Difference between revisions of "C4xC4"
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== Blocks with defect group <math>C_4 \times C_4</math> == | == Blocks with defect group <math>C_4 \times C_4</math> == | ||
| − | These are blocks were first classified over <math>\mathcal{O}</math> in [[References|[EKKS14]]] using the [[Glossary#CFSG|CFSG]]. Each <math>k</math>-Morita equivalence class lifts to an unique <math>\mathcal{O}</math>-Morita equivalence class. The automorphism group of <math>C_4 \times C_4</math> is | + | These are blocks were first classified over <math>\mathcal{O}</math> in [[References|[EKKS14]]] using the [[Glossary#CFSG|CFSG]]. Each <math>k</math>-Morita equivalence class lifts to an unique <math>\mathcal{O}</math>-Morita equivalence class. The automorphism group of <math>C_4 \times C_4</math> is SmallGroup(96,195), which has isomorphism type <math>(C_2)^4:S_3</math>. |
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| − | |[[M(16,2,1)]] || <math>k(C_4 \times C_4)</math> || 1 ||16 ||1 ||<math>1</math> ||<math>(C_4 \times C_4): | + | |[[M(16,2,1)]] || <math>k(C_4 \times C_4)</math> || 1 ||16 ||1 ||<math>1</math> ||<math>(C_4 \times C_4):({\rm Aut}(C_4 \times C_4))</math> || ||1 ||1 || |
|- | |- | ||
| − | |[[M(16,2,2)]] || <math>k((C_4 \times C_4):C_3)</math> || 1 ||8 ||3 ||<math>C_3</math> || | + | |[[M(16,2,2)]] || <math>k((C_4 \times C_4):C_3)</math> || 1 ||8 ||3 ||<math>C_3</math> || || ||1 ||1 || |
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Latest revision as of 07:13, 4 June 2019
Blocks with defect group [math]C_4 \times C_4[/math]
These are blocks were first classified over [math]\mathcal{O}[/math] in [EKKS14] using the CFSG. Each [math]k[/math]-Morita equivalence class lifts to an unique [math]\mathcal{O}[/math]-Morita equivalence class. The automorphism group of [math]C_4 \times C_4[/math] is SmallGroup(96,195), which has isomorphism type [math](C_2)^4:S_3[/math].
| 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(16,2,1) | [math]k(C_4 \times C_4)[/math] | 1 | 16 | 1 | [math]1[/math] | [math](C_4 \times C_4):({\rm Aut}(C_4 \times C_4))[/math] | 1 | 1 | ||
| M(16,2,2) | [math]k((C_4 \times C_4):C_3)[/math] | 1 | 8 | 3 | [math]C_3[/math] | 1 | 1 |
