The endomorphism rings of permutation modules of 3/2-transitive permutation groups

Recent classification of 3/2-transitive permutation groups leaves us with six families of groups which are $2$-transitive, or Frobenius, or one-dimensional affine, or the affine solvable subgroups of AGL(2, q), or special projective linear group PSL(2, q), or PΓ L(2, q), where q=2ᵖ with p prime. According to a case by case analysis, we prove that the endomorphism ring of the natural permutation module for a 3/2-transitive permutation group is a symmetric algebra.