[GAP Forum] question

[Alexander Hulpke]

Dear GAP Forum,

On Apr 24, 2011, at 2:43 AM, parivash nosratpoor wrote:

> Dear Gap Forum:
> How you introduce Twice Chevalley group 2E6(2) in Gap progeram?

For many of the simple groups the ATLAS web pages (here:
http://brauer.maths.qmul.ac.uk/Atlas/v3/exc/TE62/
)
and in particular the `atlasrep' package are your friends:

LoadPackage("atlasrep");
g:=AtlasGroup("2E6(2)");

This is however a rather large matrix group and GAPs default functions are likely to choke on it. We thus need to help the system with finding a permutation representation of minimal degree 3968055

The following vector was computed as fixed-vector of an involution centralizer for an element in class 2A (found as power of a random element in class 22, since for this order all 11th powers must lie in class 2A), using Bray's method. (If you have other representations, youd have to do this yourself)

v:=[ 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 
  1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 
  1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 
  1, 0, 0 ]*Z(2);

Now we can act:
orb:=Orbit(g,v);;
p:=Action(g,orb); #isomorphic permutation group
SetSize(p,Size(g)); # help GAP with computing a stabilizer chain

Creating a stabilizer chain for p now  takes about 2.5GB of workspace. Now (with further workspace) you could perform more involved calculations in this group.

Hope this helps,

   Alexander Hulpke




-- Colorado State University, Department of Mathematics,
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