C₃×#3771 #88918

order	432
isoclinism	isoclinic class of AGL(1,𝔽₉)
automorphism	Aut(G) = C₂×AGL(1,𝔽₉)⋊C₄ (order 576) · Inn(G) = AGL(1,𝔽₉) · Out(G) = C₂×C₄
homology	Abelianization (H₁) = C₃×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

derived	C₃² ⋊ C₃×C₁₆
Sylow	C₃³ ⋊ C₁₆

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3)(5,10,12,6,8,9,7,11)(13,18,21,20,23,28,15,19,17,25,27,14,16,24,22,26);(4,7,12)(5,10,6)(8,11,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 565);