Shortly after her release from Ravensbrück in 1945, Comtesse Germaine de Renty attended a dinner party in Paris with old friends. One guest complimented her on how well she was looking, concluding that “life in Ravensbrück was not nearly as terrible as we’ve been told”. De Renty stared at the woman for a moment, before explaining icily that a typical day in the camp began by stepping over the corpses of friends who had died in the night. They would probably have no eyes, she added, since the rats had already eaten them. And with that, the comtesse stood up and swept out.

Ravensbrück always had a credibility issue, explains Lynne Olson in this consistently thoughtful book. The camp, although only 50 miles north of Berlin, had been liberated late, which gave the SS plenty of time to burn incriminating records. There was limited visual evidence, too, since no cameramen accompanied the Soviet army when it knocked down the gates on 30 April 1945. While images from Auschwitz and Dachau of starving prisoners and rotting corpses were flashed before a horrified world, Ravensbrück left little trace in the moral imagination.

The camp – which, unusually, was single sex – is better known now, thanks in part to Sarah Helm’s outstanding 2015 book If This Is a Woman. Helm not only drew on new documentary evidence that became available with the fall of the iron curtain, but also interviewed many of Ravensbrück’s elderly survivors. Olson, by contrast, focuses on just one small subgroup, the handful of French resistance members who arrived from 1942 onwards. She follows them from arrest, deportation and internment right through to the distinctive and coordinated way that they lobbied for recognition and reparations after the war.

Ravensbrück had been built to house 3,000 women, but at its peak held more than 45,000 Jews, Roma, and other groups considered enemies by the Third Reich. There was one latrine per 200 prisoners. Medical intervention was more likely to kill than save and minor ailments quickly escalated into matters of life and death. One woman with a tooth abscess died of septicaemia within a few days. Over a period of six years, around 40,000 women lost their lives through starvation, disease, torture, medical experiments and, from December 1944, a gas chamber that the SS hurriedly installed, having underestimated how long it would take to work everyone to death at the nearby Siemens factory.

Even before they arrived at Ravensbrück, the résistantes had been designated by the Germans as falling under the Nacht und Nebel [night and fog] decree, political prisoners targeted for disappearance. Olson shows how the Frenchwomen turned this vaporous status to their advantage, flitting from block to block under cover of darkness to deliver medicine, tapping out messages along pipes and orchestrating strikes in munitions factories. They specialised, too, in a certain Gallic insouciance, delighting in subverting the heavy-footed Germans without letting on exactly how it had been done.

But they knew too that their indeterminate status would make it doubly difficult to explain to the postwar world what they had been through. To be believed, they needed to find a way of documenting their experience. Step forward Germaine Tillion, an ethnologist who had completed years of PhD study on the Berbers of Algeria before having her notes confiscated when she was arrested at the Gare de Lyon in 1942.

Deported to Ravensbrück, Tillion embarked on an anthropological study of camp life. She noted the names of guards, dates of transports and details of gas chamber “selections”, carefully disguising her data as recipes for dishes she might cook in happier times. Dispersing her notes among trusted friends, Tillion reassembled her material after the war, publishing her seminal work, Ravensbrück, in 1946 and adding to it as she unearthed new sources. The final updated version appeared in 1988.

Tellingly, Tillion could not find a French publisher for her book – it came out under a Swiss imprint – due to that country’s reluctance to confront its own war record and high levels of collaboration. In the face of this wilful amnesia, the women of Ravensbrück founded the National Association of Former Female Deportees and Internees of the Resistance (ADIR) through which they lobbied for housing, healthcare and employment for survivors. It is this phase that gives Olson’s account of the “Ravensbrück Sisterhood” its satisfying final act.

The ADIR’s biggest task was to ensure that the thousands of SS officials, guards and others who had worked at Ravensbrück were brought to justice: of the 38 men and women put on trial, 19 were executed, with the rest given either prison sentences or acquitted. As ever, lack of documentary evidence was the sticking point: oral testimony, though compelling, could easily be dismissed by defence barristers as “hearsay”. Furious at what they considered a gross miscarriage of justice, the résistantes continued to push for prosecutions despite a diminishing appetite in the culture at large.

In 1950, Ravensbrück’s former commandant Fritz Suhren was finally arrested while working as a waiter in a Berlin beer cellar. This time, Tillion’s contemporaneous notes were allowed to be read at trial, and she was able to show that the wretched Suhren, who claimed to have had nothing to do with the gassing of inmates, had indeed signed an order for the execution of 500 women on 6 April 1945. On 12 June 1950 he faced a firing squad.