We will introduce a large class of N=1 superconformal theories Sk which is obtained from Gaiotto’s N=2 class S via orbifolding. We will study the Coulomb branch of the theories in the class by constructing and analyzing their spectral curves. Using our experience from the N=2 AGT correspondence we will search for a 2D/4D relations (AGTk) for the N=1 theories of class Sk. From the curves we will identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of the Virasoro/W-algebra, that underlie the 2D theory and reproduce the Seiberg-Witten curves of the N = 1 gauge theories. We find that the blocks corresponding to the SU(N) Sk gauge theories involve fields in certain non-unitary representations of the WkN algebra. These conformal blocks give a prediction for the instanton partition functions of the 4D N = 1 SCFTs of class Sk.