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Dec 6, 2023 at 8:40 comment added YCor @gdre It is a split extension and an argument for this is given in the answer.
Dec 6, 2023 at 8:37 comment added YCor @gdre the dihedral group of order $2n$ is denoted $D_n$ or $D_{2n}$ according to authors.
Dec 6, 2023 at 8:35 comment added gdre Sorry,if $D4$ in your answer is $D8$?When $D4$ is $D8$,the extension $D8$ by $C2$ isn't split extension.
Dec 6, 2023 at 5:09 history edited Joachim König CC BY-SA 4.0
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Dec 6, 2023 at 5:02 history answered Joachim König CC BY-SA 4.0