C₂×#10958 #354045

order	512
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

3990 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);(4,6)(11,12,15,17,16,13,14,18);(7,8,9,10)(11,13,16,12)(14,17,15,18);(3,4,5,6)(11,12,16,13)(14,17,15,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261241);