C₂×#3771 #64217

order	288
isoclinism	isoclinic class of AGL(1,𝔽₉)
automorphism	Aut(G) = #11892456 (order 1152) · Inn(G) = AGL(1,𝔽₉) · Out(G) = #41
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

C₃² ⋊ C₂×C₁₆

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 2 generators on 27 points:

(4,5,6,9,7,10,11,8)(12,13,14,17,15,18,20,23,16,19,21,24,22,25,26,27);(1,2)(3,6,11)(4,9,5)(7,10,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 865);