C₃⋊(C₉⋊AGL(1,𝔽₅)) #10587379

order	540
isoclinism	isoclinic class of C₃⋊(C₉⋊AGL(1,𝔽₅))
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product	C₃⋊(C₉⋊AGL(1,𝔽₅))
unambiguous semidirect product	C₉⋊ΓL(1,𝔽₁₆)

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃×C₅×C₉	C₄
Frattini	C₃	C₃⋊ΓL(1,𝔽₁₆)
socle	C₃²×C₅	Dic₃
prime radical	C₃²×D₅	D₃
cosocle	C₃×C₉×D₅	C₂
LCS	G ▷ C₃×C₅×C₉
UCS	C₁

60 conjugacy classes of subgroups.

μ_t(G) = 135

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(540, 39);