C₂×#10745 #353425

order	512
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂¹⁰

Aliases

6334 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);(3,4)(5,6)(11,12)(13,17,18,15)(14,16);(7,8,9,10)(11,13)(12,15)(14,18)(16,17);(4,6)(11,12)(13,15)(14,16)(17,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260621);