Characters in GAP

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Having a character of a representation $V$ over a finite group in characteristic zero, how to obtain the characters of symmetric or exterior powers of $V$ in GAP?

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You are searching for he commands SymmetricParts(tbl,characterlist,exponent), respectively AntiSymmetricParts for exterior powers. See the manual https://www.gap-system.org/Manuals/doc/ref/chap72.html#X85CE68CA87CA383A

for more details. Your character table needs to know suitable power maps.