#7744⋊C₃ #11709103

order	768
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂²

Aliases

Fitting, Sylow	#7744 ⋊ C₃
derived	#2810 ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₂	#1658⋊C₃
commutator, cosocle, hypocenter	#2810	C₂×C₃
Frattini	C₂×C₄²	C₂×A₄
Fitting	#7744	C₃
socle	C₂³	#120⋊C₃
LCS	G ▷ #2810
UCS	C₁ ◁ C₂

108 conjugacy classes of subgroups.

μ_t(G) = 24

Polycyclic presentation:

3,2^8|c^2=gi,d^2=g,e^2=g,f^2=i,b^a=beg,c^a=dgi,d^a=cd,e^a=fh,f^a=efg,g^a=i,h^a=hi,i^a=gi,c^b=ce,d^b=df,e^b=eg,f^b=fi,e^c=eg,f^c=fh,e^d=eh,f^d=fi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083484);