[GAP Forum] Cartesian Group Direct Product

[Justin C. Walker]

Dear Paul & Forum,

On Dec 3, 2007, at 20:36 , PAUL HJELMSTAD wrote:

> Can someone tell me what the right function is for the "Cartesian"  
> style group direct product?
> (For example, D4 X S3)? I know they use the double-format for  
> dihedral groups, so this would
> be Dihedral(8) I guess.
>
> The one I have been playing with isn't right for my purposes,  
> taking sums instead of Cartesian products. I need the form that  
> ends up with 12 terms in its cycle-structure G X H

The manual describes something called, suspiciously,  
DirectProduct :-}.  Does that help?

Trying your example:

gap> D4:=DihedralGroup(4);
<pc group of size 4 with 2 generators>
gap> S3:=SymmetricGroup(3);
Sym( [ 1 .. 3 ] )
gap> G:=DirectProduct(D4,S3);
<group of size 24 with 4 generators>

and looking at G, it may not be quite what you want :-} (it's  
combining a PC group and a permutation group), but you may be able to  
coax it into something useful for you.

FWIW, Gap comes with an index that covers all 5 of the manuals.

Justin

--
Justin C. Walker, Curmudgeon at Large
Director
Institute for the Enhancement of the Director's Income
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