diff --git a/.gitignore b/.gitignore
index d21b35f57..058d8cf4e 100644
--- a/.gitignore
+++ b/.gitignore
@@ -5,3 +5,7 @@ last.png
 diff.png
 /test/screenshotter/tex/
 /test/screenshotter/diff/
+/test/symgroups.tex
+/test/symgroups.aux
+/test/symgroups.log
+/test/symgroups.pdf
diff --git a/src/symbols.js b/src/symbols.js
index 62b9ecb29..e5b1fd471 100644
--- a/src/symbols.js
+++ b/src/symbols.js
@@ -920,22 +920,22 @@ var symbols = {
         // AMS Delimiters
         "\\ulcorner": {
             font: "ams",
-            group: "textord",
+            group: "open",
             replace: "\u250c"
         },
         "\\urcorner": {
             font: "ams",
-            group: "textord",
+            group: "close",
             replace: "\u2510"
         },
         "\\llcorner": {
             font: "ams",
-            group: "textord",
+            group: "open",
             replace: "\u2514"
         },
         "\\lrcorner": {
             font: "ams",
-            group: "textord",
+            group: "close",
             replace: "\u2518"
         },
 
@@ -2172,12 +2172,12 @@ var symbols = {
         },
         "\\barwedge": {
             font: "ams",
-            group: "textord",
+            group: "bin",
             replace: "\u22bc"
         },
         "\\veebar": {
             font: "ams",
-            group: "textord",
+            group: "bin",
             replace: "\u22bb"
         },
         "\\odot": {
@@ -2207,12 +2207,12 @@ var symbols = {
         },
         "\\circledcirc": {
             font: "ams",
-            group: "textord",
+            group: "bin",
             replace: "\u229a"
         },
         "\\boxdot": {
             font: "ams",
-            group: "textord",
+            group: "bin",
             replace: "\u22a1"
         },
         "\\bigtriangleup": {
@@ -2327,32 +2327,32 @@ var symbols = {
         },
         "\\uparrow": {
             font: "main",
-            group: "textord",
+            group: "rel",
             replace: "\u2191"
         },
         "\\Uparrow": {
             font: "main",
-            group: "textord",
+            group: "rel",
             replace: "\u21d1"
         },
         "\\downarrow": {
             font: "main",
-            group: "textord",
+            group: "rel",
             replace: "\u2193"
         },
         "\\Downarrow": {
             font: "main",
-            group: "textord",
+            group: "rel",
             replace: "\u21d3"
         },
         "\\updownarrow": {
             font: "main",
-            group: "textord",
+            group: "rel",
             replace: "\u2195"
         },
         "\\Updownarrow": {
             font: "main",
-            group: "textord",
+            group: "rel",
             replace: "\u21d5"
         },
         "\\coprod": {
@@ -2447,7 +2447,7 @@ var symbols = {
         },
         "\\ldots": {
             font: "main",
-            group: "punct",
+            group: "inner",
             replace: "\u2026"
         },
         "\\cdots": {
diff --git a/test/symgroups.js b/test/symgroups.js
new file mode 100644
index 000000000..70664d34c
--- /dev/null
+++ b/test/symgroups.js
@@ -0,0 +1,151 @@
+"use strict";
+
+var fs = require("fs");
+var childProcess = require("child_process");
+
+var opts = require("nomnom")
+    .option("spacing", {
+        flag: true,
+        help: "Print mismatches involving spacing commands"
+    })
+    .parse();
+
+var symbols = require("../src/symbols");
+var keys = Object.keys(symbols.math);
+keys.sort();
+var types = [
+    "mathord", "op", "bin", "rel", "open", "close", "punct", "inner",
+    "spacing", "accent", "textord"
+];
+
+process.nextTick(writeTexFile);
+
+function writeTexFile() {
+    var tex = fs.createWriteStream("symgroups.tex");
+    tex.on("finish", typeset);
+    tex.write("\\documentclass{article}\n" +
+              "\\usepackage{textcomp,amsmath,amssymb,gensymb}\n" +
+              "\\begin{document}\n" +
+              "\\showboxbreadth=\\maxdimen\\showboxdepth=\\maxdimen\n\n");
+    keys.forEach(function(key, idx) {
+        var sym = symbols.math[key];
+        var type = types.indexOf(sym.group) + 1;
+        tex.write("$" + idx + "+" + key + "+" + type + "\\showlists$\n\n");
+    });
+    tex.end("\\end{document}\n");
+}
+
+function typeset() {
+    var proc = childProcess.spawn(
+        "pdflatex", ["--interaction=nonstopmode", "symgroups"],
+        {stdio: "ignore"});
+    proc.on("exit", function(code, signal) {
+        if (signal) {
+            throw new Error("pdflatex terminated by signal " + signal);
+        }
+        fs.readFile("symgroups.log", "ascii", evaluate);
+    }).on("error", function(err) {
+        throw err;
+    });
+}
+
+/* Consider the symbol "\sim" as an example. At the time of this
+ * writing, it has index 431 in our list, and is of group "rel" which
+ * is the fourth of the types listed above. So we construct an input line
+ * $431+\sim+4\showlists$ and receive corresponding output
+ *
+ * ### math mode entered at line 870
+ * \mathord
+ * .\fam0 4
+ * \mathord
+ * .\fam0 3
+ * \mathord
+ * .\fam0 2
+ * \mathbin
+ * .\fam0 +
+ * \mathrel
+ * .\fam2 '
+ * \mathbin
+ * .\fam0 +
+ * \mathord
+ * .\fam0 4
+ * ### horizontal mode entered at line 870
+ *
+ * This is what we parse, using some regular expressions.
+ */
+
+// Extract individual blocks, from switch to math mode up to switch back.
+var reMM = /^### math mode entered.*\n([^]*?)###/mg;
+
+// Identify the parts separated by the plus signs
+var reParts = /([^]*^\.\\fam0 \+\n)([^]+)(\\mathbin\n\.+\\fam0 \+[^]*)/m;
+
+// Variation of the above in case we have nothing between the plus signs
+var reEmpty = /^\.\\fam0 \+\n\\mathbin\n\.\\fam0 \+/m;
+
+// Match any printed digit in the first or last of these parts
+var reDigit = /^\.\\fam0 ([0-9])/mg;
+
+// Match the atom type, i.e. "\mathrel" in the above example
+var reAtom = /\\([a-z]+)/;
+
+function evaluate(err, log) {
+    if (err) {
+        throw err;
+    }
+
+    var match, nextIndex = 0;
+    while ((match = reMM.exec(log)) !== null) {
+        var list = match[1];
+        match = reParts.exec(list);
+        if (!match) {
+            match = reEmpty.exec(list);
+            if (match) {
+                console.log(keys[nextIndex] + " (index " + nextIndex +
+                            ") in LaTeX apparently " +
+                            "doesn't contribute to the output.\n");
+                nextIndex++;
+                continue;
+            }
+            console.error("Can't split this into parts:");
+            console.error(list);
+            process.exit(2);
+        }
+        var idx = extractDigits(match[1]);
+        var atom = match[2];
+        var katexType = types[extractDigits(match[3]) - 1] || "???";
+        match = reAtom.exec(atom);
+        if (!match) {
+            console.error("Failed to find atom type");
+            console.error(atom);
+            console.error(list);
+            process.exit(3);
+        }
+        var latexType = match[1];
+        if (katexType !== latexType && "math" + katexType !== latexType &&
+            (katexType !== "textord" || latexType !== "mathord") &&
+            (katexType !== "spacing" || opts.spacing)) {
+            console.log(keys[idx] + " (index " + idx + ") has '" + katexType +
+                        "' in KaTeX, but LaTeX uses '" + latexType + "':");
+            console.log(atom);
+        }
+        if (nextIndex !== idx) {
+            console.error("Index " + nextIndex + " not found in log");
+            process.exit(4);
+        }
+        nextIndex = idx + 1;
+    }
+    if (nextIndex !== keys.length) {
+        console.error("Processed " + nextIndex +
+                      " out of " + keys.length + " symbols");
+        process.exit(4);
+    }
+}
+
+function extractDigits(str) {
+    var match, res = "";
+    while ((match = reDigit.exec(str)) !== null) {
+        res += match[1];
+    }
+    return +res;
+}