# 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 |