#7852⋊C₃ #11709113

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

Aliases

Fitting, Sylow	#7852 ⋊ C₃
derived	#1273 ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₂	#1455⋊C₃
commutator, cosocle, hypocenter	#1273	C₂×C₃
Frattini	C₂×C₄²	C₂×A₄
Fitting	#7852	C₃
socle	C₂³	C₂×C₄²⋊C₃
LCS	G ▷ #1273
UCS	C₁ ◁ C₂

162 conjugacy classes of subgroups.

μ_t(G) = 24

Polycyclic presentation:

3,2^8|b^2=f,c^2=g,f^2=h,g^2=i,b^a=cdg,c^a=bcegh,e^a=ehi,f^a=g,g^a=efgi,h^a=i,i^a=hi,c^b=ce,d^b=dh,d^c=di

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083494);