C₉×Dic₃⋊C₄ #88485

order	432
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂⁵×C₃×D₃ (order 576) · Inn(G) = C₂×D₃ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₂×C₄×C₉ · Schur multiplier (H₂) = C₂

Aliases

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 132);