C₄×#2427 #514882

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

Aliases

4222 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);(9,10,12,11)(13,14,16,17)(15,19,20,18);(5,6)(7,8)(9,11,12,10)(14,17)(18,19);(6,8)(10,11);(13,15,16,20)(14,18,17,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 422078);