n=4の時は回転が
(cosθ,-sinθ,0,0)
(sinθ,cosθ,0,0)
(0,0,cosθ,-sinθ)
(0,0,sinθ,cosθ)
でimproperな回転が
(cosθ,sinθ,0,0)
(sinθ,-cosθ,0,0)
(0,0,cosθ,sinθ)
(0,0,sinθ,-cosθ)

n=5の時は回転が
(1,0,0,0,0)
(0,cosθ,-sinθ,0,0)
(0,sinθ,cosθ,0,0)
(0,0,0,cosθ,-sinθ)
(0,0,0,sinθ,cosθ)
でimproperな回転が
(-1,0,0,0,0)
(0,cosθ,-sinθ,0,0)
(0,sinθ,cosθ,0,0)
(0,0,0,cosθ,-sinθ)
(0,0,0,sinθ,cosθ)

n=6の時は回転が
(cosθ,-sinθ,0,0,0,0)
(sinθ,cosθ,0,0,0,0)
(0,0,cosθ,-sinθ,0,0)
(0,0,sinθ,cosθ,0,0)
(0,0,0,0,cosθ,-sinθ)
(0,0,0,0,sinθ,cosθ)
でimproperな回転が
(cosθ,sinθ,0,0,0,0)
(sinθ,-cosθ,0,0,0,0)
(0,0,cosθ,sinθ,0,0)
(0,0,sinθ,-cosθ,0,0)
(0,0,0,0,cosθ,sinθ)
(0,0,0,0,sinθ,-cosθ)

n=7の時は回転が
(1,0,0,0,0,0,0)
(0,cosθ,-sinθ,0,0,0,0)
(0,sinθ,cosθ,0,0,0,0)
(0,0,0,cosθ,-sinθ,0,0)
(0,0,0,sinθ,cosθ,0,0)
(0,0,0,0,0,cosθ,-sinθ)
(0,0,0,0,0,sinθ,cosθ)
でimproperな回転が
(-1,0,0,0,0,0,0)
(0,cosθ,-sinθ,0,0,0,0)
(0,sinθ,cosθ,0,0,0,0)
(0,0,0,cosθ,-sinθ,0,0)
(0,0,0,sinθ,cosθ,0,0)
(0,0,0,0,0,cosθ,-sinθ)
(0,0,0,0,0,sinθ,cosθ)

:

となるのですね。