I found several sources on the web, not perfectly consistent
http://www.opencourse.info/astronomy/introduction/36.universe_evolution/
[[Analysis of the data indicates that we are moving at a speed of 390 km/s towards Leo.
Taking into account our motion around the galaxy (horizontally to the right), this means that the entire galaxy must be moving at a speed of 600 km/s in the direction of Centaurus, somewhat closer to the center of this figure (in the green).]]
I still have doubts and will try for something more authoritative.
Earlier I found a 1994 announcement, but it was unclear whether they had subtracted out the sun's motion or were talking about combined motion. They say here the direction is in Leo, which sounds like the combined velocity, but they say the speed is something equivalent to 600 km/s, which sounds like the center-of-galaxy motion.
http://hubblesite.org/newscenter/archive/1994/15/text
Here is a quote from that possibly unreliable Hubblesite.org page
[[Astronomers generally assume that the diffuse glow of microwave radiation left over from the Big Bang provides the backdrop or rest frame of the universe. In the mid 70's astronomers found that temperature of this radiation is slightly hotter towards the direction of the constellation of Leo.
This effect has been interpreted to mean that the Milky Way is drifting with respect to the rest of the universe at about 380 miles per second in this direction. It has also been assumed that most of this motion is due to the gravitational attraction of more distant galaxies; however, these galaxies have never been positively identified.]]
Still need to pursue this.