C₃×D₃×D₉ #66422

order	324
isoclinism	isoclinic class of D₃×D₉
automorphism	Aut(G) = C₂×D₃×AGL(1,ℤ/9) (order 648) · Inn(G) = D₃×D₉ · Out(G) = C₂×C₃
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

C₃×D₃×D₉

Fitting, Sylow	C₃²×C₉ ⋊ C₂²
derived	C₃×C₉ ⋊ C₂²×C₃

	subgroup	G/H
center, hypercenter	C₃	D₃×D₉
commutator, cosocle, hypocenter	C₃×C₉	C₂²×C₃
Frattini	C₃	C₃×D₃²
Fitting	C₃²×C₉	C₂²
socle	C₃³	C₂×D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₃

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 114);