Soccer Mania

The Clay's Bar Premier Soccer League has 20 teams, each of whom plays every other team twice, so every team plays 38 games. If the match ends in a win, the winning team gets 3 points and the losing team 0 in the standings. A tie gives both teams 1 point each. The league winner is the team with the highest total points.

In 2016, Lester City won the league with 77 points, edging out Mean City and Totty Hipsters who had 75 points each (defending champion Cheesy finished in 12\(^\text{th}\) place with a mere 51 points).

In the course of winning the league, did Lester City go undefeated?

Note: Ties do not count as defeats.

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