C32

Blocks with defect group [math]C_{32}[/math]

These are blocks with cyclic defect groups and so they are described by Brauer trees.

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(32,1,1)	[math]kC_{32}[/math]	1	32	1	[math]1[/math]	[math]C_{32}:(C_8 \times C_2)[/math]	[math]k^{30}:k^*[/math]	1	1