The sweet shop named "Olympiad" sells boxes containing either 6, 9, or 20 chocolates. Groups of students from a nearby school collect money to buy chocolates so that each student receives one. They buy a box and distribute the chocolates accordingly. For example, students can form groups of 15 (using one box of 6 and one box of 9 chocolates) or 38 (using two boxes of 9 and one box of 20 chocolates).

The shopkeeper has assured the students that he can fulfill the chocolate needs of any group. If a new box needs to be opened for any group size that doesn't fit perfectly (such as groups of 4, 7, or 10 students), then the shopkeeper will give all the chocolates for free to that group.

Is it possible to construct the largest group that receives free chocolates, and if so, how many students are there in this group?

Let's think step by step and output the final answer within \boxed{}.
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