Difference between revisions of "C4xC2xC2"
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| − | |[[M(16,10,1)]] || <math>k(C_4 \times C_2 \times C_2)</math> || 1 ||16 ||1 ||<math>1</math> || || ||1 ||1 || | + | |[[M(16,10,1)]] || <math>k(C_4 \times C_2 \times C_2)</math> || 1 ||16 ||1 ||<math>1</math> || <math>\mathcal{L}(B)=(C_4 \times C_2 \times C_2):{\rm Aut}(C_4 \times C_2 \times C_2)</math> || ||1 ||1 || |
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| − | |[[M(16,10,2)]] || <math>B_0(k(C_4 \times A_5))</math> || 1 ||16 ||3 ||<math>C_3</math> || || ||1 ||1 || | + | |[[M(16,10,2)]] || <math>B_0(k(C_4 \times A_5))</math> || 1 ||16 ||3 ||<math>C_3</math> || <math>D_8 \times C_2</math> || ||1 ||1 || |
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| − | |[[M(16,10,3)]] || <math>k(C_4 \times A_4)</math> || 1 ||16 ||3 ||<math>C_3</math> || || ||1 ||1 || | + | |[[M(16,10,3)]] || <math>k(C_4 \times A_4)</math> || 1 ||16 ||3 ||<math>C_3</math> || <math>D_8 \times S_3</math>|| ||1 ||1 || |
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Revision as of 09:49, 5 December 2018
Blocks with defect group [math]C_4 \times C_2 \times C_2[/math]
These are blocks were classified over [math]\mathcal{O}[/math] in [EL18a] using the CFSG. Each [math]k[/math]-Morita equivalence class lifts to an unique [math]\mathcal{O}[/math]-Morita equivalence class.
| 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(16,10,1) | [math]k(C_4 \times C_2 \times C_2)[/math] | 1 | 16 | 1 | [math]1[/math] | [math]\mathcal{L}(B)=(C_4 \times C_2 \times C_2):{\rm Aut}(C_4 \times C_2 \times C_2)[/math] | 1 | 1 | ||
| M(16,10,2) | [math]B_0(k(C_4 \times A_5))[/math] | 1 | 16 | 3 | [math]C_3[/math] | [math]D_8 \times C_2[/math] | 1 | 1 | ||
| M(16,10,3) | [math]k(C_4 \times A_4)[/math] | 1 | 16 | 3 | [math]C_3[/math] | [math]D_8 \times S_3[/math] | 1 | 1 |
