python pandas groupby() result

I have the following python pandas data frame:

df = pd.DataFrame( {
   'A': [1,1,1,1,2,2,2,3,3,4,4,4],
   'B': [5,5,6,7,5,6,6,7,7,6,7,7],
   'C': [1,1,1,1,1,1,1,1,1,1,1,1]
    } );

df
    A  B  C
0   1  5  1
1   1  5  1
2   1  6  1
3   1  7  1
4   2  5  1
5   2  6  1
6   2  6  1
7   3  7  1
8   3  7  1
9   4  6  1
10  4  7  1
11  4  7  1

I would like to have another column storing a value of a sum over C values for fixed (both) A and B. That is, something like:

    A  B  C  D
0   1  5  1  2
1   1  5  1  2
2   1  6  1  1
3   1  7  1  1
4   2  5  1  1
5   2  6  1  2
6   2  6  1  2
7   3  7  1  2
8   3  7  1  2
9   4  6  1  1
10  4  7  1  2
11  4  7  1  2

I have tried with pandas groupby and it kind of works:

res = {}
for a, group_by_A in df.groupby('A'):
    group_by_B = group_by_A.groupby('B', as_index = False)
    res[a] = group_by_B['C'].sum()

but I don't know how to 'get' the results from res into df in the orderly fashion. Would be very happy with any advice on this. Thank you.