MNA(2,2)

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