D3d point group matrices
One of the usual setup for the coordination system would be that $x$ axis coincident with a two-fold axis. If we use this setup, we can easily write out the matrix for rotation around this 2-fold axis:
$$\begin{bmatrix}
1&amp;0&amp;0\\
0&amp;-1&amp;0\\
0&amp;0&amp;-1
\end{bmatrix}.$$

Then you can combine this with the transform matrix of the 3-fold axis to get the transform matrices of the other two 2-fold axes. That's just matrix multiplication.

In this setup, $yz$ is one of the reflection plane and the corresponding matrix is
$$\begin{bmatrix}
-1&amp;0&amp;0\\
0&amp;1&amp;0\\
0&amp;0&amp;1
\end{bmatrix}.$$

Note that this is just the combination of the previous matrix with inversion. You can apply the 3-fold axis rotation to it (once again, matrix multiplication) to obtain the matrix with regard to other two reflection planes.