Hi Electric Chicken, welcome to the forum. Does the the solenoid you are asking about look like the one, on the right, in the photograph? If it does, it is a 12 volt solenoid with a latching relay built in to the top, second photo.
If your generator has auto stop/start (Startomatic) Then you will also have the second solenoid shown, on the left, in the photo. This one runs 240 volt or 110 volt depending on your continent.
Bob