python 3.x – Combining two pandas dataframes/tables of unequal lengths

I have two dataframes of different lengths.
df1: df2:

  Column1  Column2             ColumnA ColumnG ColumnSG
0    ab1       bc1                ab1      A      AA
1    ab2       ab5                bc1      B      BB   
2    ab3       bc4                ab3      C      CC
3    ab4       ab5                ab1      D      DD
4    ab5       ab1                ab5      E      EE 
                                  bc4      F      FF    
                                  ab2      G      GG
                                  ab4      H      HH

I would like an output that looks something like this:

df1:

OUTPUT

What I tried so far?

for row in df1, df2:
   if df1[Column1] == df2[ColumnA]:
      df1[ColumnG1] = df2[ColumnG]
      df1[ColumnSG1] = df2[ColumnSG]

But, this gave me an error saying,
ValueError: Can only compare identically-labeled Series objects

How can I solve this?