= Projective special linear group over the field with five elements
{title2=$PSL_2(5)\cong A_5$}
= PSL2 over F5
{c}
{synonym}
The <special linear group> $SL_2(5)$ has $24$ nonzero first columns and five second columns giving determinant one, hence order $120$; its centre is $\{I,-I\}$. In the quotient by this centre, the nonidentity <conjugacy classes> have sizes $15,20,12,12$, corresponding to projective element orders $2,3,5,5$. These arise from trace zero, paired traces $\pm1$, and paired unipotent traces $\pm2$. No proper union of these classes with the identity has size dividing $60$, so the quotient is simple. The <simple groups with order a power of two times fifteen> result identifies it with $A_5$.
Back to article page
