# C3

## Blocks with defect group $C_3$
There are two $\mathcal{O}$-Morita equivalence classes, accounting for all the possible Brauer trees.
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(3,1,1) $kC_3$ 1 3 1 $1$ $S_3$ $k:k^*$ 1 1
M(3,1,2) $kS_3$ 1 3 2 $C_2$ $C_2$ $k^* \times C_2$ 1 1