Q₈×#360 #497620

order	512
nilpotency class	4
isoclinism	isoclinic class of #481415
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

766 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,4,6)(3,7,8,5);(1,3,4,8)(2,5,6,7);(10,14,15,23)(11,17)(12,20)(16,18,21,24)(19,22);(9,10)(11,18)(12,21)(13,15)(14,22)(16,20)(17,23)(19,24)

maximal subgroup of	#72313407, #72313420, #72313481, …
maximal normal subgroup of	#72313407, #72313420, #72313481, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 404816);