Use detect.js? It's a bit big for just trying to figure out what family your browser is. There's only 4 out there (2 variations of each) and they all have custom prefixed navigator objects. Lets just look for those! Detect.js-like output in 373chars (minified).

Better than detect.js Browser family

window.detect={
  parse: function() {
    var o = 'orientation' in window, prop, br, pre=['ms', 'moz','webkit'];
    return {
      isMobile: o,
      browser: {
        family: (o? "Mobile ":"Desktop ") + (function() {
          for (prop in navigator) {
            for (br in pre) {
              if (!prop.indexOf(br)) { // IE 9 - Edge has "ms", else moz or webkit
                return br==='webkit'?(
                    ~navigator.vendor.indexOf("Google")?"Chrome":
                    ~navigator.vendor.indexOf("Apple")?"Safari":
                    "Webkit") :
                  br=="ms" ? "Internet Explorer" : "Firefox";
              }
            }
          }
          return "Unknown"
        })()
      }
    };
  }
};