[GAP Forum] Print the irreducible characters of the normal ordinary character table format.

[Hongyi Zhao]

Hi GAP team,

I use the following code snippet to compute the irreducible characters
of a finitely presented group:

gap> f := FreeGroup( "p", "q");;
gap> g42:= f/[ [ f.1 , f.1^-1 ], [ f.2 , f.2^-1 ], [ f.2 *f.1, f.1 *f.2 ] ];
<fp group on the generators [ p, q ]>
gap> Elements( g42 );
[ <identity ...>, p, q, p*q ]
gap> StructureDescription( g42 );
"C2 x C2"
gap> IsomorphismPermGroup(g42);
[ p, q ] -> [ (1,2)(3,4), (1,3)(2,4) ]

gap> ConjugacyClasses(g42);
[ <identity ...>^G, p^G, q^G, p*q^G ]

gap> Irr(g42);
[ Character( CharacterTable( C2 x C2 ), [ 1, 1, 1, 1 ] ),
  Character( CharacterTable( C2 x C2 ), [ 1, -1, 1, -1 ] ),
  Character( CharacterTable( C2 x C2 ), [ 1, -1, -1, 1 ] ),
  Character( CharacterTable( C2 x C2 ), [ 1, 1, -1, -1 ] ) ]

As commented here [1], the standard character table has the following
format (layout):

```
In group theory, a branch of abstract algebra, a character table is a
two-dimensional table whose rows correspond to irreducible
representations, and whose columns correspond to conjugacy classes of
group elements.
```

So, I want to get a pretty printed result with the rows correspond to
irreducible representations, and the columns correspond to conjugacy
classes of group elements.

Are there any clues to achieve this goal?

[1] https://en.wikipedia.org/wiki/Character_table

Regards
-- 
Assoc. Prof. Hongsheng Zhao <hongyi.zhao at gmail.com>
Theory and Simulation of Materials
Hebei Vocational University of Technology and Engineering
No. 473, Quannan West Street, Xindu District, Xingtai, Hebei province