#8804⋊C₃ #11709135

order	768
isoclinism	isoclinic class of #8804⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Fitting, Sylow	#8804 ⋊ C₃
derived	C₈² ⋊ C₃×C₄

56 conjugacy classes of subgroups.

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

Polycyclic presentation:

3,2^8|b^2=g,c^2=efh,d^2=e,e^2=hi,f^2=h,b^a=bfhi,c^a=cdefi,d^a=cef,e^a=efhi,f^a=ehi,g^a=ghi,h^a=hi,i^a=h,c^b=ce,d^b=df,e^b=eh,f^b=fi,g^c=gi,g^d=ghi

maximal subgroup of	#72245048, #72245099, #72245104
maximal normal subgroup of	#72245048, #72245099, #72245104

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083516);