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In any rational chiral CFT with a non-trivial simple current,we construct a finite group acting on the corresponding conformal blocks.Our groups are generalisations of the finite Heisenberg groups appearing in U(1) Chern-Simons theory and the chiral CFT of a compactified free boson,and of finite groups appearing in the SU(2) TFTs constructed by Blanchet et al.The action of these finite groups have implications for the mapping class group representations carried by conformal blocks,as will be illustrated by examples in the case of chiral SU(N) WZW models.