C₃×#3664 #88460

order	432
isoclinism	isoclinic class of Dic₃₆
automorphism	Aut(G) = C₂²×D₄×AGL(1,ℤ/9) (order 1728) · Inn(G) = D₃₆ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

Fitting	C₃×C₈×C₉ ⋊ C₂
Sylow	C₃×C₉ ⋊ SD₁₆

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 107);