C(2^n)

Blocks with defect group [math]C_{2^n}[/math]

[math]{\rm Aut}(C_{2^n})[/math] is a 2-group for all [math]n[/math], hence every block with such a defect group is nilpotent.

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([math]2^n[/math],1,1)	[math]kC_{2^n}[/math]	[math]2^n[/math]	1	[math]1[/math]	[math]C_{2^n} : C_{2^{n-1}}[/math]		1	1