  Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in
detail. Their modular data - S, T and fusion matrices - are computed
explicitly, and illustrated by means of fusion graphs. This allows us to
reexamine certain identities on these tensor product or fusion multiplicities
under conjugation of representations that had been discussed in our recent
paper [J. Phys. A: Math. Theor. 44 (2011), 295208, 26 pages, arXiv:1103.2943],
proved to hold for simple and affine Lie algebras, and found to be generally
wrong for finite groups. It is shown here that these identities fail also in
general for Drinfeld doubles, indicating that modularity of the fusion category
is not the decisive feature. Along the way, we collect many data on these
Drinfeld doubles which are interesting for their own sake and maybe also in a
relation with the theory of orbifolds in conformal field theory.
