Clustering algorithms for high dimensional binary sparse data
How many ethnic groups did you identify?

If I had to visualize your problem, I'd determine the key influencers for each of the ethnic groups in a Naive Bayes like approach.
These genes (gene combinations?!) (including their values) may strongly correlate to some ethnic group, while not (or inverse) correlate to another. 

Place them on top of a pyramid graph. Place bars to the left and right for the correlation values.