C₂×A₄×C₃⋊D₃ #89117

order	432
isoclinism	isoclinic class of A₄×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²×C₃

Aliases

direct product	C₂×A₄×C₃⋊D₃
unambiguous semidirect product	(C₂×C₃)⋊(D₃×A₄)

Fitting, socle	C₂³×C₃² ⋊ C₂×C₃
derived	C₂²×C₃² ⋊ C₂²×C₃

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

266 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 3 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 764);