C₄×#1622 #209670

order	512
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

1178 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);(6,9)(7,11)(10,12)(14,17)(15,19)(18,20);(5,6,8,10)(7,12,11,9)(15,19)(17,20);(13,14)(15,20)(16,18)(17,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 116866);