C8

Blocks with defect group [math]C_8[/math]

These are blocks with cyclic defect groups and so they are described by Brauer trees.

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
[math]M(8,1,1)[/math]	[math]kC_8[/math]	8	1	[math]1[/math]	[math]C_8:(C_2 \times C2)[/math]		1	1