C₃×#3673 #88502

order	432
isoclinism	isoclinic class of #3672
automorphism	Aut(G) = C₂²×D₄×AGL(1,ℤ/9) (order 1728) · Inn(G) = #611 · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

Fitting	C₃×D₄×C₉ ⋊ C₂
Sylow	C₃×C₉ ⋊ D₈

82 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)(4,5,8,10,12,11,6,9,7)(14,17)(15,20)(18,19);(5,7)(6,10)(8,9)(11,12)(13,14)(15,17)(16,19)(18,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 149);