> < ^ Date: Thu, 05 Jun 1997 09:21:00 +0100 (MET)
> < ^ From: Thomas Breuer <Thomas.Breuer@Math.RWTH-Aachen.DE >
> < ^ Subject: Re: Generating a Character Table

Dear GAP Forum,

Mark L. Lewis wrote about a problem with the computation of a character
table of a group.

I load in a file with the following group.

```c := AbstractGenerator ("c");
d := AbstractGenerator ("d");
a1 := AbstractGenerator ("a1");
a2 := AbstractGenerator ("a2");
b1 := AbstractGenerator ("b1");
b2 := AbstractGenerator ("b2");

g3 := AgGroupFpGroup( rec(
generators := [d,c,a1,a2,b1,b2],
relators := [b1^2,b2^2,a1^2*(b1)^(-1),a2^2*(b2)^(-1),c^3,d^2,
(a1^c)*(a2)^(-1),(a2^c)*(a1*a2)^(-1),
(b1^c)*(b2)^(-1),(b2^c)*(b1*b2)^(-1),
(c^d)*(c^2)^(-1),
(a2^d)*(a1*a2)^(-1),(b2^d)*(b1*b2)^(-1)]));
```

This group seems to load ok, but when I ask GAP to compute the character
table of g3, I get the following response.
...

The problem is that the given presentation for `g3' is not consistent
as a presentation of a solvable group with composition length 6.

To see this, we use the ``clean'' way to define a finitely presented
group, and ask for the size.

```gap> f:= FreeGroup( 6 );;
gap> c := f.1;;
gap> d := f.2;;
gap> a1 := f.3;;
gap> a2 := f.4;;
gap> b1 := f.5;;
gap> b2 := f.6;;
gap>
gap> g3:= g / [b1^2,b2^2,a1^2*(b1)^(-1),a2^2*(b2)^(-1),c^3,d^2,
gap>                 (a1^c)*(a2)^(-1),(a2^c)*(a1*a2)^(-1),
gap>                 (b1^c)*(b2)^(-1),(b2^c)*(b1*b2)^(-1),
gap>                 (c^d)*(c^2)^(-1),
gap>                 (a2^d)*(a1*a2)^(-1),(b2^d)*(b1*b2)^(-1)];;
gap> Size( g3 );
24
```

Kind regards
Thomas

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