order	432
isoclinism	isoclinic class of D₃×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	D₃×C₃⋊(C₃⋊C₈)
unambiguous semidirect product	(C₃×D₃)⋊(C₃⋊C₈)

Splittings

C₃³ ⋊ C₂×C₈

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×C₃⋊D₃
commutator, hypocenter	C₃³	C₂×C₈
Fitting, cosocle	C₃³×C₄	C₂²
socle	C₂×C₃³	C₂×C₄
prime radical	C₂×C₃²×D₃	C₄
LCS	G ▷ C₃³
UCS	C₁ ◁ C₄

164 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 430);