  We study the higher Frobenius-Schur indicators of the representations of the
Drinfel'd double of a finite group G, in particular the question as to when all
the indicators are integers. This turns out to be an interesting
group-theoretic question. We show that many groups have this property, such as
alternating and symmetric groups, PSL_2(q), M_{11}, M_{12} and regular
nilpotent groups. However we show there is an irregular nilpotent group of
order 5^6 with non-integer indicators.
