We study the higher Frobenius-Schur indicators of the representations of the Drinfeld 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.
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