C(2^n)

Blocks with defect group $C_{2^n}$
${\rm Aut}(C_{2^n})$ is a 2-group for all $n$, hence every block with such a defect group is nilpotent.
Class Representative $k(B)$ $l(B)$ Inertial quotients ${\rm Pic}_\mathcal{O}(B)$ ${\rm Pic}_k(B)$ ${\rm mf_\mathcal{O}(B)}$ ${\rm mf_k(B)}$ Notes
M($2^n$,1,1) $kC_{2^n}$ $2^n$ 1 $1$ $C_{2^n} : C_{2^{n-1}}$ 1 1