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

$FSZ$-groups and Frobenius-Schur Indicators of Quantum Doubles