M16

Blocks with defect group [math]M_{16} \cong \langle x,y|x^8=y^2=1, yx=x^5y \rangle[/math]

[math]M_{16}[/math] is a metacyclic group of nonmaximal class, and so by [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(16,6,1)	[math]kM_{16}[/math]	1	10	1	[math]1[/math]	[math]M_{16}:{\rm Aut}(M_{16})[/math]		1	1