Heh... you've discovered a simple method of code obfuscation and job security. 
As you posted, the partition represented by "Column19" contains 28.2 million rows. Let me ask you... if it were a single table instead of a partition of a larger table, what indexes would you have in play to join to the table? For example, looking at the join that uses Column29, do you have an index on Column29?
Also, when working with such a relatively large number of rows, it's very likely that some "pre-aggregation" of the larger tables into a Temp table and then joining on that Temp table instead of the larger table would serve you very well. Still, you are talking about essentially doing a full scan of a 28.2 million row table and unless there is some extraordinary properly indexed criteria available, it's going to take some time with a little "Divide'n'Conquer" and "pre-aggeegation", this could do quite well.
I also suspect that the following code should actually be in the WHERE clause..
AND Object2.Column28 = 'Y'
Of course, I might as well be talking out of my hat because you've not provided the "Actual Execution Plan" as an .sqlplan attachment, I know virtually nothing about your tables or indexes, and I don't even know the datatype of your partitioning column nor whether or not the related clustered index has been made unique by inclusion of the PK or what. I'll also tell you that GROUP BY is capable of hiding a wealth of sins in the form of accidental many-to-many joins but, again, no one on this side of the conversation can tell because there's nothing we can see that would be a reasonable indication. Heh... for that matter, it may be that everything is perfect and this is the best that can be done (although I seriously doubt that) but, again, can't tell from here.
To help you with this and future queries, I suggest downloading Grant Fritchey's ebook on how to use and interpret Execution Plans. There's also a wealth of other free book downloads at the following URL and some of them (like Grant's book) are written by best-of-class authors. Here's the link...
http://www.sqlservercentral.com/Books/