# C32

## Blocks with defect group $C_{32}$
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(32,1,1) $kC_{32}$ 1 32 1 $1$ $C_{32}:(C_8 \times C_2)$ $k^{30}:k^*$ 1 1