Difference between revisions of "C4xC4"
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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):S_3</math> || ||1 ||1 || | |[[M(16,2,1)]] || <math>k(C_4 \times C_4)</math> || 1 ||16 ||1 ||<math>1</math> ||<math>(C_4 \times C_4):S_3</math> || ||1 ||1 || | ||
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| − | |[[M(16,2,2)]] || <math>k((C_4 \times C_4):C_3)</math> || 1 ||8 ||3 ||<math>C_3</math> ||<math>S_3</math> || ||1 ||1 || | + | |[[M(16,2,2)]] || <math>k((C_4 \times C_4):C_3)</math> || 1 ||8 ||3 ||<math>C_3</math> ||<math>C_2 \times S_3</math> || ||1 ||1 || |
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Revision as of 14:16, 14 November 2018
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 isomorphic to [math]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):S_3[/math] | 1 | 1 | ||
| M(16,2,2) | [math]k((C_4 \times C_4):C_3)[/math] | 1 | 8 | 3 | [math]C_3[/math] | [math]C_2 \times S_3[/math] | 1 | 1 |
