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

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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 |