Dear GAP Forum,
If I do:
gap> S4:=SymmetricGroup(4);
Sym( [ 1 .. 4 ] )
gap> Display(CharacterTable(S4));
CT1
2 3 2 3 . 2
3 1 . . 1 .
1a 2a 2b 3a 4a
2P 1a 1a 1a 3a 2b
3P 1a 2a 2b 1a 4a
X.1 1 -1 1 1 -1
X.2 3 -1 -1 . 1
X.3 2 . 2 -1 .
X.4 3 1 -1 . -1
X.5 1 1 1 1 1
but if I do:
gap> IdGroup(S4);
[ 24, 12 ]
gap> G:=SmallGroup(24,12);
<pc group of size 24 with 4 generators>
gap> Display(CharacterTable(G));
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
so I get two different ordering for the row and columns of the table,
which is not entirely surprising since different algorithms are used
here.
My question is whether there are some standard order for printing
character table. This would be useful for interoperability between
software (or two version of the same software) by using a common
numbering for characters which could avoid mistakes.
Cheers,
Bill.
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