C₉×#239 #88720

order	432
automorphism	Aut(G) = C₂²×C₃×D₃×S₄ (order 1728) · Inn(G) = C₂²×D₃ · Out(G) = C₂²×C₃×D₃
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₃×Q₈×C₉ ⋊ C₂
Sylow	C₃×C₉ ⋊ #41

132 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 367);