Q₈×#361 #497622

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

Aliases

846 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);(9,10,12,16,13,18,23,17)(11,19,21,15,22,14,20,24);(10,14)(11,20)(12,23)(15,16)(17,24)(18,19)(21,22)

maximal subgroup of	#72342445, #72342448, #72342450, …
maximal normal subgroup of	#72342445, #72342448, #72342450, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 404818);