C(2^m)xC(2^m)

Blocks with defect group [math]C_{2^m} \times C_{2^m}[/math] for [math]m\gt 1[/math]

These blocks were classified them over [math]\mathcal{O}[/math] in [EKKS14] using the CFSG. The Picard groups with respect to [math]\mathcal{O}[/math] follow from [BKL18].

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([math]C_{2^m} \times C_{2^m}[/math],1)	[math]k(C_{2^m} \times C_{2^m})[/math]	1	[math]2^{2m}[/math]	1	[math]1[/math]	[math](C_{2^m} \times C_{2^m}):(C_{2^{m-1}} \times S_3)[/math]		1	1
M([math]C_{2^m} \times C_{2^m}[/math],2)	[math]k(C_{2^m} \times C_{2^m}):C_3[/math]	1	[math](2^{2m}+8)/3[/math]	3	[math]C_3[/math]	[math]S_3 \times C_{2^{m-1}}[/math]		1	1