When I open the Game Center and select friends it freezes on a white page

Have you tried closing the Game Center app and all of the other apps on the iPad and then reset the device?

To close an app, drag the app up from the multitasking display. Double tap the home button and you will see apps lined up going left to right across the screen. Swipe to get to the app that you want to close and then swipe "up" on the app preview thumbnail to close it.

Reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.

You can try this, but if you do it, you will have to enter of the device settings again and that does take some time to do but no data is lost.

Reset all settings. Settings>General>Reset>Reset All Settings.