GAP Manual: 48.33. RealClassesCharTable

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 inG 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.