Default [Q] NFC Card


I have a school library NFC card which I use to open library doors.
Is it possible to copy the contents from that NFC card to a NFC tag and use the tag
the same way?

The NFC card is Mifare Classic and has Factory default key (not sure whether it is important to mention).
If I understand correctly, I will have to crack the secret key in order to have full access to the NFC card contents
and thus be able to make NFC tags?

What methods are used for cracking this key?