C₂²×#1434 #513335

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂¹¹×C₄

Aliases

12322 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 5 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420531);