C₂×#21059 #6371635

order	512
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

3874 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278831);