Hochschild cohomology for the integer group ring of the semidihedral group

We compute the Hochschild cohomology group for the integer group ring of the semidihedral 2-group $SD_{2^k}$. In calculations, we use the free bimodule resolution of the corresponding group ring. In turn, to construct that, we first construct the usual resolution of the trivial $SD_{2^k}$-module $\mathbb Z$.