C₂³×C₃⋊D₉ #88913

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

Aliases

C₂³×C₃⋊D₉

Fitting	C₂³×C₃×C₉ ⋊ C₂
derived, Sylow	C₃×C₉ ⋊ C₂⁴

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

670 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 216

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 560);