C4xC2
Revision as of 12:47, 28 August 2018 by Charles Eaton (talk | contribs) (Created page with "== Blocks with defect group <math>C_4 \times C_2</math> == <math>{\rm Aut}(C_4 \times C_2)</math> is an abelian <math>2</math>-group and so every block with this defect group...")
Blocks with defect group [math]C_4 \times C_2[/math]
[math]{\rm Aut}(C_4 \times C_2)[/math] is an abelian [math]2[/math]-group and so every block with this defect group is nilpotent.
There is a unique [math]\mathcal{O}[/math]-Morita equivalence class.
| 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(8,2,1)[/math] | [math]k(C_4 \times C_2)[/math] | 8 | 1 | [math]1[/math] | [math](C_4 \times C_2):(C_2 \times C_2 \times C_2)[/math] | 1 | 1 |
