C3

Blocks with defect group [math]C_3[/math]

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

There are two [math]\mathcal{O}[/math]-Morita equivalence classes, accounting for all the possible Brauer trees.

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(3,1,1)	[math]kC_3[/math]	1	3	1	[math]1[/math]	[math]S_3[/math]	[math]k:k^*[/math]	1	1
M(3,1,2)	[math]kS_3[/math]	1	3	2	[math]C_2[/math]	[math]C_2[/math]	[math]k^* \times C_2[/math]	1	1