射影線型群
| PGL  ( n , q ) | = q n ( n − 1 ) / 2 ∏ i = 2 n ( q i − 1 ) / ( q − 1 ) , | PSL  ( n , q ) | = q n ( n − 1 ) / 2 ∏ i = 2 n ( q i − 1 ) / d , d = ( n , q − 1 ) . {\displaystyle {\begin{aligned}\vert \operatorname {PGL} (n,q)\vert &=q^{n(n-1)/2}\prod _{i=2}^{n}(q^{i}-1)/(q-1),\\\vert \operatorname {PSL} (n,q)\vert &=q^{n(n-1)/2}\prod _{i=2}^{n}(q^{i}-1)/d,\qquad d=(n,q-1).\end{aligned}}}