Abstract Recently, Beierle and Leander found two new sporadic quadratic APN permutations in dimension 9. Up to EA-equivalence, we present a single trivariate representation of those two permutations as C u:(F 2 m) 3→(F 2 m) 3,(x, y, z)↦(x 3+ u y 2 z, y 3+ u x z 2, z 3+ u x 2 y), where m= 3 and u∈ F 2 3∖{0, 1} such that the two permutations correspond to different choices of u. We then analyze the differential uniformity and the nonlinearity of C u in a more general case. For m≥ 3 being a multiple of 3 and u∈ F 2 m not being a 7-th power, we show that the differential uniformity of C u is bounded above by 8, and that the linearity of C u is bounded above by 8 1+⌊ m 2⌋. Based on numerical experiments, we conjecture that C u is not APN if m is greater than 3. We also analyze the CCZ-equivalence classes of the quadratic APN permutations in dimension 9 known so far and derive a lower bound on the number of their EA-equivalence classes. We further show that the two sporadic APN permutations share an interesting similarity with Gold APN permutations in odd dimension divisible by 3, namely that a permutation EA-inequivalent to those sporadic APN permutations and their inverses can be obtained by just applying EA transformations and inversion to the original permutations.