Yes. This is easily obtained by selecting Tables ► Summary and choosing your by-group and the median statistic for the variable (column) of interest.
Note: you can also get these by first right-clicking on the by-group column, then selecting New Formula Column ► Group By, and then right-clicking on the column to calculate the median statistic on and selecting New Formula Column ► Aggregate ► Median.
[Previously JMP Note 35808]