A subgroup of generated by rotations of orders 4 and 8

We prove that a subgroup of the real 3-dimensional special orthogonal group generated by a pair of rotations of respective orders 4 and 8 (belonging to a family of such groups considered by Radin and Sadun in [C. Radin, L. Sadun, On 2-generator subgroups of SO(3), Trans. Amer. Math. Soc. 351 (1999) 114469–114480]) has an epimorphic image which is one of PSL(2,p), PSL(2,p2), PGL(2,p) or PGL(2,p2) (depending on the congruence ofp ( )) for all odd primes p, by considering its reduction as a linear group.