C₂×#21504 #6372788

order	512
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

3322 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);(4,6)(7,8,10,9)(11,12)(13,17)(14,16)(15,18);(3,4,5,6);(12,16)(13,14)(17,18);(7,9,10,8)(11,13,15,14)(12,17,18,16)

maximal subgroup of	C₂×D₄×#440, C₂×#6630193, C₂×#6444783
maximal normal subgroup of	C₂×D₄×#440, C₂×#6630193, C₂×#6444783

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279984);