#7014⋊C₃ #11709092

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

Aliases

	subgroup	G/H
center, hypercenter	C₄	C₈²⋊C₃
commutator, Fitting, cosocle, hypocenter	#7014	C₃
Frattini	C₄³	A₄
socle	C₂³	#95⋊C₃
LCS	G ▷ #7014
UCS	C₁ ◁ C₄

73 conjugacy classes of subgroups.

μ_t(G) = 48

Polycyclic presentation:

3,2^8|b^2=e,c^2=f,d^2=g,e^2=h,f^2=i,b^a=bcdfh,c^a=bdefg,e^a=defi,f^a=ehi,h^a=ghi,i^a=h,c^b=cd,f^b=fg,e^c=eg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083473);