[Python] pandas find max value in groupby and apply function

I've got a dataframe df like the following:

H,Nu,City
1,15,Madrid
3,15,Madrid
3,1600,Madrid
5,17615,Madrid
2,55,Dublin
4,5706,Dublin
2,68,Dublin
1,68,Dublin


I would like to find the max value / city of the Nu column. Then find the corresponding values of H and add a new column df['H2'] = df['H']/max(H/city). So far I tried:

d = df.groupby('City').apply(lambda t: t[t.Nu==t.Nu.max()])


which correctly returns:

H Nu City
City
Dublin 5 4 5706 Dublin
Madrid 3 5 17615 Madrid


How may I set my maximum H value (4 for Dublin and 5 for Madrid) as a constant / city in order to apply the function all over the DataFrame? The expected df would appear as:

H,Nu,City,H2
1,15,Madrid,0.2
3,15,Madrid,0.6
3,1600,Madrid,0.6
5,17615,Madrid,1.0
2,55,Dublin,0.5
4,5706,Dublin,1.0
2,68,Dublin,0.5
1,68,Dublin,0.25

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