How should I implement items that are normalized in the Database, in Object Oriented Design?

First of all, the most common practice is to use an ORM (object-relational mapping) tool. These are available to most any modern OO language, and they take care of generating the classes needed to interact with the database, managing retrieval and updating, and managing connection lifetime.

Yes, you need a Group class. It looks like it has a 1:many relationship with Inventory, where Group is the parent. Group will have a reference to a collection or set of Inventory.

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