C₂³×(C₃⋊D₃)⋊C₃ #88911

order	432
isoclinism	isoclinic class of (C₃⋊D₃)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

	subgroup	G/H
center, hypercenter	C₂³	(C₃⋊D₃)⋊C₃
commutator, cosocle, hypocenter	C₃²	C₂⁴×C₃
Frattini	C₃	C₂³×C₃×D₃
Fitting	C₂³×H(3,𝔽₃)	C₂
socle	C₂³×C₃	C₃×D₃
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂³

501 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 4 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 558);