Orbit invariants and an application to the Baby monster

We prove that the minimal base size for the permutation action of the sporadic simple Baby monster group B on the cosets of its 7th and 8th maximal subgroup (in decreasing order of size) is 3 and 2 respectively. Motivated by the large sizes of these permutation actions, we develop new computational methods to prove that an orbit is regular and to show that two orbits are disjoint.