Question: What date were several dozen Jewish men executed during a program in which Algirdas Klimaitis was famous for his role in?

Context paragraphs:
Kaunas pogrom: The Kaunas pogrom was a massacre of Jewish people living in Kaunas, Lithuania that took place on June 25–29, 1941 – the first days of the Operation Barbarossa and of Nazi occupation of Lithuania.  The most infamous incident occurred in the Lietūkis garage, where several dozen Jewish men were publicly tortured and executed on June 27.  After June, systematic executions took place at various forts of the Kaunas Fortress, especially the Seventh and Ninth Fort.

Ridgeway Hill Viking burial pit: The Ridgeway Hill Viking burial pit at Ridgeway Hill near Weymouth, Dorset, was a mass grave of 54 skeletons and 51 heads of Scandinavian men executed some time between AD 970 and 1025.  The men are believed to have been Vikings executed by local Anglo-Saxons.  The dismembered skeletons were discovered by archaeologists in June 2009, and their identity and approximate ages were later confirmed by forensic analyses.  Although the immediate circumstances of the deaths is unknown, the event occurred at a time of conflict between the native Anglo-Saxons and Viking invaders, and it has been suggested that the Vikings had been captured during an attempted raid into Anglo-Saxon territory.

Operation Agatha: Operation Agatha (Saturday, June 29, 1946) sometimes called Black Sabbath ("השבת השחורה") or Black Saturday because it began on the Jewish sabbath, was a police and military operation conducted by the British authorities in Mandatory Palestine.  Soldiers and police searched for arms and made arrests in Jerusalem, Tel Aviv, and Haifa, and in several dozen settlements; the Jewish Agency was raided.  The total number of British security forces involved is variously reported as 10,000, 17,000, and 25,000.  About 2,700 individuals were arrested, among them future Israeli Prime Minister Moshe Sharett.  The officially given purpose of the operation was to end "the state of anarchy" then existing in Palestine.  Other objectives included obtaining documentary proof of Jewish Agency approval of sabotage operations by the Palmach and of an alliance between the Haganah and the more violent Lehi (Stern Gang) and Irgun, to destroy the Haganah's military power, to boost army morale and to prevent a coup d'état being mounted by the Lehi and Irgun.

Labour service (Hungary): Labour service (Hungarian: "munkaszolgálat" ) was required of "political unreliable" and Jewish men in Hungary during World War II after they were prohibited from serving in the regular armed forces by passage of the Hungarian anti-Jewish laws.  In Hungary, Jews comprised over eight percent of the population, and the government imposed an alternative to military service.  Labour service was forced labour, performed by labour battalions conscripted by the German-allied Hungarian regime primarily from Hungarian Jewish men during World War II.  These units were an outgrowth of World War I units, when Jews served in the Hungarian armed forces along with Christians, as in Germany and other European countries.  The Fascist, Nazi-allied Regime commanders treated the Jewish units with extreme cruelty, abuse, and brutality.  Men who worked in mine quarries were frequently pushed to their deaths off the man-made cliffs and embankments.  These units were stationed all over Hungary, including 130,000 men at the Eastern Front in Ukraine, where most of the men died.  The gendarmes and Army men who guarded these "slaves" were mostly members of the Nyilas fascist anti-Semitic political party.

Birds' Head Haggadah: The Birds' Head Haggadah (c. 1300) is the oldest surviving illuminated Ashkenazi Passover Haggadah.  The manuscript, produced in the Upper Rhine region of Southern Germany in the early 14th century, contains the full Hebrew text of the Haggadah, a ritual text recounting the story of Passover – the liberation of the Israelites from slavery in ancient Egypt – which is recited by participants at a Passover Seder.  The text is executed in block calligraphy and accompanied by colorful illustrations of Jews performing the Seder practices and reenacting Jewish historical events.  The Birds' Head Haggadah is so called because all Jewish men, women, and children depicted in the manuscript have human bodies with the faces and beaks of birds. Non-Jewish and non-human faces (such as those of angels, the sun, and the moon) are blank or blurred.  Numerous theories have been advanced to explain the unusual iconography.  The Haggadah is in the possession of the Israel Museum in Jerusalem, where it is on permanent exhibition.

Anton Schmid: Anton Schmid (January 9, 1900 in Vienna, Austria – April 13, 1942 in Vilnius, Lithuania) was an Austrian conscript to the Wehrmacht in World War II who, as a sergeant (feldwebel) in Vilnius, Lithuania, was executed by his superiors for helping 250 Jewish men, women, and children escape from extermination by the Nazi SS during the European Jewish Holocaust.  He did this by hiding them and supplying them with false ID papers.

Dozen: A dozen (commonly abbreviated doz or dz) is a grouping of twelve.  The dozen may be one of the earliest primitive groupings, perhaps because there are approximately a dozen cycles of the moon or months in a cycle of the sun or year.  Twelve is convenient because it has the most divisors of any number under 18.  The use of twelve as a base number, known as the duodecimal system (also as "dozenal"), originated in Mesopotamia (see also sexagesimal).  This could come from counting on one's fingers by counting each finger bone with one's thumb.  Using this method, one hand can count to twelve, and two hands can count to 144.  Twelve dozen (12 = 144) are known as a gross; and twelve gross (12 = 1,728, the duodecimal 1,000) are called a great gross, a term most often used when shipping or buying items in bulk.  A great hundred, also known as a small gross, is 120 or ten dozen.  A baker's dozen, also known as a big or long dozen, is 13.  Varying by country, some products are packaged or sold by the dozen, often foodstuff (a dozen eggs).  Dozen may also be used to express a large number of items as in "several dozen" (ex.  dozens of people came to the party).

Algirdas Klimaitis: Algirdas Klimaitis (1910 in Kaunas – August 29, 1988 in Hamburg) was a Lithuanian paramilitary commander, infamous for his role in the Kaunas pogrom in June 1941.

Arthur Hodges: Arthur Hodges (c. 1893 – December 18, 1914) was a white man who became the first person in Clark County, Arkansas to be executed by means of the electric chair.  Prior to that all executions were carried out by way of hanging or firing squad.  He was the fourth person so executed in Arkansas and one of eight men executed by the state in a 16-day period.  The eight executions in a 16-day period were the subject of an article, "Eight to Die in Arkansas", published in "The Kansas City Star".

Sydney Jewish Museum: The Sydney Jewish Museum is a museum in Sydney, Australia, which documents the Holocaust and the history of the Jewish people in Australia.  The museum is located at 148 Darlinghurst Road, Darlinghurst, and is housed in the historic Maccabean Hall built to commemorate Jewish men and women from New South Wales who served in World War I.  This New South Wales Jewish War Memorial, formally opened by Sir John Monash on Armistice Day 1923, has long been a hub of Jewish life in Sydney and was judged an appropriate site for the Sydney Jewish Museum.

Supporting paragraphs: Algirdas Klimaitis Kaunas pogrom
Answer: June 27