C₉×C₄⋊Dic₃ #88486

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) = C₂

Aliases

direct product	C₉×C₄⋊Dic₃
unambiguous semidirect product	C₄⋊(C₉×Dic₃)

94 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)(17,18,19,20);(2,3)(13,14,15,16)(18,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 133);