C₃⋊(A₄⋊C₁₆) #10590113

order	576
isoclinism	isoclinic class of C₃⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₂×C₃

Aliases

unambiguous semidirect product	C₃⋊(A₄⋊C₁₆)
unambiguous semidirect product	A₄⋊(C₃⋊C₁₆)

C₃×A₄ ⋊ C₁₆

	subgroup	G/H
center, Frattini, hypercenter	C₈	C₃⋊S₄
commutator, hypocenter	C₃×A₄	C₁₆
Fitting	C₂²×C₃×C₈	D₃
socle	C₂³×C₃	C₃⋊C₈
prime radical	C₂×C₃×A₄	C₈
cosocle	C₃×C₈×A₄	C₂
LCS	G ▷ C₃×A₄
UCS	C₁ ◁ C₈

86 conjugacy classes of subgroups.

μ_t(G) = 144

Polycyclic presentation:

2^4,3^2,2^2|a^2=b,b^2=c,c^2=d,e^a=e^2,f^a=f^2,g^a=h,h^a=g,g^e=h,h^e=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 1995);