C₂²×#2311 #7625274

order	512
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

26386 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 6 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532470);