"Don't yet rejoice in his defeat, you men... the bitch that bore him is in heat again." Brecht reminds us, in Arturo Ui, of hellish history repeating itself.

The barbarism of the Nazis and the Holocaust should be told over and over again.

John Donoghue's book is timely. The news these days is alarmingly full of the murder of Jews and attacks on synagogues. There are executions of Christians in Libya and Syria, while three Muslim students were shot down on campus in North Carolina, and many more are being killed in their own countries. The Jobbik Party in Hungary are on the rise, and Golden Dawn remains strong even in Syriza Greece. Western news reports prefer not to make much of Ukraine's Azov Battalion.

But it is a risky business making a fiction, a form of entertainment, out of racism, genocide, and human brutality. Although much of The Death's Head Chess Club is perceptive and written with feeling and integrity Donoghue, like all writers, has had to make difficult decisions.

His story moves around in time - a little dizzyingly - from the 1930s to the 1960s. At its centre is the network of Nazi concentration camps in Auschwitz. The central plot is a chess competition run in the camps and the "friendship" formed over years between Emil Clément, a French Jewish prisoner and SS Obersturmführer Paul Meissner. Donoghue goes into exhaustive detail about German army ranks, divisions, sections, the intricate workings of Nazi brutality. There are lots of footnotes and an appendix clarifying subtle differences. His research was no doubt undertaken with respect, a sense of responsibility towards victims and their families, but it comes perilously close to the morbid voyeurism of all those Nazi-obsessed television "history" programmes.

Less contentiously, there is also a lot about chess moves and strategies: Latvian Gambits and Chigorin Defences. Donoghue is a writer in the tradition of Frederic Forsyth and has pages on the inner workings of rifles. But the biggest risk of all is in the novel's depiction of its three central characters.

Meissner and Clément meet again in 1962 at a chess competition. The old SS Storm Leader has since become a bishop of the Catholic Church. The Frenchman - now Israeli - is essentially still traumatised by what happened to him and his family. Their friendship grows improbably quickly. In the book's flashbacks Meissner has fewer saving graces than I think Donoghue intended. The third member of their postwar group is Schweninger, now a chess master, then a member of the Nazi Ministry of Propaganda.

"There is no such thing as a good German", Clément says early on. Later, Schweninger claims "In their heart of hearts the German people dreamed the same dream as Hitler." I find both those statements unlikely from either character. German communists, democrats, resistance fighters, gays and religious groups were gunned down, rounded up, interned, exterminated. Clément himself is only too aware of the perfidy of his fellow French and the enthusiasm of Polish and Hungarian fascists as much as German ones to kill him and wipe out his people. If we believe what the novel has to say about chess masters, we would imagine that Célment might have known the darkness in all human hearts, and worked out the disastrous political moves - austerity, German war debt - that led to catastrophe.

Most challenging of all is the book's central scheme: that it takes Bishop Meissner to show Jewish Clément the way to forgiveness, as if Catholicism, despite its own nefarious record before and after the war, had a monopoly on the stuff. Donoghue is aware of that, but I'm not sure he has managed to make it work, politically or psychologically, in the story.

For a first novel, The Death's Head Chess Club has much to recommend it. It is at times elegantly written, and it certainly does not flinch from the horrors it deals with (occasionally overdone, particularly in trying to capture the vile verbal violence of camp guards' anti-Semitism). It is tightly potted, and finally moving. If there is a major flaw, then it is in its ambition. For a first-time novelist that is surely not a bad flaw to have.