nLab 7d spherical space forms -- table

$N$ Killing spinors on spherical space form $S^7/\widehat{G}$	$\phantom{AA}\widehat{G} =$	spin-lift of subgroup of isometry group of 7-sphere	3d superconformal gauge field theory on back M2-branes with near horizon geometry $AdS_4 \times S^7/\widehat{G}$
$\phantom{AA}N = 8\phantom{AA}$	$\phantom{AA}\mathbb{Z}_2$	cyclic group of order 2	BLG model
$\phantom{AA}N = 7\phantom{AA}$	—	—	—
$\phantom{AA}N = 6\phantom{AA}$	$\phantom{AA}\mathbb{Z}_{k\gt 2}$	cyclic group	ABJM model
$\phantom{AA}N = 5\phantom{AA}$	$\phantom{AA}2 D_{k+2}$ $2 T$, $2 O$, $2 I$	binary dihedral group, binary tetrahedral group, binary octahedral group, binary icosahedral group	(HLLLP 08a, BHRSS 08)
$\phantom{AA}N = 4\phantom{AA}$	$\phantom{A}2 D_{k+2}$ $2 O$, $2 I$	binary dihedral group, binary octahedral group, binary icosahedral group	(HLLLP 08b, Chen-Wu 10)

• José Figueroa-O'Farrill et al. 2009 (arXiv:0909.0163, pdf slides)