#10358⋊C₃ #11709148

order	768
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

Fitting, Sylow	#10358 ⋊ C₃
derived	#2844 ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₂	#1655⋊C₃
commutator, cosocle, hypocenter	#2844	C₂×C₃
Frattini	C₂×C₄²	C₂×A₄
Fitting	#10358	C₃
socle	C₂³	#120⋊C₃
LCS	G ▷ #2844
UCS	C₁ ◁ C₂

119 conjugacy classes of subgroups.

μ_t(G) = 48

Polycyclic presentation:

3,2^8|b^2=e,c^2=e,f^2=h,g^2=hi,b^a=bci,c^a=bhi,d^a=dghi,f^a=fghi,g^a=fi,h^a=i,i^a=hi,c^b=ce,d^b=df,f^b=fh,g^b=gi,d^c=dg,f^c=fi,g^c=ghi,f^d=fh,g^d=ghi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083529);