C₉×#217 #88518

order	432
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×C₃×D₃×#120 (order 1152) · Inn(G) = C₂×D₃ · Out(G) = C₂²×C₃×D₄
homology	Abelianization (H₁) = C₂×C₄×C₉ · Schur multiplier (H₂) = C₂²

Aliases

134 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 165);