You could store everything in a single class and persist it to a single table row if you would always have only one external authentication option. In this case breaking that class down into 2 would not make much difference.
However, a single external authentication option is usually not the case. Even if you think at the moment that you only ever need to authenticate with Facebook you will usually later find the need to support other auth options. Thus it usually makes sense to design for multiple authentication options.
In your case you already know that there will be multiple authentication providers, so it makes sense to store them in a separate table and have a separate persistent entity class for that. You can still have authentication code in one place and easily extend functionality later by adding more auth providers.
Having said that if you would use MongoDB for example which lets you embed documents (rows) quite easily you could debate whether or not to store user and auth details as a single entity/row/document in DB. Even in this case both options would be of an equal preference in my opinion. But since you store data in relational DB - MySQL you should definitely normalize it to reasonable extent, and splitting it into 2 tables is the best option.