# C4:C4

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

[math]C_4: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(16,4,1) | [math]k(C_4:C_4)[/math] | 1 | 10 (8,2) | 1 | [math]1[/math] | 1 | 1 |