I'm sad to say: We are sh*t out of luck on this one.
I'd like to refer you to the author of WhichBrowser: Everybody lies.
Basically, no browser is being honest. No matter if you use Chrome or IE, they both will tell you that they are "Mozilla Netscape" with Gecko and Safari support. Try it yourself on any of the fiddles flying around in this thread:
or any other... Try it with Chrome (which might still succeed), then try it with a recent version of IE, and you will cry. Of course, there are heuristics, to get it all right, but it will be tedious to grasp all the edge cases, and they will very likely not work anymore in a year's time.
Take your code, for example:
<div id="example"></div>
<script type="text/javascript">
txt = "<p>Browser CodeName: " + navigator.appCodeName + "</p>";
txt+= "<p>Browser Name: " + navigator.appName + "</p>";
txt+= "<p>Browser Version: " + navigator.appVersion + "</p>";
txt+= "<p>Cookies Enabled: " + navigator.cookieEnabled + "</p>";
txt+= "<p>Platform: " + navigator.platform + "</p>";
txt+= "<p>User-agent header: " + navigator.userAgent + "</p>";
document.getElementById("example").innerHTML=txt;
</script>
Chrome says:
Browser CodeName: Mozilla
Browser Name: Netscape
Browser Version: 5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/40.0.2214.115 Safari/537.36
Cookies Enabled: true
Platform: Win32
User-agent header: Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/40.0.2214.115 Safari/537.36
IE says:
Browser CodeName: Mozilla
Browser Name: Netscape
Browser Version: 5.0 (Windows NT 6.1; WOW64; Trident/7.0; SLCC2; .NET CLR 2.0.50727; .NET CLR 3.5.30729; .NET CLR 3.0.30729; Media Center PC 6.0; .NET4.0C; .NET4.0E; InfoPath.3; rv:11.0) like Gecko
Cookies Enabled: true
Platform: Win32
User-agent header: Mozilla/5.0 (Windows NT 6.1; WOW64; Trident/7.0; SLCC2; .NET CLR 2.0.50727; .NET CLR 3.5.30729; .NET CLR 3.0.30729; Media Center PC 6.0; .NET4.0C; .NET4.0E; InfoPath.3; rv:11.0) like Gecko
At least Chrome still has a string that contains "Chrome" with the exact version number. But, for IE you must extrapolate from the things it supports to actually figure it out (who else would boast that they support .NET
or Media Center
:P), and then match it against the rv:
at the very end to get the version number. Of course, even such sophisticated heuristics might very likely fail as soon as IE 12 (or whatever they want to call it) comes out.