# MNA(2,2)

## Blocks with defect group $MNA(2,2)=\langle x,y|x^4=y^4=[x,y]^2=[x,[x,y]]=[y,[x,y]]=1 \rangle$
The defect groups are minimal nonabelian $2$-groups. The $\mathcal{O}$-Morita equivalence classes are classified in [EKS12].
Class Representative # lifts / $\mathcal{O}$ $k(B)$ $l(B)$ Inertial quotients ${\rm Pic}_\mathcal{O}(B)$ ${\rm Pic}_k(B)$ ${\rm mf_\mathcal{O}(B)}$ ${\rm mf_k(B)}$ Notes
M(32,2,1) $k(MNA(2,2))$ 1 20 (16,4) 1 $1$ 1 1
M(32,2,2) $k(MNA(2,2):C_3)$ 1 12 (8,4) 3 $C_3$ 1 1