# C2xC2

## Blocks with defect group $C_2 \times C_2$
These are blocks are examples of tame blocks and were first classified over $k$ by Erdmann (see [Er82] ). Linckelmann classified them over $\mathcal{O}$ in [Li94] , in which he also showed that the source algebras lie within three infinite families. In [CEKL11] the CFSG was used to show that only one source algebra can occur for each 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(4,2,1) $k(C_2 \times C_2)$ 1 4 1 $1$ $(C_2 \times C_2):S_3$ $(k \times k):GL_2(k)$ 1 1
M(4,2,2) $B_0(kA_5)$ 1 4 3 $C_3$ $C_2$ $(k^* \times k^*):C_2$ 1 1 $D(3 {\cal A})_1$
M(4,2,3) $kA_4$ 1 4 3 $C_3$ $S_3$ $(k^* \times k^* \times C_3):C_2$ 1 1 $D(3 {\cal K})$