Apex domains cannot have CNAME records.
Question and response
Question
dig aup.dk. NS
Answer
aup.dk. 5 NS nelly.ns.cloudflare.com.
aup.dk. 5 NS hunts.ns.cloudflare.com.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0