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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}):Aut(C_{2^m} \times C_{2^m})[/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] 1 1