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This question is copied from math.stackexchange, in hope that it might get some attension.

I want to understand the proof of

There is a projective representation of $A_6 \hookrightarrow PSU(3).$

I am looking for a reference, but could not find. Suggestions are welcome.

EDIT: We have a central extension: $$0 \to C_3 \hookrightarrow \hat{A}_6 \twoheadrightarrow A_6 \to 0. $$ From a result of Schur, the determining the projective representation reduces to determining a linear representation from the central group extension $$\hat{A}_6 \to SU(3).$$ Now I don't know what the next step should be.

A reference will be very helpful to me.

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