Ganesha (also called Ganesh or Ganesa) is one of the most worshiped deities in the Hindu pantheon and is known as the Lord of Obstacles, Lord of Beginnings, god of wisdom and intelligence, and patron of arts and science. He is the son of Shiva and Parvati and depicted as having the head of an elephant (often with one broken tusk), a pot-belly, and anywhere from two to six arms.
There are several popular Hindu stories as to Ganesha's origins and how he got his elephant head. While some say Ganesha was born with the head of an elephant, most say it was replaced by Shiva. In one story Parvati placed Ganesha as the guard to her bathhouse to which he agreed. When Shiva came and wished to see his wife, Ganesha refused, which infuriated Shiva. The two battled until Shiva in his anger cut off Ganesha's head. When Parvati saw what Shiva had done, he apologized and hastily searched for a new head. He took the first head he saw, which was that of an elephant, and placed it on Ganesha's shoulders. In some versions of this story, Ganesha already had an elephant's head, and it was at this point that Shiva threw his trident and broke off one of his tusks.
In another story, Parvati was so proud of her new born son that she invited all the other devas to a feast so that they may see how perfect and handsome he was. Among the guests was Parvati's brother Shani, who was cursed with the evil eye. When he looked upon Ganesha his head was instantly burned to ashes. Luckily Brahma was present and agreed that he would allow Ganesha to live if the head of the first creature that was found was placed on his shoulders. Vishnu sent out Garuda to search for a head, and he returned with the head of an elephant. The head was placed on Ganesha's shoulders, and he was allowed to live again.
"Origin: India. The son of Shiva. He is a god of wisdom and good fortune, and has an elephant's head. He is said to remove obstacles and bring about wealth. He is depicted with four arms, mounted on an enormous mouse."
"The elephant-headed god in Hindu mythology. He was originally created by Parvati out of dirt to prevent anyone watching her bathe. Shiva knocked his head off, but replaced it with an elephant's head."
—Shin Megami Tensei III: Nocturne Compendium
Ganesha can be obtained by evolving Purski when he has reached a high enough level.
"A god of wisdom and good luck in Indian mythology. He is the son of the supreme god Shiva and his wife Parvati, the goddess of good luck. He is said to protect against disasters, bestow wisdom, and bring wealth and fortune. For this reason, many Indian restaurants have statues or pictures of Ganesha. In Japan, Ganesha is known as Kankiten or Seiten. He is often depicted with an elephant's head and four arms. Ganesha was originally a young man created by Parvati from her own filth to guard against Shiva seeing her bathe. But when Shiva returned one day to find his path blocked by Ganesha, he cut the youth's head off, not knowing who he was. Seeing this, Parvati was stricken with grief, and Shiva, in panic, cut off the head of a passing elephant and placed it on Ganesha's shoulders. Ganesha was not happy with this, but came to accept it after being given a variety of powers. Each god in Indian mythology is said to have his or her own mount to ride, Ganesha's is a mouse."
—Shin Megami Tensei IMAGINE Compendium
Ganesha can be contracted on Shinagawa field. He appears as a miniboss with Shiva.
"The elephant-headed god in Hindu myth. He was originally created by Parvati to prevent anyone from watching her bathe. Shiva batted his head off, but replaced it with an elephant's head."
—Persona 4 Compendium
Ganesha is a Persona of the Star Arcana that can be found in Shuffle Time in the Heaven dungeon.
The second-last request that Margaret makes for her Social Link is for a Ganesha with the Tetrakarn skill. This can be achieved by either of two Fusion options. Firstly, the player may opt to fuse a Decarabia with a Cu Chulainn. Secondly, the player may opt to perform a Hexagon Fusion with a Mithra , a Yatsufusa, a Decarabia, a Kaiwan, a Neko Shogun and a Fuu-ki.
"An elephant-headed god of knowledge, learning, wealth, and prosperity in Hindu lore. He is the son of Shiva and Parvati. He is depicted with the head of an elephant. Originally Parvati created him to stop anyone from watching her bathe. Shiva batted his head off but replaced it with an elephant's head, resulting in his current form. Because he destroys obstacles and brings about good fortune and success, he is popular with merchants. He is also known as Vinayaka in Japanese Buddhism."