From Block library
Jump to: navigation, search

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