C₃×#3667 #88478

order	432
isoclinism	isoclinic class of Dic₁₈
automorphism	Aut(G) = C₂²×D₄×AGL(1,ℤ/9) (order 1728) · Inn(G) = C₂×D₉ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₉ ⋊ M₁₆

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3)(4,9,11,10,5,7,6,12,8)(14,17)(18,20);(5,7)(6,10)(8,9)(11,12)(13,18,19,14,16,20,15,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 125);