C4xC4

Blocks with defect group [math]C_4 \times C_4[/math]

These are blocks were first classified over [math]\mathcal{O}[/math] in [EKKS14] using the CFSG. Each [math]k[/math]-Morita equivalence class lifts to an unique [math]\mathcal{O}[/math]-Morita equivalence class. The automorphism group of [math]C_4 \times C_4[/math] is isomorphic to [math]S_3[/math].

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(16,2,1)	[math]k(C_4 \times C_4)[/math]	1	16	1	[math]1[/math]	[math](C_4 \times C_4):S_3[/math]		1	1
M(16,2,2)	[math]k((C_4 \times C_4):C_3)[/math]	1	8	3	[math]C_3[/math]	[math]S_3[/math]		1	1