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Nov 14 at 17:47 comment added lin @Dave, thanks a lot for your example! I revised the matrix to be valued in $\mathbb Q$.
Nov 14 at 16:22 history edited Dave Benson CC BY-SA 4.0
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Nov 14 at 16:22 comment added Geoff Robinson So the group $G$ in your example is $S_{3}$ acting naturally on $\{1,2,3\}$ and fixing $\{4,5,6\}$ elementwise?
Nov 14 at 16:06 history answered Dave Benson CC BY-SA 4.0