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We describe the group of braided tensor autoequivalences of the Drinfeldcentre of a finite group $G$ isomorphic to the identity functor (just as afunctor) as a semi-direct product $Aut^1_{br}(\Z(G))\ \simeq\Out_{2-cl}(G)\ltimes B(G)\ $ of the group of double class preservingautomorphisms and the Bogomolov multiplier of $G$. The Bogomolov multiplier$B(G)$ is the subgroup of its Schur multiplier $H^2(G,k^*)$ of classesvanishing on abelian subgroups of $G$. We show that elements of$Aut^1_{br}(\Z(G))$ give rise to different realisations of the chargeconjugation modular invariant for $G$-orbifolds of holomorphic conformal fieldtheories.

Bogomolov multiplier, double class-preserving automorphisms and modular invariants for orbifolds