What is a person called that came to power outside of constitutional or legal means in Greece?

Tyrant.

They usually arose as a political solution when there was irreconcilable strife in a state, and set out to settle the political problems and rule benevolently. However in such circumstances there were losers, who did not appreciate the tyranny, and tried to overthrow it. To stay in power, tyrants had to have a bodyguard, and to pay for that they had to tax, which reduced their popularity even amongst those who had supported them.

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