How can I send an email to a google contact group on my iOS devices?
Unfortunately, there's not a way of doing it with the native iOS app. Try using the Gmail app (which I personally prefer). If not, there's this little workaround: http://red66.com/2009/07/how-to-send-group-emails-from-your-iphone/

The gist of the workaround is to make one contact for the group and add a comma separated list of emails to the singular email field for the "group contact"

This doesn't allow you to leverage arbitrary groups and does require some manual setup, but once that's done you can email limited group sizes from iOS without needing a computer.