Pandas: Groupby to create table with count and count values

My objective is simple but not sure if it's possible. Reproducible example:

Can you go from this:

raw_data = {'score': [1, 3, 4, 4, 1, 2, 2, 4, 4, 2],
        'player': ['Miller', 'Jacobson', 'Ali', 'George', 'Cooze', 'Wilkinson', 'Lewis', 'Lewis', 'Lewis', 'Jacobson']}
df = pd.DataFrame(raw_data, columns = ['score', 'player'])
df

    score   player
0   1       Miller
1   3       Jacobson
2   4       Ali
3   4       George
4   1       Cooze
5   2       Wilkinson
6   2       Lewis
7   4       Lewis
8   4       Lewis
9   2       Jacobson

To this:

        score    col_1       col_2       col_3       col_4     
score   
1       2        Miller      Cooze       n/a         n/a
2       3        Wilkinson   Lewis       Jacobson    n/a
3       1        Jacobson    n/a         n/a         n/a
4       4        Ali         George      Lewis       Lewis

Via a groupby?

I can get this far df.groupby(['score']).agg({'score': np.size}) but can't work out how to create the new columns with the column values.