The general orthogonal group is the Subgroup of all elements of the Projective General Linear Group that fix the particular nonsingular Quadratic Form . The determinant of such an element is .
See also Projective General Linear Group
Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A.
``The Groups , ,
, and .'' §2.4 in
Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England:
Clarendon Press, pp. xi-xii, 1985.