The fact that you have a cabinet model number leads me to believe that it's as Janey said, you may have something quite different and the model number does not apply to the Singer database. Though - someone could have easily put an older machine into a newer case/cabinet in the 30's or 40's - a lot can happen over the years. A picture is going to be the best solution to the mystery.
BTW - The Hexagon was made by Standard, and they were bought out and Singer did end up with them and made some Singer machine using a modified design of the Hexagon machine, they were sold as a variation of the model 128