The only way to create a donation pledge page for both a group and a participant is to add them as a participant. When creating the group, this does not create a "group page" that can accept direct donations.

The group itself is only for organizing the participants and having a group leaderboard. So the group will sum the total received by the participants within the group.

If you want donors to be able to donate to the group itself (not a specific participant), then you'll have to create a participant pledge page for the group.

An example use-case would be when you want teachers to be able to receive donations directly, not through a student.