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fixed confusing minus size to dash
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YCor
YCor
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Let $G=\operatorname{SO}^{+}_{2n}(2)$. I did some Magma computation and found there were $3$ orbits on the natural $G$-set when $n=2,3,4$. The orbit sizes are $1-9-6, 1-35-28, 1-135-120$$1$-$9$-$6$, $1$-$35$-$28$, $1$-$135$-$120$.

Is there a formularformula for the orbit sizes in general? Thank you.

Let $G=\operatorname{SO}^{+}_{2n}(2)$. I did some Magma computation and found there were $3$ orbits on the natural $G$-set when $n=2,3,4$. The orbit sizes are $1-9-6, 1-35-28, 1-135-120$.

Is there a formular for the orbit sizes in general? Thank you.

Let $G=\operatorname{SO}^{+}_{2n}(2)$. I did some Magma computation and found there were $3$ orbits on the natural $G$-set when $n=2,3,4$. The orbit sizes are $1$-$9$-$6$, $1$-$35$-$28$, $1$-$135$-$120$.

Is there a formula for the orbit sizes in general? Thank you.

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user488802
user488802
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Orbit sizes of $G=\operatorname{SO}^{+}_{2n}(2)$

Let $G=\operatorname{SO}^{+}_{2n}(2)$. I did some Magma computation and found there were $3$ orbits on the natural $G$-set when $n=2,3,4$. The orbit sizes are $1-9-6, 1-35-28, 1-135-120$.

Is there a formular for the orbit sizes in general? Thank you.