C7

Blocks with defect group [math]C_7[/math]

These are blocks with cyclic defect groups and so they are described by Brauer trees. There are candidate Brauer trees with no known block realising them.

All [math]k[/math]-Morita equivalence classes lift to [math]\mathcal{O}[/math]-classes.

CLASSIFICATION INCOMPLETE

Class	Representative	[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(7,1,1)	[math]kC_7[/math]	7	1	[math]1[/math]			1	1
M(7,1,2)	[math]kD_{15}[/math]	5	2	[math]C_2[/math]			1	1
M(7,1,3)	[math]B_0(kPSL_2(13))[/math]	5	2	[math]C_2[/math]			1	1
M(7,1,4)