Who is Agave (from The Bacchae) from Euripides V and what is their importance?

Agave is Pentheus' mother and Cadmus' daughter. She is driven insane by Dionysus, and and she lives her life roaming the mountainside, reveling and performing miraculous feats under the influences of the deity. When Pentheus comes to the mountain, Agave spots him. Under Dionysus' influence, Agave leads the attack of women, who tear her son to pieces. After Pentheus' murder, Agave is still insane, believing she's killed a mountain lion rather than her son. She carries his head back to Thebes on her wand, but when she finally comes out of her deluded state, she is horrified by her actions. Despite the fact that Dionysus inspired her to murder, he punishes her by banishment from Thebes.