I would also hesitate to label whites as the "dominant culture group", not only due to the geographically distinct cultures within the United States but the fact that ultimately, class is a far more reliable indicator of power than race (though the latter certainly has some say--see black incarceration rates for drug offenses despite using drugs at a lower rate than whites).
There's a difference between saying "whites are the dominant culture group" and "all whites are in positions of power." And in the US at least, race and class are very interrelated:
Those are median numbers for household net worth among different racial groups in America (as of 2010).
Household net worth (a lot of which comes from the pre-2007 culture that everyone needed a big generic exurban house) is not the best indicator of actual wealth. The most important factor is that the overwhelming majority of people are not receiving the full value of their labor, while the minute ruling class, while a good bit whiter than the general population, are certainly not uniformly so.