A₄×C₃⋊Dic₃ #88980

order	432
isoclinism	isoclinic class of A₄×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	A₄×C₃⋊Dic₃
unambiguous semidirect product	C₃⋊(Dic₃×A₄)

C₂²×C₃² ⋊ C₃×C₄

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

146 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 3 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 627);