Derived block spaces for the Drinfel'd double of S3 in characteristic 3 carry new SL(2,Z)-representations in cohomological degrees 1 and 2 mod 4 that are not generated from degree zero under the Yoneda product.
Evens, The cohomology of groups, Oxford Math
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Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups II
Derived block spaces for the Drinfel'd double of S3 in characteristic 3 carry new SL(2,Z)-representations in cohomological degrees 1 and 2 mod 4 that are not generated from degree zero under the Yoneda product.