#8130⋊C₃ #11709119

order	768
isoclinism	isoclinic class of #8130⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₄

Aliases

Fitting, Sylow	#8130 ⋊ C₃
derived	#1309 ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#1309	C₂×C₃
Frattini	C₂×C₄²	C₂×A₄
Fitting	#8130	C₃
socle	C₂²	C₂×#95⋊C₃
LCS	G ▷ #1309
UCS	C₁

115 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,d^2=hi,f^2=h,g^2=i,b^a=cdefgh,c^a=bcde,d^a=degi,e^a=eh,f^a=ghi,g^a=efghi,h^a=i,i^a=hi,c^b=ce,d^b=dh,e^b=eh,g^b=gi,e^c=ei,f^c=fh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083500);