C₄×#2464 #514847

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

4504 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422043);