is it "he is chair of the firm's business law and transactions practice group"

or

"he is chair of the firm's business law and transactions' practice group"

?

(second one has the apostrophe after the "s" at the end of "transactions")

No.

Consider "business law and transactions practice group" as a single entity.

And if you consider "business law" and "transactions practice group" as separate entities, then group should be groups.


Even so, it sounds wordy. Delete "practice." Brevity is the soul of wit...and good writing.