C₈×#535 #6377662

order	512
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

2654 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6284858);