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For groups represented as permutations. Group transitivity, rank 3 groups, orbits and suborbits, stablizers, permutation characters, primitivity are all on-topic.

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The number of orbits of a two-point stabilizer of the symplectic group $Sp(2m,2)$

I am trying to figure out the number of orbits of a two-point stabilizer of the action of $Sp(2m,2)$ on its two orbits $\Omega^+$ and $\Omega^-$ as detailed in Dixon and Mortimer's "Permutation Groups …
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