Finite groups with many values in a column or a row of the character table

Many results show how restrictions on the degrees of the irreducible characters of a finite group G, influence the structure of G. In the current article we study groups with restrictions on the values of a nonidentity rational element of the group G. We show that the symmetric group on 3 letters is the only nonabelian finite group that contains a rational element g assuming different values on any two distinct irreducible characters. We comment that the dual statement is also true.