I need to remove some package groups for the following software eg: X window system and Graphical Internet. I need to know how I can find out the package groups available on the system.

To see what package groups you have on your system try:

$ rpm -qa --qf "%-30{name} %-{group}\n" |sort -k2

You could attempt to remove all the packages in that group that with:

# rpm -e `rpm --group "User Interface/X"

However you will almost definately run into dependencies on those packages that will stop their uninstallation. Graphical Internet packages would be among those dependencies. It would be easier if you had either yum or apt available in which case you could try

# yum remove `rpm --group "User Interface/X"`

or

# apt-get remove `rpm --group "User Interface/X"`