C₂×#8068 #181661

order	512
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

2160 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88857);