A class of 2-groups admitting an action of the symmetric group of degree 3

Kieran Roberts, Sergey Shpectorov

A biextraspecial group of rank $m$ is an extension of a special 2-group $Q$ of the form $2^{2+2m}$ by $L\cong L_2(2)$, such that the 3-element from $L$ acts on $Q$ fixed-point-fr…