Catalyzes the synthesis of alpha-glucan from sucrose. Catalyzes, in addition, sucrose hydrolysis, maltose and maltotriose synthesis by successive transfers of the glucosyl moiety of sucrose onto the released glucose, and finally turanose and trehalulose synthesis, these two sucrose isomers being obtained by glucosyl transfer onto fructose (By similarity). [(1->4)-alpha-D-glucosyl](n) + sucrose = [(1->4)-alpha-D-glucosyl](n+1) + D-fructose Monomer. Belongs to the glycosyl hydrolase 13 family.