Q₈×#365 #497932

order	512
nilpotency class	4
isoclinism	isoclinic class of #483463
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

496 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);(10,14,15,20)(11,17)(12,19)(16,23,22,21)(18,24);(9,10,11,14,12,16,17,21,13,15,18,20,19,22,24,23)

maximal subgroup of	#72313208, #72313209, #72313220, …
maximal normal subgroup of	#72313208, #72313209, #72313220, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 405128);