Я не уверен, но работает ли следующий код?
var groups = from p in dc.Pool
join pm in dc.PoolMembers on p.ID equals pm.PoolID
group p by p.Group into grp
select grp.Select(g=> g.ID);
EDIT
var groups = from p in dc.Pool
join pm in dc.PoolMembers on p.ID equals pm.PoolID
group p by p.Group into grp
select grp.Select(g=> new{
Id = g.Id,
GroupName = grp.Key.Name,
Contribution = pm.Contribution,
GameName = p.GameName, });