[GAP Forum] Fwd: [GAP Support] char Table and LLL

[Thomas Breuer]

Dear GAP Forum,

Andrea Previtali wrote

> I'm trying to get the character table of PSp(4,9) using your  
> suggestions but
> I get a weird answer:
>
> tbl:= rec();;
>     tbl.Size:=74;;
>     tbl.UnderlyingCharacteristic:= 0;;
>     tbl.SizesConjugacyClasses:= [ 1, 3321, 298890, 3280, 3280, 236160,
> [...]
>     ConvertToLibraryCharacterTableNC( tbl );;
>     vecs:=[
>      [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  
> [...]
>     ]
>  ;;
>     LLL( tbl, vecs );
>
> PRODUCES THIS ANSWER   !!!!!!!
>
> rec( irreducibles := [  ], remainders := [ VirtualCharacter(  
> [...]
>           0, 0, 0, 0, 0, 0, 0, 0, 0 ] ) ], norms := [ 860803200/37,
> 860803200/37, 860803200/37, 860803200/37 ] )

The problem is that the `Size' attribute of a character table refers
to the order of the underlying group and not to the dimension of the
matrix of irreducible characters;
the value is used in the computations of scalar products of characters
for this table.

In fact, many of those attributes and properties of groups
for which the value can be computed from the information
in the character table object are defined also for character tables.
(See the chapter "Character Tables" in the GAP Reference Manual,
in particular the section "Attributes and Properties of Character Tables".)

All the best,
Thomas