We characterise the Morita equivalence classes of blocks with extraspecial defect groups \(p_+^{1+2}\) for \(p \ge 5\) , and so show that Donovan’s conjecture and the Alperin-McKay conjecture hold for such p-groups. For \(p=3\) we reduce Donovan’s conjecture for blocks with defect group \(3_+^{1+2}\) to bounding the Cartan invariants for such blocks of quasisimple groups. We apply the characterisation to the case \(p=5\) as an example, to list the Morita equivalence classes of such blocks.
