Women working for big global companies say they aren’t getting the international assignments they need for career advancement because employers think they’re less mobile than men, according to a new PwC survey.

More than 70% of millennial women in the study said they want to work outside their home country. Yet only 20% of international postings are filled by female workers, according to a poll of 3,900 male and female professionals and companies with headquarters in 23 countries. The study, released on March 3 by the consulting firm, defined millennials as people born between 1980 and 1995.

“Too many overseas assignments are still today generated by an old-boy network” that assumes men are more willing to relocate, said Peter Clarke, PwC’s global mobility services leader. Companies “need a fact-based understanding of people’s willingness to take an assignment.”

Women make up just 4.4% of S&P 500 chief executive officers and hold about 20% of board seats, even though they now represent almost half of college graduates and entry-level employees at large firms.

Six in 10 of the companies surveyed said international assignments are critical to potential managers gaining experience, connecting with more senior role models and getting promoted, according to the survey.

Only about 20% of the companies said they align diversity goals with programs to help executives move around the world, Clarke said.

“CEOs are worried about the talent pipeline,” he said. “But right in front of them is this tremendous growth experience of global mobility that can transform the career of women, particularly early on. It’s so underutilized.”