C₉×D₂₄ #88465

order	432
isoclinism	isoclinic class of #204
automorphism	Aut(G) = C₂×C₃×D₃×AGL(1,ℤ/8) (order 1152) · Inn(G) = D₁₂ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₂₄

Fitting	C₃×C₈×C₉ ⋊ C₂
Sylow	C₃×C₉ ⋊ D₈

74 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)(4,5,7,6,8,10,9,11,12)(13,14,18,20,16,19,15,17);(2,3)(14,17)(15,18)(19,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 112);