D8xC2

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