C₂×#21778 #6374190

order	512
nilpotency class	3
isoclinism	isoclinic class of #21776
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

5064 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 5 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281386);