For several years now the study of 4d supersymmetric SCFT's by the compactification of 6d SCFT's on a Riemann surface has been a very active research direction. This has mostly concentrated on the compactification of 6d (2,0) SCFT's, the so called class S theories. Yet, recently people started more in dept study also of compactifications of 6d (1,0) SCFT's. In this lecture we consider a class of theories, called class $S_k$, which are the 4d SCFT's conjectured by Gaiotto and Razamat to correspond to the compactification on a Riemann surface of the 6d SCFT living on N M5-branes probing a $C^2/Z_k$ singularity. We shall calculate various properties of the 4d theories from both the 6d construction and the conjectured 4d field theories, and match them. This provides a non-trivial test of the class $S_k$ construction.