D₃²×C₉ #66423

order	324
isoclinism	isoclinic class of D₃²
automorphism	Aut(G) = C₂×C₃×GO⁺(4,𝔽₂) (order 432) · Inn(G) = D₃² · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃²×C₉
unambiguous semidirect product	(C₃×D₃)⋊(C₂×C₉)

Fitting, Sylow	C₃²×C₉ ⋊ C₂²
derived	C₃² ⋊ C₂²×C₉

86 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 2 generators on 15 points:

(1,2,3)(5,6)(7,8,10,9,11,13,12,14,15);(2,3)(4,5,6)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 115);