C₃²×AGL(1,ℤ/9) #92379

order	486
isoclinism	isoclinic class of AGL(1,ℤ/9)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₃³

Aliases

direct product	C₃²×AGL(1,ℤ/9)
unambiguous semidirect product	D₉⋊C₃³
unambiguous semidirect product	(C₃×D₉)⋊C₃²

Fitting, Sylow	C₃²×3₋¹⁺² ⋊ C₂
derived	C₉ ⋊ C₂×C₃³

	subgroup	G/H
center, hypercenter	C₃²	AGL(1,ℤ/9)
commutator, cosocle, hypocenter	C₉	C₂×C₃³
Frattini	C₃	C₃³×D₃
Fitting	C₃²×3₋¹⁺²	C₂
socle	C₃³	C₃×D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₃²

270 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 224);