On the automorphism Group of a putative code

A long standing open question in coding theory is whether a binary self-dual [72,36,16] code exists. It was shown recently that the automorphism group order of such code is equal to 2
ⁱ
middot3
^j
middot5middot7, 2
ⁱ
middot3
^j
middot7, 2
ⁱ
middot3
^j
middot5, or 2
ⁱ
middot3
^j
for some nonnegative integers i and j. We show that the group order is not a multiple of 35 and find that only 22 orders are possible