Title: Integrable deformations of Z2 and Z4 permutation cosets.

Strings on certain AdS3 space-times are described by integrable 2d sigma models on Z2 and Z4 permutation cosets with G x G symmetry group. The product structure of the symmetry group leads to a richer space of integrable deformations. In this talk I will outline recent progress in mapping out this space and some of the physical consequences of the symmetry structure.