> < ^ Date: Mon, 23 Aug 1999 17:51:00 +0200 (CEST)
> < ^ From: Davide L. Ferrario <ferrario@matapp.unimib.it >
> ^ Subject: A couple of questions

Dear Gap-Forum,

I'm working on some small programs in gap, and I have the following 2 questions:
(I'm running a gap4r1 bugfix 1 version, compiled on a linux box
i686-pc-linux-gnu-gcc, with pargapmpi installed)

1. Consider the following strange behavior:

```---BEGIN

gap> G:=DihedralGroup(6);
<pc group of size 6 with 2 generators>
gap> tm:=TableOfMarks(G);
TableOfMarks( Group( [ f1, f2 ] ) )
gap> H:=RepresentativeTom(tm,2);
Group([ f2 ])
gap> th:=CharacterTable(H);
CharacterTable( Group([ f2 ]) )
gap> Size(H);
2
gap> SizesConjugacyClasses(th);
[ 1, 2/3, 2/3 ]
gap> Display(tm);
1:  6
2:  3 1
3:  2 . 2
4:  1 1 1 1
```

gap> Display(th);
CT1

List Element: <list>[3] must have an assigned value at
cen[prime][i] := Number( fak, function ( x )
return x = prime;
end );
Display( tbl, rec(
) ); called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop, you can 'quit;' to quit to outer loop,
or you can return after assigning a value to continue
brk>

```---END
```

What am I doing wrong? What does it mean? How can I avoid this problem?

2. Is there a fast method to compute the isotropy subgroups of a representation
of an arbitrary group G (given the character)?
(i.e. the isotropy groups of the action of G on the space)
By counting the dimensions of the spaces fixed by its subgroups it is
possible to do it, but it's slow: do you know references to this problem?

Thank you very much in advance,

Davide Ferrario

Universita' di Milano-Bicocca

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