M₁₆×#108 #183713

order	512
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂³×C₄

Aliases

751 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:

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

maximal subgroup of	#72310100, #108×AGL(1,ℤ/8), #72310109, …
maximal normal subgroup of	#72310100, #108×AGL(1,ℤ/8), #72310109, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 90909);