CyberFaction

The Faction, as they were designated by the history computer, were a particular group of Cyberman. They stood in contrast to CyberMondans.

Whereas the Mondans wished to retain some connection to their biological form, the Faction saw greater logic in fully embracing cybernetics. They thus retained a smaller percentage of their organic systems than Mondans. (PROSE: Iceberg)

History
Thousands of years before the 20th century, the Faction left Mondas for Planet 14. (PROSE: Iceberg)

20th century
In 1969, (PROSE: Who Killed Kennedy) 1970, (PROSE: No Future, Killing Ground) 1975, (AUDIO: Last of the Cybermen) or the late 1970s; (TV: The Web of Fear, The Invasion) the Faction put into motion what would later be recorded as the first attempted Cyberman invasion of Earth. (PROSE: Iceberg)

Prior to coming to Earth, the Faction had invaded the planet Isos II and converted its humanoid population into Cybermen. By repurposing Isos II's monorail system, a dimensional warp was created which led to Earth. A large invasion fleet of Cybermen waited on Isos II while a smaller amount of Cybermen and a Cyber-Planner went through the warp to establish themselves on Earth and put the planet into a weakened state. (AUDIO: The Isos Network)

After several years, (PROSE: Prelude Iceberg) they had established a base on the dark side of Earth's Moon. The Cyber-Planner had contacted the industrialist Tobias Vaughn, the head of the International Electromatics corporation. Vaughn installed mind control circuits in his company's appliances, paving the way for an invasion. He also grafted cybernetic arms onto several of his workers.

Vaughn had a Cyber-Planner installed in his office. The plot was uncovered by the newly formed UNIT and the Second Doctor, who helped avert the invasion on the Earth and at the Cyberman base on the Moon. (TV: The Invasion) The invasion fleet from Isos II came to Earth when the planet was put under cybercontrol by radio waves from IE products, but it was destroyed in a chain reaction started by missiles fired by UNIT. (TV: The Invasion, AUDIO: The Isos Network)

Bits and pieces of damaged Cybermen remained in the London sewers. One Cyberman managed to cannibalise garbage it found in the sewers to repair itself and create a considerable amount of Cybermats. The Third Doctor and Jo Grant stopped it from infecting an entire hospital with cybermites. (PROSE: The Piper)

In 1975, two Cyberman heads were found in the sewers; one from Deffry Vale station was sent to the Leamington Spa Lifeboat Museum (GAME: Security Bot) while the other head would eventually end up in Henry van Statten's Vault. (TV: Dalek)

Some Cybermen survived the destruction of the invasion fleet. Many were propelled into deep space. One Cybership crashed in Antarctica, where it remained frozen and hidden for two decades. (PROSE: Iceberg) Another Cybership managed to escape back to Isos II. The Second Doctor, Jamie McCrimmon, and Zoe Heriot followed the ship and destroyed all traces of the Cybermen on Isos II. (AUDIO: The Isos Network)

Vaughn survived his apparent death by transmitting his mind into a robotic copy of himself created with cybertechnology. For many centuries, Vaughn continued to influence Earth while repairing his robotic body with parts salvaged from failed Cyberman attacks on humanity. (PROSE: Original Sin, AUDIO: Original Sin)

In the 1970s, Gareth Arnold uncovered a Cyberman ship that had crashed in Cambridge many years beforehand and experimented with the technology that had survived. Using Cybermats, Arnold attempted to convert all of Cambridge, but was stopped by the Third Doctor. During this incident, Liz Shaw was almost converted. The Cybermen that Arnold had created went into stasis on the ship, awaiting an activation signal. (AUDIO: The Blue Tooth)

The Faction had been opposed to the plan of the Mondans to pilot Mondas back to Earth to rob their twin planet of its energy. When that plan failed in 1986, and Mondas exploded, the Faction were apparently the only group of Mondasian Cybermen left in existence. They thus emerged as the "victorious" branch of the Cyber race. (PROSE: Iceberg)

21st century
In December 2006, exactly 20 years after Mondas returned to Earth, Cybermen of the Faction who had been in hiding in the South Pole since the International Electromatics invasion attempted to sabotage the FLIPback project and take over the Earth in the ensuing chaos. With the help of Ruby Duvall, the Seventh Doctor prevented the Cybermen from carrying out their plan and destroyed them. (PROSE: Iceberg)

UNIT has a cyber-helmet from the International Electromatics invasion at the Underbase. (COMIC: The Age of Ice) Kate Stewart had another leftover cyber-helmet. (TV: Death in Heaven)

22nd century
By the speculations of Hegelia of the ArcHive, a further group of Cybermen diverged from the Planet 14 Cybermen and became the CyberNomads. (PROSE: Killing Ground)

Behind the scenes
The term "the Faction" has its origins in the non-narrative encyclopaedic book, Doctor Who: Cybermen, by David Banks. Among the terms and theories invented by Banks to explain the variations in the costumes (worn by Banks and his fellow Cyber-performers over the years) was that of "the CyberFaction". None of Banks's proposed terms garnered much attention amongst DWU authors, and weren't carried forward in narratives until Banks's own novel Iceberg.

While Iceberg did introduce many of Banks's earlier-stated concepts into Doctor Who fiction proper, it is worth noting that even he failed to use his own coinage ‘CyberFaction’ in said novel, with the Cybermen in question being only referred to as ‘the Faction’. Even then, Banks remained the only author ever to speak of “the Faction”, for all that his treatment of said Faction implies that a vast majority of the Cybermen encountered by the Doctor up until then had belonged to said Faction.

Other Faction-related facts from Doctor Who: Cybermen not reinstated anywhere in fiction include the idea that after the destruction of Mondas, parts of the Faction became CyberNomads and left Sol to explore Mutter's Spiral; and that following the attack on the Gravitron, the Faction abandoned the Sol system and journey into the galaxy to colonise a suitable planet, eventually landing on Telos, which they colonised in 2175, resulting in ‘CyberTelosians’, thus accounting for the apparently-native Telos Cybermen in The Tomb of the Cybermen in the same way suggested by Attack of the Cybermen three years prior — namely, that the Cybermen in question had actually been the results of Mondasian Cybermen taking over the planet.

Neither of these events are taken into account by this Wiki, as Doctor Who: Cybermen, being non-narrative, is not considered a valid source here.