C₃³×D₉ #92375

order	486
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₃³

Aliases

C₃³×D₉

Fitting, Sylow	C₃³×C₉ ⋊ C₂
derived	C₉ ⋊ C₂×C₃³

	subgroup	G/H
center, hypercenter	C₃³	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₃³
Frattini	C₃	C₃³×D₃
Fitting	C₃³×C₉	C₂
socle	C₃⁴	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₃³

324 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 162

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 220);