Endomorphism structure of special linear group:SL(2,5)

special linear group of degree two over a finite field, i.e., $SL(2,q)$ for field of size $q$ field:F5, i.e., the group $SL(2,5)$ endomorphism structure of special linear group of degree two over a finite field
double cover of alternating group degree $n = 5$, i.e., the group $2 \cdot A_5$ endomorphism structure of double cover of alternating group