SL(2,ℤ/9) #10620122

order	648
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₁

Aliases

special linear	SL(2,ℤ/9)
symplectic	Sp(2,ℤ/9)
unambiguous semidirect product	#6296⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	#1113⋊C₃
commutator, cosocle, hypocenter	#6296	C₃
Fitting, socle	C₂×C₃³	A₄
LCS	G ▷ #6296
UCS	C₁ ◁ C₂

48 conjugacy classes of subgroups.

μ_t(G) = 24

Polycyclic presentation:

3,2^3,3^3|b^2=d,c^2=d,b^a=c,c^a=bc,e^a=f,f^a=g,g^a=e,c^b=cd,e^b=e^2,g^b=g^2,e^c=e^2,f^c=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 641);