RealClassesCharTable( tbl )
returns a list of the real classes of the group G with character table tbl.
gap> RealClassesCharTable(L3_2);
[ 1, 2, 3, 4 ]
An element x in G is called real, if it is conjugate with its inverse. And as x^{-1} = x^{o(x)-1}, this fact is tested by looking at the powermap of tbl.
Real elements take only real character values.
GAP 3.4.4