C₄×#1654 #209683

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

Aliases

1246 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);(6,10)(7,8)(11,12)(13,14,17,20)(15,18,16,19);(5,6,9,11)(7,10,8,12)(14,18)(15,16)(19,20);(5,7,9,8)(6,10,11,12)(14,19)(15,16)(18,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 116879);