C₄×#2309 #513434

order	512
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁷×C₄³

Aliases

7930 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420630);