#8803⋊C₃ #11709134

order	768
isoclinism	isoclinic class of #8803⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Fitting, Sylow	#8803 ⋊ 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=ef,d^2=e,e^2=hi,f^2=h,b^a=bh,c^a=def,d^a=cdhi,e^a=fhi,f^a=ef,h^a=i,i^a=hi,c^b=ce,d^b=df,e^b=eh,f^b=fi,g^c=gi,g^d=ghi

maximal subgroup of	#72245040, #72245099, #72245104
maximal normal subgroup of	#72245040, #72245099, #72245104

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083515);