One of the most important innovations to Greek tragedy was the use of dramatic irony. In fact, dramatic irony may be the single most employed dramatic device in all of drama. Irony represents the gap between two things that are true and at the same time ought "not" to be true. The greater the gap, the greater the irony. Dramatic irony is something a bit more specific and was used by Sophocles, according to Aristotle, to great dramatic effect. Dramatic irony creates suspense through the fact that the audience knows more than the characters do. Hence, everyone knows that Oedipus is guilty. He is even told this by the blind prophet. Dramatic irony works to create suspense even though we already know the truth. In a film like "Titanic," for instance, everyone goes in knowing the ship will sink. Everyone knows except the characters in the movie. They are blissfully if fatally ignorant. Or with a horror film like "Halloween," where all the children are happily out getting their trick or treats while the monster lurks in the shadows. We know but the characters do not. Ironically, this knowledge creates great suspense in the audience. This knowledge would seem to drain the suspense but it actually enhances it. Sophocles knew this well and "Oedipus Rex" gives us one ironic event after another. Indeed party of Oedipus pride stems from his denials which we know to be untrue.
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In Sophocles' "Oedipus Rex" all the things you are looking for, character, irony, and conflict can all be boiled down to one simple statement: Oedipus, the protagonist, inadvertently kills his father and marries his mother.
The irony is that his father had learned from an oracle that his son was destined to kill him, so he decides to literally take fate into his own hands by abandoning his infant son and leaving the boy to die.
But Oedipus does not die. He if found, and grows up strong and healthy. One day, he encounters his father (whom he does not know is his father). An argument ensues, and Oedipus kills the man. Not much later, he ends up marrying his mother, the now widow of his father, again, of course, not knowing that she is his mother.
Fate has not been avoided, thus the irony and conflict, all rolled up into one.