Using the representation theory of the subgroups SL2 (Z(p)) of the mod
ular group we investigate the induced fusion algebras in some simple e
xamples. Only some of these representations lead to ''good'' fusion al
gebras. Furthermore, the conformal dimensions and the central charge o
f the corresponding rational conformal field theories are calculated.
Two series of representations which can be realized by unitary theorie
s are presented. We show that mort of the fusion algebras induced by a
dmissible representations are realized in well-known rational models.