3 +^3
Blocks with defect group [math]3_+^{1+2}[/math]
CLASSIFICATION INCOMPLETE
The table below is still being populated. Please feel free to add blocks!
| 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(27,3,1) | [math]k3_+^{1+2}[/math] | 1 | 11 | 1 | [math]1[/math] | 1 | 1 | |||
| M(27,3,2) | [math]k((C_3 \times C_3):C_6)[/math] | 10 | 2 | [math]C_2[/math] | 1 | 1 | SmallGroup(54,5) | |||
| M(27,3,3) | [math]k(3_+^{1+2}:C_2)[/math] | 10 | 2 | [math]C_2[/math] | 1 | 1 | SmallGroup(54,8) | |||
| M(27,3,?) | [math]B_0(kSL_3(3))[/math] | 16 | 5 | 1 | 1 | |||||
| M(27,3,?) | [math]B_0(k(SL_3(3).2))[/math] | 13 | 7 | 1 | 1 | |||||
| M(27,3,?) | [math]B_0(k(3.M_{22}))[/math] | 16 | 5 | 1 | 1 | |||||
| M(27,3,?) | [math]B_0(k(3.M_{22}.2))[/math] | 14 | 7 | 1 | 1 | |||||
| M(27,3,?) | [math]B_6(k(6.M_{22}))[/math] | 16 | 5 | 1 | 1 | |||||
| M(27,3,?) | [math]B_6(k(6.M_{22}.2))[/math] | 14 | 7 | 1 | 1 | |||||
| M(27,3,?) | [math]B_{10}(k(12.M_{22}))[/math] | 16 | 5 | 1 | 1 |
