite Group
Representations, e.g. for Sz(8) see

http://brauer.maths.qmul.ac.uk/Atlas/v3/exc/Sz8/

E.g. you can download  permutations for 22.Sz(8):3
from http://brauer.maths.qmul.ac.uk/Atlas/v3/permrep/4Sz8d3G1-p2080B0
 
This data is also available directly in GAP via the package
AtlasRep, see http://www.gap-system.org/Packages/atlasrep.html

Hope this helps,
Dima