Porphyrion

Porphyrion is often said to be the king of the Giants, or Gigantes, in Greek/Roman mythology. According to most sources, Porphyrion rose from the mud created by the blood of the deity Ouranos's death. He is arguebly the most powerful of the giants just as Zeus is the most powerful god. However, he is also sometimes said to have been sired by the primordial deity of the abyss, Tartarus. Although this may have risen as a result of another version of the legend, in which the Giants rose from Tartarus after being imprisoned there by Kronos.

Greek Mythology
In ancient times, the Titans such as Kronos and Hyperion were defeated by the young gods, namely the six children of Kronos (Zeus, Poseidon, Hades, Hestia, Hera, and Demeter) and by their allies. Soon after, however, Gaia brought forth the Giants, who were solely born to avenge their elder siblings' deaths. By this time, all of the younger Olympians (Zeus' children) had been born, and were preparing the way for the new demigods. Porphyrion started the first war between the gods and the giants by kidnapping Hera after being shot with an arrow of Eros. This, of course, made him fall in love with the Queen of the Olympians, so he started the war to keep Hera and to avenge the Titans. Led by Alcyoneus and (of course) the king, Porphyrion, the Gigantomachy attacked Olympus. Warned by the Fates that the Olympians could not defeat the Giants without the help of a lion-skinned-mortal, Zeus decided that this must mean his son, Heracles, and sent Athena to find him.

Heracles defeated Alcyoneus after injuring him in the Giant's homeland, Pallene (where Alcyoneus was immortal) and then killed him outside of Pallene's borders. Porphyrion later dueled both Zeus and Heracles, but the combination of both god and demigod working together destroyed him (Like all giants, in order to bring him down, gods and demigods need to work together).

Trivia
This giant is one of the 24 anguipede giants who made war on Olympus. He also tried to strangle Hera on his revolt on Olympus. Because of the arrow from the bow of Eros, Porphyrion developed lust on Hera. He tore Hera's robes and tried to rape her before Zeus interfered and shot him with a thunderbolt.

The Lost Hero
In The Lost Hero, Gaia uses Hera's power to release Porphyrion from Tartarus, and is trying to awaken other Giants to fight the gods. He is also a son of Gaia and Tartarus, or perhaps Ouranos (paternity is uncertain). He uses a 20-foot spear for a weapon. He is the "anti-Zeus" meaning he was born specifically to beat Zeus, as he said, and as such nearly killed Jason Grace, if not for Hera being freed at the right instant. He rose at the Wolf House, which is the climbing location for the Roman demigods. He fought against Jason but fled after Hera/Juno was freed from her prison to avoid her wrath. However, Porphyrion really gave up, and followed Enceladus's Plan to Greece by travelling through the earth( how fast he can go is uncertain). The Giants' plan is to defeat the Olympians by destroying their very roots in Greece. Demigods and gods still need to work together to defeat him later on.

Powers
Not much is known about the true extent of Porphyrion's abilities. He made his spear glow, possibly with electricity or magic, shortly before nearly killing Jason Grace, possibly aluding to him being the Anti-Zeus. He slammed his spear into the ground and he vanished, "as if dropping down a chute", however this may have simply been Gaia aiding him, and not his own abilities. He may have the ability of Enceladus to be faster than should be possible for a being of his size while standing on the ground, however, this may again be due to Gaia's abilities, and not the giants' own. Being a Giant, he would have the same regenerative abilties in his skin and armor as Enceladus if anything besides a demigod and god(at the same time) were attacking him.