[GAP Forum] Structure Description of Small Group [32,6]

[Bill Allombert]

On Wed, Feb 23, 2011 at 12:42:51PM +0000, Sandeep Murthy wrote:
> Hi,
> 
> There is a small group with ID [32,6] and
> structure description:
> 
> (C2 x C2) . (C4 x C2)
> 
> I'm not sure what the dot represents.

According to the documentation:

   | C(G) . G/C(G) = G' . G/G'         ; non-split extension
                                       ; (equal alternatives and
                                       ; trivial extensions omitted)

> What is the nature of this group?

There is an non-split exact sequence:
1->H->G->G/H->1 where H = (C2 x C2) and G/H = (C4 x C2).

Cheers,
Bill.