C₂³×C₃×D₉ #88909

order	432
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×C₃×D₉

	subgroup	G/H
center, hypercenter	C₂³×C₃	D₉
commutator, cosocle, hypocenter	C₉	C₂⁴×C₃
Frattini	C₃	C₂³×C₃×D₃
Fitting	C₂³×C₃×C₉	C₂
socle	C₂³×C₃²	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂³×C₃

434 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 4 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 556);