It is not a license. Period. Not class 2, not class 3, not class 87. IT IS NOT A LICENSE, IT IS A TAX.
Dealers that have a license to sell NFA items have a Type 3
Special Occupation Tax Federal Firearms License. That's probably where "class 3" came from - from someone misunderstanding or misremembering "Type 3 SOT". But the guy that buys the machinegun, or the sawed off shotgun, or the silencer does not have a license. There is no license. It is a one-time tax.
If you are in the business of making silencers, you get a Type 2 SOT FFL. Type 3 is for selling. Type 2 is for making.
If you are making one silencer, for your own use, you fill out and send in an NFA Form 1. This is an application to make and register a firearm. You don't need a Type 2 SOT. You are not in the business of making silencers. You fill out and send in a Form 1. http://www.titleii.com/pdf/010205-Form1.pdf
If you are buying the silencer from someone else, you fill out and send in an NFA Form 4. This is an application to transfer a firearm. Again, you don't need a Type 2 SOT. You are not making them to sell. You are buying one from someone. All you need is to fill out a Form 4. http://www.atfmachinegun.com/form4.pdf