C₃²×C₃⋊D₉ #92382

order	486
isoclinism	isoclinic class of C₃⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃²

Aliases

direct product	C₃²×C₃⋊D₉
unambiguous semidirect product	C₃⋊(C₃²×D₉)

Fitting, Sylow	C₃³×C₉ ⋊ C₂
derived	C₃×C₉ ⋊ C₂×C₃²

	subgroup	G/H
center, hypercenter	C₃²	C₃⋊D₉
commutator, cosocle, hypocenter	C₃×C₉	C₂×C₃²
Frattini	C₃	C₃²×C₃⋊D₃
Fitting	C₃³×C₉	C₂
socle	C₃⁴	D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₃²

288 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 54

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 227);