MNA(2,2)
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Blocks with defect group [math]MNA(2,2)=\langle x,y|x^4=y^4=[x,y]^2=[x,[x,y]]=[y,[x,y]]=1 \rangle[/math]
The defect groups are minimal nonabelian [math]2[/math]-groups. The [math]\mathcal{O}[/math]-Morita equivalence classes are classified in [EKS12].
| 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(32,2,1) | [math]k(MNA(2,2))[/math] | 1 | 20 (16,4) | 1 | [math]1[/math] | 1 | 1 | |||
| M(32,2,2) | [math]k(MNA(2,2):C_3)[/math] | 1 | 12 (8,4) | 3 | [math]C_3[/math] | 1 | 1 |
