  Using the representation theory of the subgroups SL_2(Z_p) of the modular
group we investigate the induced fusion algebras in some simple examples. Only
some of these representations lead to 'good' fusion algebras. Furthermore, the
conformal dimensions and the central charge of the corresponding rational
conformal field theories are calculated. Two series of representations which
can be realized by unitary theories are presented. We show that most of the
fusion algebras induced by admissible representations are realized in well
known rational models.
