Q₈×#347 #493262

order	512
nilpotency class	2
isoclinism	isoclinic class of #180873
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴

Aliases

554 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);(9,10,11,15,12,17,19,23,13,16,18,24,20,14,21,22);(10,14,16,17)(11,18)(15,23,24,22)(19,21)

maximal subgroup of	#72309480, #72309489, #72309500, …
maximal normal subgroup of	#72309480, #72309489, #72309500, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400458);