C16xC2

Blocks with defect group [math]C_{16} \times C_2[/math]

[math]{\rm Aut}(C_{16} \times C_2)[/math] is a [math]2[/math]-group and [math]C_{16} \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(32,16,1)	[math]k(C_{16} \times C_2)[/math]	1	32	1	[math]1[/math]	[math](C_{16} \times C_2):{\rm Aut}(C_{16} \times C_2)[/math]		1	1