Mirror symmetry of nonabelian Landau–Ginzburg orbifolds with loop type potentials

We study the bigraded vector space structure of Landau–Ginzburg orbifolds with permutation symmetries variables. calculate formula Poincaré polynomial for a certain loop orbifoldized by semidirect product diagonal symmetry group and cyclic check that generalization Berglund–Hübsch transpose gives mirror symmetric pairs these cases.