Yes, it is not a typo. It is not "great" and not "get." The word "Geat" really exists in the English language, even though it is not known to about 99.9 percent of the English-speaking population. Moreover, not only does Geat exist in our language, but such words as "Geatland", "Weather-Geats", "Sea-Geats" are also part of the English heritage. To be more specific, Geat is of Old English origin, and it simply means "a member of a Scandinavian people of southern Sweden." However, it holds much more than can be seen at the first sight, for a legendary hero, a man of strength and courage belongs to this tribe. His name is Beowulf.
Geat refers to a tribe living in southern Sweden in the Middle Ages. At the time, this area was populated by a number of Germanic tribes. And it seems that Geats were not the most important one. Vikings and Goths lived near by; Danes were also not very far away. It is rather hard to find anything specific about Geats alone since even at their time they were often confused with Danes and other tribes by Roman writers and churchmen. Germanic tribes lived in southern part of Scandinavian peninsula until about twelfth century. In the Middle Ages, they were rather active invading neighboring peoples since the Roman Empire that ruled the area for hundreds of years just fell, and it did not look like it was getting up. So Germanic tribes became very successful, invading and conquering everywhere from the British Isles to Rome itself. It is unlikely that Geats were a crucial element in medieval history since their number was not very significant.
The most important achievement of the Geat people is that they are the center of medieval epic Beowulf, the first and possibly the most significant work written in Old English. Manuscript of Beowulf was preserved till our times almost in full. Beowulf tells a story about a legendary hero with a "handgrip the strength of thirty men, a man famous in battle." [Norton, 32] The story of the epic is rather cliche and simple. Beowulf comes to the king of Danes and helps him, out of his own good will, to get rid of a monster named Grendel and his mother. He then returns to Geatland, and rules his people for 50 years, after his friend and lawful heir to the throne, Heardred, dies. After that he is forced to fight with a dragon who attacks the Geat people. Even in his old age and after being deserted by his retainers, he kills the dragon, but his own wounds are fatal, and the epic ends with the death and funeral of Beowulf.
Beowulf is the major source for the history of Geats even though it is fictional. The epic describes "the folk of the Geats" as brave people. Descriptions like that one are probably biased and totally false, but the lineage of Geat rulers is likely to be true or close to true since Beowulf is known to list a number of historical events that can be checked by outside sources. The Geat family tree is represented below, and the short history is as follows. Originally, the Geats were ruled by Hrethel who died after his son, Haethcyn, accidentally killed his elder brother, Herebeald. Haethcyn became a Geatish king. He was followed by Hygelac, his other brother and Beowulf's uncle. After Hygelac's death, the throne went to his son, Heardred, and since Heardred had no sons, he was followed by Beowulf, his cousin.
"Geat" refers to the tribe living in southern Sweden; however, its meaning is more important in connection with Beowulf. Beowulf is the most significant, and probably the only, work about "the folk of the Geats," for whenever one thinks about Geats he thinks about Beowulf.