Just days after Facebook filed papers to go public, a large California pension fund is criticizing the social media giant for having an all-male board of directors.

In a letter addressed to Facebook CEO Mark Zuckerberg, the California State Teachers' Retirement System raised concerns about the lack of diversity on Facebook's board. Anne Sheehan, the director of corporate guidance for CalSTRS, said the board named in the company's IPO filing does not have a wide spectrum of corporate experience and lacks gender and racial diversity.

"This is particularly glaring at a time when there is clear evidence that companies with diverse boards perform far better than the companies with more homogenous boards," Sheehan wrote.

Sheehan added that Facebook Chief Operating Officer Sheryl Sandberg had been supportive of calls for diversity on the board.

CalSTRS, the second largest U.S. pension fund, has invested in Facebook through its private equity allocation and has plans to invest in the company's stock once it goes public. The pension fund has often asked for changes with the companies it invests. Last year, it lobbied for corporations to disclose their political donations; and in 2009 the pension fund sent a letter to 300 of its largest portfolio companies to let shareholders have an advisory vote on executive compensation.

Facebook has not commented on the CalSTRS letter.

Facebook filed its initial IPO papers last week which could value the company at around $100 billion. CalSTRS has invested about $30 million as of June 30.

CalSTRS said it decided to send the letter after seeing Facebook's IPO filing and seeing the composition of its seven member board. The board includes Zuckerberg, former Clinton White House Chief of Staff Erskine B. Bowles, Washington Post CEO Donald E. Graham, Internet entrepreneur Marc L. Andreessen, Netflix CEO Reed Hastings and venture capitalists James W. Breyer and Peter A. Thiel.

"We want them to be cognizant of the fact the board is rather homogenous," CalSTRS spokesman Ricardo Duran said Tuesday. "As far as we could tell, it's mostly tech people, mostly friends of Mr. Zuckerberg, and we would like to see the company make a greater effort to expand the board and to include, in that expansion, a more diverse set of candidates."

Zuckerberg controls 57 percent of Facebook's voting share power. The CalSTRS letter said "we realize that Facebook will be a controlled company in which the public stockholders will have little influence."