C₂×#1355 #11909

order	256
nilpotency class	4
isoclinism	isoclinic class of #1355
automorphism	Aut(G) = #72306524 (order 4096) · Inn(G) = #329 · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

183 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 4897);