  In this paper we explicitly determine all indicators for groups isomorphic to
the semidirect product of two cyclic groups by an automorphism of prime order,
as well as the generalized quaternion groups. We then compute the indicators
for the Drinfel'd doubles of these groups. This first family of groups includes
the dihedral groups, the non-abelian groups of order $pq$, and the semidihedral
groups. We find that the indicators are all integers, with negative integers
being possible in the first family only under certain specific conditions.
