> < ^ Date: Mon, 11 Mar 2002 16:41:41 -0500
> < ^ From: Igor Schein <igor@txc.com >
> < ^ Subject: Re: SmallGroup(40,3)

Dear GAP forum,

```On Sun, Mar 10, 2002 at 04:51:03PM -0000, rogerberesford wrote:
>       On Friday Mar. 8th 2002, Igor Schein asked about GAP SmallGroup(40,3).
> Using g4003 and similar abbreviations, g4003 has generators (a^5=b^8=1,
> ba=aab), with the second part being a non-abelian re-write rule. It has
> g2001 (Q20, with a^5=b^4=1, ba=aaaab) as a subgroup, and g2003 (with
> a^5=b^4=1, ba=aab) as a factor (quotient) group. The CayleyTable determinant
> has two linear factors, one quadratic factor, one unrepeated fourth order
> and two fourth order factors that are each repeated four times.
>       Similar groups:- g2401 is (a^3=b^8=1, ba=aab),  g4001 is (a^5=b^8=1,
> ba=aaaab), g4007 is (a^5=b^4=c^2=1, ba=aaaab), g4012 is (a^5=b^4=c^2=1,
> ba=aab), g4013 is (a^5=b^2=c^2=d^2=1, ba=aaaab)

g4012 is isomorphic to TransitiveGroup(20,9), and g4013 is isomorphic to
TransitiveGroup(20,8), so these 2 groups are not really *similar* to
g4003.  Now, let's consider g4001, g003 and g4007.  g4001 has g2002 (
abelian ) as a subgroup.  g4007 has g2001 ( just like g4003 ) and also
g2005 ( abelian ) as a subgroup. Now, what are factor groups of g4001
and g4007?  I couldn't figure out how to compute them in GAP4, so
anyone could give me a clue on that, it'd be great.  In particular,
I'd like to know how to obtain in GAP the result above, that g2003 is
a factor group of g4003.
```

Thanks to everbody for very insightful answers to my original question.

Igor