Let V_\pi be a nontrivial irreducible representation of G. Then the isotype to the trivial representation of \pi is the null space.
\eta(1,2)= \begin{pmatrix} -1 &2 \\ 0& 1\end{pmatrix}, \quad \eta(1,3)=\begin{pmatrix} \frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & -1 \end{pmatrix},\quad \eta(2,3)= \begin{pmatrix}0& -2\\-\frac{1}{2} & 0\end{pmatrix}.