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Blocks with defect group [math]C_8 \times C_2[/math]

[math]{\rm Aut}(C_8 \times C_2)[/math] is a [math]2[/math]-group and [math]C_8 \times C_2[/math] is abelian, so there is only one possible fusion system. Hence every block with this defect group is nilpotent.

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

Class Representative # lifts / [math]\mathcal{O}[/math] [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(16,5,1) [math]k(C_8 \times C_2)[/math] 1 16 1 [math]1[/math] [math](C_8 \times C_2):{\rm Aut}(C_8 \times C_2)[/math] 1 1