Hi Roxy1987,
By Default, The TaskSummary object does not have information about the name of the group.
If you are using JBPM5.4, you can look at the query to get content of TaskSummary at
jbpm-human-task-war.war\WEB-INF\classes\META-INF\Taskorm-JPA2.xml
You can try to modify that query, or you can just query the database directly to get the name of the group.
Regards,
Thomas Setiabudi