Grouping data in mongo using stored json data

This is the data I have in my mongo db:

{
    "_id": ObjectId("556d1c7716efd4a035d8e473"),
    "products": [
        {
            "gtin": 77770000222313,
            "gpc": 10000068
        },
        {
            "gtin": 77770000222312,
            "gpc": 10000068
        }
    ]
}

      

        
        
        
      

    

How do I do this to get the gpc value and then the array under the gtins headers? Something like:

{
    "gpc":10000068,
    "gtin":[77770000222312,77770000222313]
}