C5

Blocks with defect group [math]C_5[/math]

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

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

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
[math]M(5,1,1)[/math]	[math]kC_5[/math]	5	1	[math]1[/math]	[math]C_5:C_4[/math]		1	1
[math]M(5,1,2)[/math]	[math]kD_{10}[/math]	4	2	[math]C_2[/math]			1	1
[math]M(5,1,3)[/math]	[math]B_0(kA_5)[/math]	4	2	[math]C_2[/math]			1	1
[math]M(5,1,4)[/math]	[math]k(C_5:C_4)[/math]	5	4	[math]C_4[/math]	[math]C_4[/math]		1	1
[math]M(5,1,5)[/math]	[math]B_0(kA_7)[/math]	5	4	[math]C_4[/math]			1	1
[math]M(5,1,6)[/math]	faithful block of [math]k(2.A_7)[/math]	5	4	[math]C_4[/math]			1	1