C₂²×#1438 #514000

order	512
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

39346 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);(10,12)(13,14,15,16)(17,18,19,20);(6,8)(10,12)(18,20);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421196);