C₂²×#2367 #7625377

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

14210 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)(9,10,12,11)(13,14)(15,16)(17,18)(19,20);(9,11,12,10)(14,18)(16,19);(5,6,7,8)(13,15)(14,19)(16,18)(17,20);(13,16,17,19)(14,15,18,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532573);