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Nov 12, 2021 at 17:31 comment added Frieder Ladisch @DimaPasechnik: For $q=3$, $5$ the 8-dimensional irreps are rational (the Schur indices over Q are trivial). For $q=7$, the characters are not rational. (Sorry for the late answer, I have not been here some time).
Jun 24, 2021 at 13:43 comment added Dima Pasechnik By the way, do you know if these 8-dimensional representations of G are rational? (They do have rational characters)
Feb 17, 2011 at 9:10 vote accept Frieder Ladisch
Feb 14, 2011 at 19:33 comment added Frieder Ladisch @Noah: Indeed, I learned a lot from your answer to the other question!
Feb 14, 2011 at 19:03 comment added Noah Snyder Nice example! Sorry for the error, but at least people seemed to have learned something from it.
Feb 14, 2011 at 16:06 history answered Frieder Ladisch CC BY-SA 2.5