Is education a part of the U.S. exports component of GDP? I was searching for this but could not find an answer.

My question is whether education of the U.S. universities provided to foreign students counts in exports component on GDP.

And if so, can we call the U.S. "the largest education exporter in the world"?
From Unesco's website:

Top 10 destination countries:

United States (18% of total mobile students)
United Kingdom (11%)
France (7%)
Australia (6%)
Germany (5%)
Russian Federation (4%)
Japan (4%)
Canada (3%)
China (2%)
Italy (2%)


This is about headcount, not value-of-services. For 2nd-in-rank UK to nevertheless generate more income in terms of value, it should be the case that average fees/cost of living in UK is ~$64$% higher than in the USA. Otherwise, USA will be also the biggest exporter of education.  

This, without taking into account the size of each country's economy.

The link mentions that Unesco's statistical data base provides further statistics.