#73203⋊C₃ #11920756

order	1152
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

unambiguous semidirect product	#73203⋊C₃
unambiguous semidirect product	#73290⋊C₃
unambiguous semidirect product	#73291⋊C₃

	subgroup	G/H
center, hypercenter	C₂	#5450⋊C₃
commutator, Fitting, cosocle, hypocenter	#2811	C₃²
Frattini, socle	C₂³	A₄²
LCS	G ▷ #2811
UCS	C₁ ◁ C₂

112 conjugacy classes of subgroups.

μ_t(G) = 24

Polycyclic presentation:

3^2,2^7|c^2=g,d^2=g,e^2=g,f^2=g,e^a=f,f^a=ef,h^a=i,i^a=hi,c^b=d,d^b=cd,h^b=i,i^b=hi,d^c=dg,e^c=ei,f^c=fhi,e^d=ehi,f^d=fh,f^e=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154767);