Creating a database objects for M by M by M relation.

Please ignore the previous post, It was posted by mistake.
Hi
I want to persist the following relation in to the database.
Student {
studentId
Name
Team {
teamId
teamName
Group {
groupId
groupName
I want to put a student in to a group and a team.
The simpler situation where a student is put in to a group is done by creating a join table like this.
StudentTable
GroupTable
GroupStudentTable
where GroupStudentTable would contain
GroupId and StudentId columns
Now how do I add a student into a team.
The intended outcome I want in my user interface is as follows
GroupName StudentName Team
GroupAA StudentA Soccer
GroupAA StudentB BasketBall
GroupAA StudentC Hockey
GroupBB StudentA BasketBall
GroupBB StudentB Swiming
GroupBB StudentC Basketball.
GroupBB StudentD Basketball.
GroupBB StudentE Basketball.
Basically what I want to show is that in GroupAA StudentA plays soccer and in GroupB he plays BasketBall.
Please not for a given group a student can play only one thing.
Thanks

Yep,
For a given group a student can belong to one team. That is a contraint within my design.
The scenario I have described is an exact representation of the intended purpose of use.
The purpose is to creata a group of objects (In this case students). Only complication is that I need to associate another object (in this case team) in as well. The exact situation is grouping of market shocks in foreign exchange calculations.
As an example I have shock A = 5% shock of current exchange rate, shock B= 3% shock, shock C= 9% etc shock in foreign exchange (In here we do not specify whether it is USD/AUD or JPY/AUD to keep it generic).
Now I would like create a Group MyShocks which contains shocks A and C. These shocks does not contain which country it relates to, but I needs it specified when some one adds these shocks in to the MyShockGroup. Therefore my description earlier try to represent:
Student = MarketShock
Team = Country
StudentGroup = MarketShockGroup
My original thought was to create GroupStudentTeam table as well. But is this the standard practice? I have seen join tables that join two tables, but haven't see join tables that join three things together.

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