C₂×#9497 #201654

order	512
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

3962 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 64

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 108850);