The rotation group can be thought of as \(3\times 3\) matrices \(R\) that satisfies \(I = R^{T}IR\), while the Lorentz group is \(\eta = \Lambda^{T}\eta\Lambda\), where \(I\) is the Euclidean metric and \(\eta\) is Lorentzian[1].

[1] Carroll Sean (2003). Spacetime and Geometry - an Introduction to General Relativity