Higher indicators for some groups and their doubles

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.