C5

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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