A short list of things the FPÖ is famous for:
The party fund scandal when then head of party H.C. Strache used 10 000€ party funds to purchase emeralds in "Clash of Clans" (I wish I made that up but I didn't).
Trying to strike a deal with a "Russian Oligarch" to purchase Austrias biggest news outlet "Krone" and turn it into a FPÖ propaganda machine. The "Russian Oligarch" was a bait and high ranking FPÖ politicians (like the mentioned H.C. Strache) had to explain themselves and said they were "having drunk fantasies". It caused the then ÖVP-FPÖ government to collapse.
A song containing the lyrics "Let's go! (which can also mean Release gas! - I wanted to mention that since it gets lost in translation) We'll make it 7 million!". Then minister of inner affairs Herbert Kickl (who ~~is now likely to~~ could become chancellor) reacted not by criticism towards his party, but by criticism towards the "Verfassungsschutz" (Federal Office for the Protection of the Constitution) who, according to him, leaked the song. He then ordered a normal police unit, that was meant to arrest drug dealers and gang members, to raid the Verfassungsschutz and they took any evidence for far right extremism linked to the FPÖ.
Now head of party Herbert Kickl is also known for:
Calling the neo nazi group "Identitäre Bewegung" a "project worth supporting".
Claiming that horse deworming medication could treat covid.
Refering to himself as "Volkskanzler" a title also used by Adolf Hitler.
Saying that "politics should be above the law and that the law should not be above politics"
Having friends that donated money to the Christchurch mass killer and that really wanted to "meet him and drink a coffee if he visits Vienna one day".
I bet I have forgotten a lot of shit that has been going on. Let's just say the last few years have been a wild ride in Austrian politics.
Edit: as has been pointed out, Herbert Kickl is not a likely but possible option for chancellor since the ÖVP could form a coalition with the SPÖ and keep Nehammer as chancellor. It was bad wording from my side, I apologize >~<