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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 SmallGroup(96,195), which has isomorphism type [math](C_2)^4: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):({\rm Aut}(C_4 \times C_4))[/math] 1 1
M(16,2,2) [math]k((C_4 \times C_4):C_3)[/math] 1 8 3 [math]C_3[/math] 1 1