Hey, Corporate America. It appears that many Millennials -- that tsunami of future workers -- don't really want to work for you. At least not the newest college graduates.

Only 15% of the class of 2015 said they would "prefer" to work for large corporations, according to a new survey by management consulting firm Accenture.

Medium-sized businesses got the most love (35%), while start-ups and government agencies were the expressed preference for just 10% of respondents.

Fun seems to be a deciding factor.

A full 60% of 2015 grads -- and 69% of 2013 and 2014 grads, who were also surveyed -- said they'd rather work for a company that has a "positive social atmosphere" even if it means lower pay.

Of course, they may think differently after a few years of working for the (low-paying) Man and after Mom and Dad stop subsidizing them.

More than 70% of all respondents said their parents are paying the majority of their rent and living expenses or at least half.

Related: Most twenty-somethings are actually saving for retirement

For corporations trying to lure Millennials, offering them a challenging project may reel them in.

About half of the 2013 and 2014 graduates surveyed consider themselves "underemployed" or in a job that doesn't really require a college degree.

And what they want most in a job, after salary and benefits, is interesting, challenging work (39%), flexible work hours (37%) and a chance to advance quickly up the ranks (34%).

Related: What workers around the world want: More flexibility

Reaching young Millennials where they live will be key to recruiting them. And where they live (at least until something better comes along) is their smart phone. Among 2015 grads, 64% said they will use or have used mobile apps in their job search.

And this just in: As of the first quarter of this year, Millennials now account for the largest share of U.S. workers, according to the Pew Research Center, which analyzed Census data.

More than half of those who took the Accenture survey from the classes of 2013 and 2014 reported being full-time employees. Another 25% said they have part-time work, 4% said they were interns, and 3% freelancers. Of the remaining 16%, 5% are currently unemployed while 11% said they've been jobless since graduation.

The Class of 2015, meanwhile, was the most likely of all three groups to say they'd considered job prospects in a given field before picking their major. And almost two-thirds of them expect to get a job in their field of study, even though only 43% of the two classes ahead of them managed to secure full-time work in their preferred fields.