ThispapercontinuestheworkofD.MacHale,D.Flannery（Proc.R.Ir.Acad.81A,209—215;83A,189—196）andtheauthor（Proc.R.Ir.Acad,90A,57—62;J.SouthwestChinaNormalUniversity15,No.1,21.—28）onthetopicon“FinitegroupswithgivenAutomorphismgroup”.Thefollowingresultisproved:LetGbeafinitegroupwithAutGaSchmidtgroup.ThenGisisomorphictoS3orKlain4-group.,orDsuchthatAutD=InnD.DisaSchmidtgroupoforder2?p.S2（∈Syl2D）isanormalandspecialgroupexoeptasupersperspecialgroupwithoutcommutativegenerators.
