#17339⋊C₃ #11709353

order	768
isoclinism	isoclinic class of #17339⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

Fitting, Sylow	#17339 ⋊ C₃
derived	C₈² ⋊ C₂²×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₈²	C₂²×C₃
Frattini	C₄²	C₂²×A₄
Fitting	#17339	C₃
socle	C₂²	C₂²×C₄²⋊C₃
LCS	G ▷ C₈²
UCS	C₁

152 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=bcdghi,c^a=bdefgh,d^a=di,e^a=ei,f^a=fgh,g^a=fh,h^a=hi,i^a=h,d^b=dh,e^b=ehi,d^c=di,e^c=eh

maximal subgroup of	#72235382, #72245025, #72245099, …
maximal normal subgroup of	#72245025, #72245099, #72245146

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083734);