Context : Aims : The BL Lac object RGB 1745+398 lies in an environment that makes it possible to study the cluster around it more deeply than the environments of other BL Lac objects . The cluster centered on the BL Lac works as a strong gravitational lens , forming a large arc around itself . The aim of this paper is to study the environment and characteristics of this object more accurately than the environments of other BL Lac objects have been before . Methods : We measured the redshifts of galaxies in the cluster from the absorption lines in their spectra . The velocity dispersion was then obtained from the redshifts . The gravitational lensing was used for measuring the mass at the center of the cluster . The mass of the whole cluster could then be estimated using the softened isothermal sphere mass distribution . Finally , the richness of the cluster was determined by counting the number of galaxies near the BL Lac object and obtaining the galaxy-BL Lac spatial covariance function , B _ { gb } . Results : The redshifts of nine galaxies in the field were measured to be near the redshift of the BL Lac object , confirming the presence of a cluster . The average redshift of the cluster is 0.268 , and the velocity dispersion \left ( 470 ^ { +190 } _ { -110 } \right ) km s ^ { -1 } . The mass of the cluster is M _ { 500 } = \left ( 4 ^ { +3 } _ { -2 } \right ) \times 10 ^ { 14 } M _ { \sun } which implies a rather massive cluster . The richness measurement also suggests that this is a rich cluster : the result for covariance function is B _ { gb } = \left ( 600 \pm 200 \right ) Mpc ^ { 1.77 } , which corresponds to Abell richness class 1 and which is consistent with the mass and velocity dispersion of the cluster . Conclusions :