This is basically the same problem discussed in here.
Surprisingly? when you define class, Python interpreter execute class field. And then if you create a new instance of the class, class field is not executed. So class field is executed once only when you define class. Like:
class someClass:
    someVar = 0        #<---This class field is executed once
    def __init__(self):
        pass
OK. Now you defined class. Next you create new instance of the class. Like:
instance1 = someClass()
instance2 = someClass()
This will create new memory and copy data from someClass.
Now instance1 and instance2 do not share memory space. They have own independent memory space. So instance1.someVar and instance2.someVar has different memory space. But 0 in instance1.someVar and 0 in instance2.someVar are completely same object(0 is on same memory space). You can ensure it doing like:
print id(instance1.someVar)==id(instance2.someVar)
So you can find 0 is completely same object.
This is not the only case when someClass.someVar = 0. Same thing will happen when you use [] replacement of 0.
Back to your code. You can simply occur your problem doing like this:
class test:
    group = []
    def __init__(self,name):
        self.name = str(name)
test0 = test(0)
test1 = test(1)
test0.group.append(100)
print test0.group
print test1.group
#[100]
#[100]
#will be printed
This is because test0.group and test1.group point same object. Like:
+-----------+
|test0.group|------+
+-----------+      |
                   v
               +-------+
               |  []   |
               +-------+
                   ^
+-----------+      |
|test1.group|------+
+-----------+
When you executed test0.group.append(100), it becomes like:
+-----------+
|test0.group|------+
+-----------+      |
                   v
               +-------+
               | [100] |
               +-------+
                   ^
+-----------+      |
|test1.group|------+
+-----------+
Also you can set another object. Like:
test1.group = "123"
Then test1.group becomes like:
+-----------+
|test0.group|------+
+-----------+      |
                   v
               +-------+
               | [100] |
               +-------+
+-----------+       +-----+
|test1.group|------>|"123"|
+-----------+       +-----+
Sorry for my bad English. I hope it helps. :)