On the Automorphism Group of a Binary Self-dual [120, 60, 24] Code

We prove that an automorphism of order 3 of a putative binary self-dual [120, 60, 24] code C has no fixed points. Moreover, the order of the automorphism group of C divides 2a ·3 ·5 ·7 ·19 ·23 ·29 with a ∈ N0. Automorphisms of odd composite order r may occur only for r = 15, 57 or r = 115 with corresponding cycle structures 3·5-(0, 0, 8; 0), 3 · 19-(2, 0, 2; 0) or 5 · 23-(1, 0, 1; 0) respectively. In case that all involutions act fixed point freely we have |Aut(C)| ≤ 920, and Aut(C) is solvable if it contains an element of prime order p ≥ 7. Moreover, the alternating group A5 is the only non-abelian composition factor which may occur.