order	432
isoclinism	isoclinic class of D₃×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₃×C₄

Aliases

Splittings

C₃³ ⋊ C₄²

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×C₃⋊D₃
commutator, hypocenter	C₃³	C₄²
Fitting, socle, prime radical, cosocle	C₂²×C₃³	C₂²
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂²

244 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 448);