C4xC2

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Blocks with defect group [math]C_4 \times C_2[/math]

[math]{\rm Aut}(C_4 \times C_2)[/math] is an abelian [math]2[/math]-group and so every block with this defect group is nilpotent.

There is a unique [math]\mathcal{O}[/math]-Morita equivalence class.

Class Representative [math]k(B)[/math] [math]l(B)[/math] Inertial quotients [math]{\rm Pic}_\mathcal{O}(B)[/math] [math]{\rm Pic}_k(B)[/math] [math]{\rm mf_\mathcal{O}(B)}[/math] [math]{\rm mf_k(B)}[/math] Notes
M(8,2,1) [math]k(C_4 \times C_2)[/math] 8 1 [math]1[/math] [math](C_4 \times C_2):(C_2 \times C_2 \times C_2)[/math] 1 1