C₂×#8416 #186183

order	512
nilpotency class	3
isoclinism	isoclinic class of #8412
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

2746 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);(4,7,8,9)(11,12,14,17,15,13,18,16);(3,4)(5,9)(6,8)(7,10)(11,13)(12,15)(14,16)(17,18);(11,12)(13,15)(14,16)(17,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 93379);