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What is the order of $Aut(PSL(3,4))$?

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Gap computes in in a couple seconds, or find it in the Atlas

The outer automorphism group is D12, the full automorphism group has order 12*20160.

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Or use the theory of automorphism groups of Chevalley groups. There is a diagonal automorphism of order $(3,4-1) = 3$, a field automorphism of order 2 (since $4=2^2$) and a graph automorphism of order 2. – Derek Holt Jun 19 '12 at 21:32

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