Symmetry of effective electroelastic tensor for point group 32

The detailed symmetry properties of a fifth-rank tensor of the type $f_{\mathrm{mijkl}}$ which possesses interchange symmetry of the pairs $\mathrm{ij}$ with $\mathrm{kl}$ but has no interchange symmetry within these pairs is investigated for the crystal symmetry of $\alpha$-quartz [point group 32 ($D_3$)]. Tensors of this type occur in the theory of the electroelastic effect. An extended matrix notation appropriate to cover this situation is proposed and used to present the results in compact form.