#4169⋊C₃ #92260

order	486
isoclinism	isoclinic class of #4169⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃²

Aliases

Fitting, Sylow	#6891 ⋊ C₂
derived	C₃×C₉ ⋊ C₂×C₃²

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₉	C₂×C₃²
Frattini, socle	C₃²	C₃²×D₃
Fitting	#6891	C₂
LCS	G ▷ C₃×C₉
UCS	C₁

129 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 27

A minimal faithful permutation representation — 2 generators on 18 points:

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

Polycyclic presentation:

2,3^5|d^3=f^2,d^a=d^2f,e^a=e^2,f^a=f^2,d^b=de,d^c=df

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 105);