Precise group information is not automatically visible after the creation of a group event. The groupid is in the record of a calendar group event in the database, but a normal moodle user cannot automatically see the name of that group after the group event has been created. It would be useful for a teacher if the group name is automatically and always visible for each group event. See the following discussion in the forum:
http://moodle.org/mod/forum/discuss.php?d=133222

Furthermore, it would be useful for a teacher to be able to select a particular group in order to filter out all group events which are not intended for that group. It can temporarily reduce the amount of information to deal with in a calendar of a course with several groups and possibly many events per group.