C₄×#2854 #607629

order	512
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

4702 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);(5,6)(7,8)(10,11)(13,14)(15,17)(16,18)(19,20);(9,10,12,11)(13,15,16,19)(14,17,18,20);(14,18)(17,20);(6,8)(9,11,12,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 514825);