D₃×Q₈×C₉ #88719

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

D₃×Q₈×C₉

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

126 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 366);