C₂²×#1819 #6370864

order	512
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹¹

Aliases

13410 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278060);