D8*C4

Blocks with defect group [math]D_8 * C_4[/math]

The invariants [math]k(B)[/math], [math]k_i(B)[/math] and [math]l(B)[/math] are determined in [Sa13b]. There is precisely one saturated fusion system on [math]D_8 * C_4 \cong Q_8*C_4[/math]. There is as yet no classification of blocks with these defect groups, and Donovan's conjecture is not known in any form.

CLASSES NOT CLASSIFIED

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(16,13,1)	[math]k(Q_8*C_4)[/math]	1	10	1	[math]1[/math]			1	1
M(16,13,2)	[math]B_0(k(SL_2(5)*C_4))[/math]	?	14	3	[math]1[/math]			1	1
M(16,13,3)	[math]k(SL_2(3)*C_4)[/math]	?	14	3	[math]1[/math]			1	1

If [math]B[/math] is not nilpotent, then [math]k_0(B)=8, k_1(B)=6, l(B)=3[/math].