# D8*C4

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## Blocks with defect group $D_8 * C_4$

The invariants $k(B)$, $k_i(B)$ and $l(B)$ are determined in [Sa13b]. There is precisely one saturated fusion system on $D_8 * C_4 \cong Q_8*C_4$. There is as yet no classification of blocks with these defect groups, and Donovan's conjecture is not known in any form.

CLASSES NOT CLASSIFIED

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(16,13,1) $k(Q_8*C_4)$ 1 10 1 $1$ 1 1
M(16,13,2) $B_0(k(SL_2(5)*C_4))$  ? 14 3 $1$ 1 1
M(16,13,3) $k(SL_2(3)*C_4)$  ? 14 3 $1$ 1 1

If $B$ is not nilpotent, then $k_0(B)=8, k_1(B)=6, l(B)=3$.