The songbook, brought to attention last week in the media, contained lyrics such as "Step on the gas… we can make it to seven million", a referens to the six million Jews killed in the Holocaust.
The timing could not have been worse for Udo Landbauer, a candidate for the far-right Freedom Party (FPÖ) in elections in Lower Austria state last Sunday – and the Germania fraternity's vice-president.
After what Landbauer called a "media witch-hunt" and protesting he knew nothing about the book, the 31-year-old resigned on Thursday and suspended his party membership pending an investigation.
Regardless of his guilt or innocence, the affair has thrown a spotlight on the FPÖ, on the nationalist fraternities that many senior party members belong to, and on conservative Chancellor Sebastian Kurz.
For historian Stefan Karner, the "biggest scandal" about the affair is that the book was produced not in the 1940s or soon after World War Two but in 1997.
"After so much research, exhibitions, discussions, witnesses talking in schools (and) Holocaust films and dealing with our past… nobody can claim to be ignorant," Karner told the Kurier daily.
The reason, believes political scientist Matthias Falter, is to do with Austria's "tardy and incomplete" process of facing up to its complicity in the atrocities of the Nazis.
"In the 1950s and 60s hardly any trials took place. Collective memory was steeped in memories of fallen soldiers," he said.
For a long time after 1945, Austria thought of itself as Hitler's "first victim", having been "annexed" – to no resistance and to general public approval – into the Third Reich in 1938.
This changed in the late 1980s when a scandal over the – actually minor – wartime record of former UN secretary general and Austrian president Kurt Waldheim prompted a collective re-think, Falter said.
But whether this process that Austria's other politicical parties went through in confronting the past has also happened to the same extent with the FPÖ is a moot point.
Party leader Heinz-Christian Strache, 48, who flirted with neo-Nazism in his youth, has toned down the party rhetoric and has expelled party members overstepping the mark.
But the party is still viewed with suspicion, even after entering a governing coalition under Kurz in December. Austria's main Jewish organization spurns all contact with FPÖ government ministers.
The student fraternities do not help. Many of them are like something from a bygone age, duelling with (blunt) sabres, wearing militaristic uniforms and believing in a "Greater Germany".
More than a third of the FPÖ's 51 MPs and ministers, including Strache, reportedly not shy of duelling in the past, belong to such organizations. They are men-only, although a handful of women-only ones exist too.
Strache, attending a fraternity Viennese ball last Friday, said that "anti-Semitism, totalitarianism (and) racism are the opposite of fraternity thinking".
Strache, now deputy chancellor, has also said he intends to organize a historical commission to delve into his party's past, although the historians have not yet been found to do the job.
"Time to lie on Freud's couch," the Die Presse daily said in a recent editorial, referring to Sigmund Freud, the Vienna-born father of psychoanalysis who had to flee the Nazis in 1938.
"The ability of the FPÖ to govern, which Strache has to prove, will be measured by its readiness to submit to an analysis and to confront its past," the paper said.
Article by AFP's Sophie Makris