order	432
isoclinism	isoclinic class of D₃×A₄
automorphism	Aut(G) = C₂×C₃×D₃×S₄ (order 864) · Inn(G) = D₃×A₄ · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	Dic₃×C₂²⋊C₉
unambiguous semidirect product	C₃⋊(C₄×C₂²⋊C₉)
unambiguous semidirect product	(C₂²×Dic₃)⋊C₉

Splittings

C₂²×C₃ ⋊ C₄×C₉

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₃×A₄
commutator, hypocenter	C₂²×C₃	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂³×C₃²	C₂×C₃
LCS	G ▷ C₂²×C₃
UCS	C₁ ◁ C₂×C₃

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3,4)(6,7,8)(10,11)(12,19,18,14,13,20,17,16,15);(5,8)(6,7)(9,10,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 271);