On the Automorphism Group of a Binary Self-Dual Doubly Even $[{72, 36, 16}]$ Code

We prove that the automorphism group of a binary self-dual doubly even [72, 36, 16] code has order 5, 7, 10, 14 or
d
where
d
divides 18 or 24, or it is
A
₄
×
C
₃
.