#17338⋊C₃ #11709352

order	768
isoclinism	isoclinic class of #17338⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₂³×C₈

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#17338	C₃
Frattini	C₄²	C₂²⋊A₄
socle	C₂²	C₂²⋊(C₄²⋊C₃)
LCS	G ▷ #17338
UCS	C₁

147 conjugacy classes of subgroups.

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 48

Polycyclic presentation:

3,2^8|b^2=f,c^2=g,f^2=h,g^2=i,b^a=bcfi,c^a=bfhi,d^a=ehi,e^a=deh,f^a=fgh,g^a=fh,h^a=hi,i^a=h,d^b=dh,e^b=ei,d^c=dhi,e^c=eh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083733);