A faster method to construct extraspecial normaliser subgroups

Abstract

We show how to improve the runtime of the construction of generators of maximal subgroups of $\operatorname{SL}(d, q), \operatorname{SU}(d, q)$ and $\operatorname{Sp}(d, q)$ which arise as normalisers of extraspecial groups or $2$-groups of symplectic type given by Holt and Roney-Dougal (2005) from $O(d^3\log d\log q+\log^2 q)$ to $O(d^2\log d\log^{1+\varepsilon} q+\log^{2+\varepsilon} q)$.