M16

Blocks with defect group $M_{16} \cong \langle x,y|x^8=y^2=1, yx=x^5y \rangle$
$M_{16}$ is a metacyclic group of nonmaximal class, and so by [Sa12b] there is only one possible fusion system. Hence every block with this defect group is nilpotent.
There is a unique $\mathcal{O}$-Morita equivalence class.
Class Representative # lifts / $\mathcal{O}$ $k(B)$ $l(B)$ Inertial quotients ${\rm Pic}_\mathcal{O}(B)$ ${\rm Pic}_k(B)$ ${\rm mf_\mathcal{O}(B)}$ ${\rm mf_k(B)}$ Notes
M(16,6,1) $kM_{16}$ 1 10 1 $1$ 1 1