  We show that the non-trivially associated tensor category constructed from
left coset representatives of a subgroup of a finite group is a modular
category. Also we give a definition of the character of an object in a ribbon
category which is the category of representations of a braided Hopf algebra in
the category. The definition is shown to be adjoint invariant and
multiplicative. A detailed example is given. Finally we show an equivalence of
categories between the non-trivially associated double D and the category of
representations of the double of the group D(X).
