C₃⋊(A₄⋊AGL(1,𝔽₅)) #10624319

order	720
isoclinism	isoclinic class of C₃⋊(A₄⋊AGL(1,𝔽₅))
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

unambiguous semidirect product	C₃⋊(A₄⋊AGL(1,𝔽₅))
unambiguous semidirect product	A₄⋊ΓL(1,𝔽₁₆)

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₃×C₅×A₄	C₄
Fitting, socle	C₂²×C₃×C₅	Dic₃
prime radical, cosocle	C₃×D₅×A₄	C₂
LCS	G ▷ C₃×C₅×A₄
UCS	C₁

100 conjugacy classes of subgroups.

μ_t(G) = 60

Polycyclic presentation:

2^2,3^2,5,2^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^3,f^a=g,g^a=f,e^b=e^4,f^c=fg,g^c=f

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 788);