Group based on a field in mongodb

Assume I have database structure as;

[
    {name: "alex" , surname: "brown" , school: "washington"},
    {name: "felix" , surname: "yellow" , school: "georgia"},
    {name: "felix" , surname: "yellow" , school: "georgia"},
    {name: "tommy" , surname: "brown" , school: "davis"},
    {name: "tommy" , surname: "brown" , school: "davis"},
    {name: "tommy" , surname: "brown" , school: "davis"},
    {name: "tommy" , surname: "brown" , school: "davis"}
]

What I want to do is group them by their school info. So expected result is;

{
    school: davis
    students: [
        {name: "tommy" , surname: "brown"},
        {name: "tommy" , surname: "brown"},
        {name: "tommy" , surname: "brown"},
        {name: "tommy" , surname: "brown"},
    ]

},
{
    school: georgia
    students: [
        {name: "felix" , surname: "yellow"}
    ]

},
{
    school: washington
    students: [
        {name: "alex" , surname: "brown"}
    ]

}

To be able to this I think about using $group as;

db.collection.aggregate([
    {$group: {"_id" : "$school", name : "$name" , surname: "$surname"}}
])

But I think, I misunderstood the $group. So how can I wrote this query?

via mmu36478