> < ^ Date: Wed, 13 Mar 2002 09:55:09 +0000
> < ^ From: John J McDermott <jjm@dcs.st-and.ac.uk >
< ^ Subject: Re: SmallGroup(40,3)

Forwarded from Ignat Soroko:

Dear GAP-Forum,

```On Monday, March 11, 2002 11:41 PM  Igor Schein <igor@txc.com> wrote:
```

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.

It can be done in GAP4 very easily. For example, for G=g4007:

```gap> G:=SmallGroup(40,7);
<pc group of size 40 with 4 generators>
gap> N:=NormalSubgroups(G);;
gap> Q:=List(N,x->G/x);
[ <pc group of size 40 with 4 generators>,
<pc group of size 20 with 3 generators>,
<pc group of size 20 with 3 generators>,
<pc group of size 20 with 3 generators>,
<pc group of size 10 with 2 generators>,
<pc group of size 8 with 3 generators>,
<pc group of size 4 with 2 generators>,
<pc group of size 4 with 2 generators>,
<pc group of size 4 with 2 generators>,
<pc group of size 2 with 1 generators>,
<pc group of size 2 with 1 generators>,
<pc group of size 2 with 1 generators>,
<pc group of size 1 with 0 generators> ]
gap> List(last,IdGroup);
[ [ 40, 7 ], [ 20, 1 ], [ 20, 1 ], [ 20, 4 ], [ 10, 1 ], [ 8, 2 ], [ 4, 1 ],
[ 4, 1 ], [ 4, 2 ], [ 2, 1 ], [ 2, 1 ], [ 2, 1 ], [ 1, 1 ] ]

The same with g4003.
```

Best,
Ignat

```+===================================+
Dr. John J. McDermott
Computing and X-ray Systems Manager
Taylor & Naismith Laboratories
University of St Andrews
BMS Building, North Haugh
St Andrews, Fife
KY16 9ST, Scotland

Tel: +44 1334 463478
Mob: +44 7941 507531
+===================================+
```