Some elementary character tables
We now illustrate the techniques we have presented so far by constructing the character tables of several groups, including the groups S4 and A4, and all dihedral groups.
18.1 The group S4
In Example 17.4, we produced three irreducible characters χ1, χ2, χ3 of S4 by lifting characters of the factor group S4/V4. We shall now use Proposition 17.14, which deals with the product of a character with a linear character, to complete the character table of S4.
Let χ4 be the character