C₂²×#1508 #6343290

order	512
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

5478 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)(7,11,12,9)(8,10)(14,18,19,20);(5,7,8,12)(6,9,10,11)(13,14)(15,18)(16,20)(17,19);(7,12)(9,11)(13,15,17,16)(14,18,19,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250486);