Three-dimensional irreducible representation of the alternating group on four letters
= Three-dimensional irreducible representation of the alternating group on four letters
The <standard representation of the symmetric group> $S_4$ restricts irreducibly to $A_4$. Its character has value $3$ at the identity and $-1$ on each nonidentity element of the normal <Klein four-group>. Restricted to that subgroup, it is the sum of the three nontrivial linear characters.