C₃²×C₄²⋊C₃ #88816

order	432
isoclinism	isoclinic class of C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃³×C₄

Aliases

direct product	C₃²×C₄²⋊C₃
unambiguous semidirect product	C₄²⋊C₃³
unambiguous semidirect product	(C₃×C₄²)⋊C₃²

Fitting	C₃²×C₄² ⋊ C₃
derived, Sylow	C₄² ⋊ C₃³

	subgroup	G/H
center, hypercenter	C₃²	C₄²⋊C₃
commutator, cosocle, hypocenter	C₄²	C₃³
Frattini	C₂²	C₃²×A₄
Fitting	C₃²×C₄²	C₃
socle	C₂²×C₃²	A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₃²

108 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 463);