C₃×#3663 #88459

order	432
isoclinism	isoclinic class of Dic₁₈
automorphism	Aut(G) = C₂⁴×AGL(1,ℤ/9) (order 864) · Inn(G) = C₂×D₉ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

Fitting	C₃×C₈×C₉ ⋊ C₂
Sylow	C₃×C₉ ⋊ M₁₆

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 144

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 106);