D₃×Dic₁₈ #88637

order	432
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

direct product	D₃×Dic₁₈
unambiguous semidirect product	(D₃×C₉)⋊Q₈

C₃×C₉ ⋊ C₂×Q₈

126 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 284);