Timeline for When is $\operatorname{Out}(G)$ isomorphic to the symmetries of the character table of $G$?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 1, 2022 at 9:09 | comment | added | Stefan Kohl♦ | The mapping $\psi$ is not always injective as it may happen that $G$ has outer automorphisms which induce the identity permutation on the set of conjugacy classes. The smallest group where this happens has order 32 -- see e.g. here. | |
| Jul 29, 2022 at 22:32 | history | edited | LSpice | CC BY-SA 4.0 |
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| Jul 29, 2022 at 22:24 | history | edited | YCor |
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| Jul 29, 2022 at 22:23 | comment | added | Benjamin Steinberg | I think it is not common for all symmetries to come from outer automorphisms. If G has exponent n and K is the cyclotomic extension obtained by adding the nth roots of unity to Q, then the Galois group of K over Q acts as symmetries of the character table and these usually don't come from automorphisms. The action is nontrivial as long as there are representations with nonrational characters. | |
| S Jul 29, 2022 at 20:59 | review | First questions | |||
| Jul 29, 2022 at 21:04 | |||||
| S Jul 29, 2022 at 20:59 | history | asked | Davi Costa | CC BY-SA 4.0 |