I have to find out the association between two variables, one of the variables has a three unbalanced group, and I choose the chi-square test, but unfortunately the number in each group was stopped me, what about the Fisher exact test?
Yes, Fisher's exact test is okay for tables with small cell counts.
Technically, it has the assumption that the total observation in each level is known for at least one variable. That is, you know ahead of time that you are starting with 10 male and 10 female students. This assumption is often ignored.
Make sure that the software you are using with perform the exact test on a 3 x X table. There may be software that only allows a 2 x 2 table.
It is not the observed values which are important for the validity of the chi-squared technique, but the expected values. A 3x2 design is still valid provided that only one cell at most has expected count between 1 and 5, and all the rest have expected count >5.