How to combine rows in attribute table using ArcGIS for Desktop?

I have an attribute table with three columns "FID" "Shape" and "Class"

All records have the same shape (polygon). Each record has its own FID. I have three classes, "A", "B", or "C". I have twenty records for Class C and would like to combine them into one record.

I have tried doing a dissolve without specific anything in the Dissolve Fields area and the result was a shapefile with all the Classes combined into one, which I don't want. I also tried doing a dissolve while specifying Class in the Dissolve Fields area. This resulted in a shapefile with the same twenty records for Class C.

How do I get those twenty polygons into one record?