Difference between revisions of "C4xC2"
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== Blocks with defect group <math>C_4 \times C_2</math> == | == Blocks with defect group <math>C_4 \times C_2</math> == | ||
| − | <math>{\rm Aut}(C_4 \times C_2)</math> is | + | <math>{\rm Aut}(C_4 \times C_2)</math> is a <math>2</math>-group and so every block with this defect group is [[Nilpotent blocks|nilpotent]]. |
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{| class="wikitable" | {| class="wikitable" | ||
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! scope="col"| Class | ! scope="col"| Class | ||
! scope="col"| Representative | ! scope="col"| Representative | ||
| + | ! scope="col"| # lifts / <math>\mathcal{O}</math> | ||
! scope="col"| <math>k(B)</math> | ! scope="col"| <math>k(B)</math> | ||
! scope="col"| <math>l(B)</math> | ! scope="col"| <math>l(B)</math> | ||
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|- | |- | ||
| − | |M(8,2,1) || <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 || | + | |[[M(8,2,1)]] || <math>k(C_4 \times C_2)</math> || 1 ||8 ||1 ||<math>1</math> || <math>(C_4 \times C_2):(C_2 \times C_2 \times C_2)</math> || ||1 ||1 || |
|} | |} | ||
Latest revision as of 08:08, 15 September 2018
Blocks with defect group [math]C_4 \times C_2[/math]
[math]{\rm Aut}(C_4 \times C_2)[/math] is a [math]2[/math]-group and so every block with this defect group is nilpotent.
| Class | Representative | # lifts / [math]\mathcal{O}[/math] | [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(8,2,1) | [math]k(C_4 \times C_2)[/math] | 1 | 8 | 1 | [math]1[/math] | [math](C_4 \times C_2):(C_2 \times C_2 \times C_2)[/math] | 1 | 1 |
