D₉×Dic₆ #88633

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

Aliases

direct product	D₉×Dic₆
unambiguous semidirect product	(C₃×D₉)⋊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)(12,17,15,14,19,16,18,13,20);(1,2,4,6)(3,7,8,5)(10,11);(13,15)(14,18)(16,19)(17,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 280);