PARVANEH ZOLFAGHARI - Department of Pure Mathematics, Farhangian University, Mashhad, Iran.

In the present paper, we investigate one of the non-abelian groups of order 18 with representation (C3 C3) / C2. At rst we describe all subgroups and automorphisms of this group.Then we use this result for the main goal where is the determiningall ultra-groups of order 3 arising from this group up to isomor-phism. Finally we indicate what of this ultra-groups is a group.

Semidirect product, automorphism, transversal,ultra-group.2000 Mathematics Subject Classi cation: 20D45, 16B50, 20A05