How can delete this default group
The group is maybe still used in Issue Manager.
In Silk Central go to Issues / Configuration / Groups and check if the group is listed there
If yes, then remove it from there and then you should be able to delete it also from User Management.
I am not sure what you mean with you didn't create a new project.
The message you receive - "Group cannot be deleted, because it is used by another module." - when you try to delete the user-group from the "User Management" area in Silk Central appears if the user-group is still used in Issue Manager's group settings.
To check if the user-group - you want to delete - is used Issue Manager's group settings, select "Issues / Configuration" from the main menu in Silk Central and click then on the "Groups" link on the left side (see attached image).
If the user-group is listed there, delete it and then you should also be able to delete this user-group from the "User Management" area in Silk Central.