[GAP Forum] Can GAP3 program construct the character table of projective general linear groups?

[Dima Pasechnik]

On Sun, May 31, 2015 at 04:48:59PM +0800, 杨高 wrote:

Do you work with GAP3?
Is it really necessary for you?

> 
> Is this the correct and most concise way to construct PGL(2,3) with GAP?
In GAP4 you can just do
gap> ProjectiveGeneralLinearGroup(2,3);
Group([ (3,4), (1,2,4) ])

> 
> 
> > W:=GeneralLinearGroup(2,3);;
> > H:=Subgroup(W,[[[Z(3),0*Z(3)],[0*Z(3),Z(3)]]]);;
> > B:=W/H;;
> 
> 
> Morevoer, I want to construct the character table of this group. But there is ian error.
> 
> 
> >Display(CharTable(B));
> Error, sorry, I don't know how to construct the table of <grp>
>  in 
> CharTable( B ) called from
> main loop

well, GAP4 has no difficulty here:
gap> H:=Subgroup(W,[[[Z(3),0*Z(3)],[0*Z(3),Z(3)]]]);;
gap> B:=W/H;;
gap> Display(CharacterTable(B));
CT2

     2  3  2  .  3  2
     3  1  .  1  .  .

       1a 2a 3a 2b 4a
    2P 1a 1a 3a 1a 2b
    3P 1a 2a 1a 2b 4a

X.1     1  1  1  1  1
X.2     1 -1  1  1 -1
X.3     2  . -1  2  .
X.4     3 -1  . -1  1
X.5     3  1  . -1 -1
gap> 

> So there are question I would like to ask. For constructing character tables, what kind of groups can GAP deal with? Can GAP construct the character table of PGL(n,m)? If the answer is yes, then how can I do this with it?
You can contruct the character table of a given group, but it gets slower as the 
size etc grows. How far do you need to go with n and m?

There are some infinite families of groups for which GAP can construct character tables directly,
see http://www.gap-system.org/Manuals/pkg/ctbllib/doc/chap4.html#X81E3F9A384365282
E.g. for n=2 one can have tables of the PSL groups.

HTH,
Dmitrii



> 
> 
> Thanks to everyone.
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