The projective special orthogonal group 
is the group obtained from
the special orthogonal group 
on factoring by the scalar matrices contained in that group.
In general, this group is not simple.
Projective Special Orthogonal Group
See also
Projective Special Linear Group, Projective Special Unitary Group, Special Orthogonal GroupExplore with Wolfram|Alpha
References
Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. "The Groups
, 
, 
, and 
, and 
." §2.4 in Atlas
of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups.
Oxford, England: Clarendon Press, pp. xi-xii, 1985.Referenced on Wolfram|Alpha
Projective Special Orthogonal GroupCite this as:
Weisstein, Eric W. "Projective Special Orthogonal Group." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProjectiveSpecialOrthogonalGroup.html