C8:C4

Blocks with defect group [math]C_8:C_4[/math]

[math]C_8:C_4[/math] is a metacyclic group of nonmaximal class, and so by [CG12 or [Sa12b] 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(32,4,1)	[math]k(C_8:C_4)[/math]	1	20 (16,4)	1	[math]1[/math]			1	1