[GAP Forum] On character tables of O8+(7) and U6(4)

[Thomas Breuer]

Dear GAP Forum,

Anvita wrote

> As I ran through the list of GAP's character table names of simple groups
> returned by
> 
> AllCharacterTableNames(IsSimple,true);
> 
> with the purpose to detect multiple names for the same table, I used the
> function
> 
> NamesOfEquivalentLibraryCharacterTables
> 
> successfully for all groups, except O8+(7) and U6(4).
> The commands
> 
> NamesOfEquivalentLibraryCharacterTables(CharacterTable("O8+(7)"));
> NamesOfEquivalentLibraryCharacterTables(CharacterTable("U6(4)"));
> 
> seem to never finish, even though groups much larger than those two present
> no problem:
> 
> gap> NamesOfEquivalentLibraryCharacterTables(CharacterTable("M"));
> [ "M" ]
> 
> I was just wondering if there is an explanation to this.

The reason is that for these two tables,
checking the equivalence of the table with itself takes a long time,
due to the fact that no table automorphisms are stored for them.

In the next version of the CTblLib package,
this problem will disappear.

Two more remarks:

1. For running over library tables of simple groups without duplicates,
   one can call
   'AllCharacterTableNames( IsSimple, true, IsDuplicateTable, false )'.

2. Often the complexity of character theoretic computations depends
   much more on the number of conjugacy classes of the group in question
   than on the group order.
   This can be viewed as one of the strengths of character theory.

All the best,
Thomas Breuer