C₉×#215 #88511

order	432
isoclinism	isoclinic class of #213
automorphism	Aut(G) = C₂²×C₃×D₃×D₄ (order 576) · Inn(G) = #67 · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₁

Aliases

Fitting	C₃×Q₈×C₉ ⋊ C₂
Sylow	C₃×C₉ ⋊ SD₁₆

72 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)(13,14,16,18)(15,20,19,17);(2,3)(14,17)(15,19)(18,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 158);