Cohomology of the double cover of the Mathieu group \(M_{12}\)
\textit{A. Adem, J. Maginnis} and \textit{R. J. Milgram} [J. Algebra 139, No. 1, 90-133 (1991; Zbl 0743.20052)] have calculated the mod two cohomology \(H^*(M_{12},F_2)\) of the Mathieu group \(M_{12}\). In this paper, the mod two cohomology of the double cover \(2M_{12}\) of \(M_{12}\) is calculated. The authors use a hypercohomology spectral sequence to determine a differential in the Lyndon-Hochschild-Serre spectral sequence of the central extension. Ungrading the \(E_\infty\) page of the Lyndon-Hochschild-Serre spectral sequence involves recourse to some computer calculations using the MAGMA computer algebra package. The programs are designed only for computing with \(p\)-groups, so this involves restrictions to a Sylow 2-subgroup of \(2M_{12}\).
scientific article; zbMATH DE number 1441823