  In this paper we calculate certain chiral quantities from the cyclic
permutation orbifold of a general completely rational net. We determine the
fusion of a fundamental soliton, and by suitably modified arguments of A. Coste
, T. Gannon and especially P. Bantay to our setting we are able to prove a
number of arithmetic properties including congruence subgroup properties for
$S, T$ matrices of a completely rational net defined by K.-H. Rehren .
