Permutation orbifolds of heterotic Gepner models

We study orbifolds by permutations of two identical N=2$N=2$ minimal models within the Gepner construction of four-dimensional heterotic strings. This is done using the new N=2$N=2$ supersymmetric permutation orbifold building blocks we have recently developed. We compare our results with the old method of modding out the full string partition function. The overlap between these two approaches is surprisingly small, but whenever a comparison can be made we find complete agreement. The use of permutation building blocks allows us to use the complete arsenal of simple current techniques that is available for standard Gepner models, vastly extending what could previously be done for permutation orbifolds. In particular, we consider (0,2)$(0,2)$ models, breaking of SO(10)$\mathit{SO}(10)$ to subgroups, weight-lifting for the minimal models and B-L lifting. Some previously observed phenomena, for example concerning family number quantization, extend to this new class as well, and in the lifted models three-family models occur with abundance comparable to two or four.