# C4xC4

## Blocks with defect group $C_4 \times C_4$
These are blocks were first classified over $\mathcal{O}$ in [EKKS14] using the CFSG. Each $k$-Morita equivalence class lifts to an unique $\mathcal{O}$-Morita equivalence class. The automorphism group of $C_4 \times C_4$ is SmallGroup(96,195), which has isomorphism type $(C_2)^4:S_3$.
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(16,2,1) $k(C_4 \times C_4)$ 1 16 1 $1$ $(C_4 \times C_4):({\rm Aut}(C_4 \times C_4))$ 1 1
M(16,2,2) $k((C_4 \times C_4):C_3)$ 1 8 3 $C_3$ 1 1