NIKOLAUS and Sporadic Simple Groups

For this puzzle you need some knowledge about character values of sporadic simple groups. It is allowed to use the ATLAS or GAP to find a solution.

If you want to give a talk at this years Nikolaus conference you can win extra 5 minutes by solving this puzzle. But you are also invited to try it when you don't want the extra minutes or even don't come to the Nikolaus conference.

Step 1: Choose your favorite sporadic simple groups

To get your personal puzzle you have to choose your favorite four sporadic simple groups (multiple choices of the same group are allowed).

Number 1:     Number 2:     Number 3:     Number 4:    

I want a puzzle with: all rational character values / only character degrees.   

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