[Python] How to get rows with unique value in a specific column in pandas

Following is my data frame.

id name class
--------------------------
0 Nick a
1 Jane b
2 Jacon a
3 Jack b
4 Cooze a
--------------------------
5 Nick b
6 Jane b
7 Jacon c
8 Jack a
9 Cooze a


I need to get all names that have unique value in class column, i.e.:

id name class count
-----------------------------------
0 Jane b 2
1 Cooze a 2



How can I do this in pandas? Thanks in advance.

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