C₂×A₄×D₉ #88893

order	432
isoclinism	isoclinic class of A₄×D₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

C₂×A₄×D₉

Fitting	C₂³×C₉ ⋊ C₂×C₃
derived	C₂²×C₉ ⋊ C₂²×C₃

	subgroup	G/H
center, hypercenter	C₂	A₄×D₉
commutator, cosocle, hypocenter	C₂²×C₉	C₂²×C₃
Frattini	C₃	C₂×D₃×A₄
Fitting	C₂³×C₉	C₂×C₃
socle	C₂³×C₃	C₃×D₃
LCS	G ▷ C₂²×C₉
UCS	C₁ ◁ C₂

125 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 540);