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We characterise the Morita equivalence classes of blocks with extraspecialdefect groups $p_+^{1+2}$ for $p \geq 5$, and so show that Donovan's conjectureand the Alperin-McKay conjecture hold for such $p$-groups. For $p=3$ we reduceDonovan's conjecture for blocks with defect group $3_+^{1+2}$ to bounding theCartan invariants for such blocks of quasisimple groups. We apply thecharacterisation to the case $p=5$ as an example, to list the Moritaequivalence classes of such blocks.

Morita equivalence classes of blocks with extraspecial defect groups $p_+^{1+2}$