C₂²×#1437 #513344

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂¹²×C₄

Aliases

22362 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 256

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420540);