By far throughout the Thing-Thing series, there were only two AutoMag weapons featured.
The original AutoMag pistol, designed by Harry Sanford in the Auto Mag Corporation, was developed to bring .44 magnum power to a semi-automatic handgun. This heavy pistol, based on a chromoly prototype engineered by Max Gera, is chambered for the powerful .44AMP cartridge and features a rotary bolt with locking lugs at the front similar to the M16/AR-15 assault rifle. The gun's production costs proved too expensive, and as a result, the Auto Mag Corporation went bust.
Years later, the Arcadia Machine and Tool (AMT) company began manufacturing pistols under the AutoMag name, and the guns are also designed by Harry Sanford, who invented the original AutoMag. The AutoMag V is one of the few semi-automatic handguns chambered for the .50 caliber Action Express (AE) cartridge, and featured compensator ports in the barrel to reduce muzzle rise to tolerable levels.
The AutoMag V is featured in Thing-Thing 2 as an unlockable weapon acquired along with an M1911 after getting 100 kills in the Zeus boss fight. Thanks to its compensator ports, the weapon has less recoil than the Desert Eagle, but don't get too arrogant; magnum ammo can still be a bit hard to find.
The original AutoMag appears in Thing-Thing Arena 2. Low rate of fire due to recoil from those powerful .44 AMP rounds, but the results against your enemies is worth it. Ammo can be rather hard to find, though.