It's not really a grass at all. It's called purple nutsedge (Cyperus rotundus) and along with its sister, yellow nutsedge (Cyperus esculentus), is one of the most difficult weeds in the world to successfully eradicate. You can't just pull it because it's got deep root systems connected by tubers ("nuts"), so you have to carefully dig down and get the nut(s).
We've been faithfully extracting these cockroaches by hand one by one every week for almost a year, except for a break in winter, and have reduced our front yard's overwhelming nutsedge population by about 95 percent.
We'll have to continue weekly or monthly extraction forever, but at least we're seeing some results without resorting to poisons, which aren't very effective on established nutgrass and require repeated applications. And even then you would have to dig out the deepest nuts by hand in your now-poisonous soil.
See how that middle one broke into three parts to try to trick us?
Here's one that grew all the way through a piece of hardwood mulch!