D8xC2

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Blocks with defect group [math]D_8 \times C_2[/math]

The invariants [math]k(B)[/math], [math]k_i(B)[/math] and [math]l(B)[/math] are determined in [Sa12]. There is as yet no classification of blocks with these defect groups, and Donovan's conjecture is not known in any form.

CLASSIFICATION INCOMPLETE
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(16,11,1) [math]k(D_8 \times C_2)[/math]  ? 10 1 [math]1[/math] 1
M(16,11,2) [math]B_0(k(PGL_2(5) \times C_2))[/math]  ? 10 2 [math]1[/math] 1
M(16,11,3) [math]k(S_4 \times C_2)[/math]  ? 10 2 [math]1[/math] 1
M(16,11,4) [math]B_0(k(PSL_2(9) \times C_2))[/math]  ? 10 3 [math]1[/math] 1
M(16,11,5) [math]B_0(k(A_7 \times C_2))[/math]  ? 10 3 [math]1[/math] 1
M(16,11,6) [math]B_0(k(PSL_2(7) \times C_2))[/math]  ? 10 3 [math]1[/math] 1


Notes