An extremal [72,36,16] binary code has no automorphism group containing Z2xZ4, Q_8, or Z_{10}
Gabriele Nebe · arXiv (Cornell University) · 2011
Let $C$ be an extremal self-dual binary code of length 72 and $g\in \Aut(C) $ be an automorphism of order 2. We show that $C$ is a free $\F_2$ module and use this to exclude certain subgroups of order 8 of $\Aut (C)$. We also show that $\Aut(C)$ does not contain an element of order 10.