On groups \(G^{5,5,180}\) (Q1281273)

The authors prove that all but finitely many alternating and symmetric groups occur as homomorphic images of the group \[ G^{5,5,180}=\langle x,y,t\mid x^2=y^5=t^2=(xt)^2=(yt)^2=(xy)^5=(xyt)^{180}\rangle, \] similar to results of \textit{M. Conder} [Q. J. Math., Oxf. II. Ser. 39, No. 154, 175-183 (1988; Zbl 0686.20029)] and \textit{Q. Mushtaq, H. Servatius} [J. Lond. Math. Soc., II. Ser. 48, No. 1, 77-86 (1993; Zbl 0737.20020)].