The maximum length is 73 characters as of this writing.

You can get it through the Admin Console GUI:

1. Go to https://admin.google.com/u/1/ac/groups.
2. Click Create group.
3. In the Group name field, enter a long name, like This is a long group name, so long that it causes a validation error to appear that specifies the field's maximum length.
4. A validation error should appear that specifies the field's maximum length.