Semidihedral groups SD_2ⁿ

A semidihedral or a quasidihedral group SD_2ⁿ is a semidirect product C_2^n-1⋊C₂, as is the dihedral group, except that C₂ acts on C_2^n-1 as x↦x^{2^n-2-1} instead of x↦x^-1. See Extensions - example.