[c#] C# Linq Group By on multiple columns

public class ConsolidatedChild
{
    public string School { get; set; }
    public string Friend { get; set; }
    public string FavoriteColor { get; set; }
    public List<Child> Children { get; set; }
}

public class Child
{
    public string School { get; set; }
    public string Name { get; set; }
    public string Address { get; set; }
    public string Friend { get; set; }
    public string Mother { get; set; }
    public string FavoriteColor { get; set; }
}

Given the two classes above, I would like to use LINQ to create a List from the List, grouped by the School, Friend and FavoriteColor properties. Is this possible with LINQ?

Please ignore the properties, the code has been written just to help with the question.

Given a list:

var list = new List<Child>()
{
    new Child()
        {School = "School1", FavoriteColor = "blue", Friend = "Bob", Name = "John"},
    new Child()
        {School = "School2", FavoriteColor = "blue", Friend = "Bob", Name = "Pete"},
    new Child()
        {School = "School1", FavoriteColor = "blue", Friend = "Bob", Name = "Fred"},
    new Child()
        {School = "School2", FavoriteColor = "blue", Friend = "Fred", Name = "Bob"},
};

The query would look like:

var newList = list
    .GroupBy(x => new {x.School, x.Friend, x.FavoriteColor})
    .Select(y => new ConsolidatedChild()
        {
            FavoriteColor = y.Key.FavoriteColor,
            Friend = y.Key.Friend,
            School = y.Key.School,
            Children = y.ToList()
        }
    );

Test code:

foreach(var item in newList)
{
    Console.WriteLine("School: {0} FavouriteColor: {1} Friend: {2}", item.School,item.FavoriteColor,item.Friend);
    foreach(var child in item.Children)
    {
        Console.WriteLine("\t Name: {0}", child.Name);
    }
}

Result:

School: School1 FavouriteColor: blue Friend: Bob
    Name: John
    Name: Fred
School: School2 FavouriteColor: blue Friend: Bob
    Name: Pete
School: School2 FavouriteColor: blue Friend: Fred
    Name: Bob