A push-to-talk (“PTT”) group call system, for use as, e.g., a public safety wireless network, includes a CDMA-based 1x-EVDO radio access network operably connected to a PTT server over an IP network. The radio access network includes base stations for radio communications with a number of distributed mobile stations. In carrying out wireless communications, the group call system combines IP-based voice and other real-time multimedia services with the 1x-EVDO radio access network's Broadcast Multicast Service. This allows a number of users to receive the same copy of an IP-based media stream for point-to-multipoint, group transmissions. To reduce call setup times, the group call system uses “standing” call groups, which are ongoing group communication channels pre-established between the PTT server and authorized group users. Thus, mobile stations link to one or more standing call groups of interest upon power-up, prior to users speaking.