Complete Analysis of Extensions of $D(n{)}_1$ Permutation Orbifolds

We give the full set of $S$ matrices for extensions of $D(n{)}_1$ permutation orbifolds, extending our previous work to the yet unknown case of integer spin spinor currents. The main tool is triality of SO(8). We also provide fixed point resolution matrices for spinor currents of $D(n{)}_1$ permutation orbifolds with $n$ even and not multiple of four, where the spinor currents have half-integer spin.