C₄×#1926 #354341

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

1700 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261537);