Fructosyltransferase that catalyzes the polymerization of the fructose moiety of sucrose to produce inulin polymer and inulin oligosaccharides such as 1-kestose and nystose. [(2->1)-beta-D-fructosyl](n) + sucrose = [(2->1)-beta-D-fructosyl](n+1) + D-glucose Optimum pH is 7. More than 85% of the activity is retained in the pH range 4.5-6.0. Activity decreases sharply at pH 7.5. Optimum temperature is 55 degrees Celsius. Activity drastically decreases at 60 degrees Celsius. Belongs to the glycosyl hydrolase 68 family.