# 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] | 1 | 1 |