The Local Group, also known as the Local Cluster, is an area in the known Universe containing a series of Galaxies, including the Milky Way. (SGA: "Rising", "The Shrine")
History
The earliest known intergalactic power in the Local Group may have been the Alterans. Who arrived from a galaxy outside of the Local Group sometime between fifty million years ago and hundred seventy-five million years ago. The Alterans spread across the Milky Way galaxy and eventually formed an alliance with three other races, the Nox, the Asgard, and the Furlings.(SG1: "The Torment of Tantalus", "The Fifth Race", "Fallen", "Lost City, Part 1", "Lost City, Part 2", "The Drift", "Avalon, Part 2", "Origin", "The Ark of Truth")
Holographic image of the Milky Way galaxy.
When a plague ravaged the Milky Way galaxy millions of years ago, the Alterans left Earth and migrated to the Pegasus galaxy. Where they spread throughout the galaxy, until they encountered the Wraith. After a long war, during which the Wraith conquered most of the Pegasus galaxy, only Atlantis remained.
They held out for a century but eventually were forced to submerged their city and retreat back to Earth. The Wraith seized control of the galaxy, though they were soon forced to fight the Asurans who they also defeated. After which they exterminated any technologically advanced races that could pose a threat to the Wraith and for millennia terrorized the human worlds of the galaxy, periodically culling their populations.(SGA: "Rising", "Progeny", "Spoils of War")
Millions of years after the Alterans left the Milky Way galaxy, a new galactic power emerged, the parastic Goa'uld. Who established feudal domains across the galaxy, using enslaved humans and a genetically-engineered race of warriors, the Jaffa. They dominated the galaxy, though their power was held in check by their infighting and the superior technology and firepower of the Asgard of the Ida galaxy. Who were unable to prevent the rise of the Goa'uld due to a threat in their home galaxy.(SG1: "Fair Game") When the Tau'ri began to travel through the stargate on Earth, it began an interstellar conflict with the Goa'uld.(SG1: "Children of the Gods", "The Enemy Within")
The Tau'ri would eventually form an alliance with the Tok'ra and Rebel Jaffa.(SG1: "The Tok'ra, Part 1", "The Tok'ra, Part 2", "Into the Fire") The turning point, came at the Battle of Dakara, when the Goa'uld image of being gods was shattered. After which Jaffa began to abandon the Goa'uld and joined the Free Jaffa Nation.(SG1: "Reckoning, Part 1", "Reckoning, Part 2") The last of the System Lords, Anubis would later be defeated, ending the rule of the System Lords.(SG1: "Threads")
Holographic image of the Pegasus galaxy.
Thousands of years after the Alterans left the Pegasus galaxy, the Tau'ri arrived at the submerged city-ship of Atlantis. They ended up encountering the Wraith and awakened them centuries before the galaxy's human population had sufficiently repopulated since the last culling grown to support all of the Wraith.(SGA: "Rising") All of the Wraith hives awakened and the Tau'ri soon found themselves at war with the Wraith.(SGA: "Rising", "The Siege, Part 1", "The Siege, Part 2", "The Siege, Part 3") Due to the shortage of humans, the Wraith hives turned on each other, in a galaxy wide civil war.(SGA: "The Lost Boys", "The Hive", "Allies") The Tau'ri would manipulate the Asurans into going to war against the Wraith again.(SGA: "Lifeline")
Which ended up being a mistake as the Asurans began to wage a war of extermination against humans in the galaxy, to starve the Wraith.(SGA: "Tabula Rasa", "The Seer") Forcing the Wraith, Tau'ri, and Travelers to join forces against the Asurans, who were defeated by the alliance.(SGA: "Be All My Sins Remember'd") The war between the Tau'ri and Wraith resumed, while the civil war among the Wraith likewise continued.(SGA: "Spoils of War", "The Queen") A Super-hive would later attack Earth but was destroyed in orbit.(SGA: "Enemy at the Gate") The Wraith civil war ended upon the defeat of Queen Death by a Tau'ri-Wraith alliance consisting of Guide's fleet and the Tau'ri forces at Atlantis (supported by the George S. Hammond battlecruiser.(SGA: "Inheritors")
Note
The Ida galaxy, may or may not be part of the Local Group. Based on the distance given of 4 million light years, it would put the Ida galaxy in the Antlia-Sextans group of galaxies. Which is at the very edge of the Local Group, with some scientists putting it in the Local Group and other scientists considering it to be independent of the Local Group and therefore the closest galaxy group.
In the Local Group are over 60 known galaxies, most of which are dwarf galaxies. The largest galaxy is Andromeda (both in size and number of stars, twice as many as the Milky Way), followed by the Milky Way, and then Triangulum (far smaller than the Milky Way). Andromeda has 11 satellite galaxies (including Pegasus) and the Milky Way has 30 satellite galaxies, including the Large Magellanic Cloud (the 4th largest galaxy in the Local Group).