PGL(2,C)

In this page, there is a list of all finite groups of $\rm{PGL}(2,\mathbb{C})$ acting on Project space $\mathbb{P}^1$.

It is well known that a finite subgroup of $\rm{PGL}(2,\mathbb{C})$ is isomorphic to one of the following groups:

• a cyclic group $C_n$;
• a dihedral group $D_{n}$ of order $2n$, $n \geq 2$;
• the tetrahedral group $A_4$ of order 12;
• the octahedral group $S_4$ of order 24;
• the icosahedral group $A_5$ of order 60.

The explicit generators of group $G$ and the Burnside symbol of $G$ acting on $\mathbb{P}^1$ are given in the following pages:

• Cyclic group $C_n$
• Dihedral group $D_n$
• Tetrahedral group $A_4$
• Octahedral group $S_4$
• Icosahedral group $A_5$