Grouping xml nodes by value of a child in Xsl

<root>
<element>
<id>1</id>
<group>first</group>
</element>

<element>
<id>2</id>
<group>second</group>
</element>


<element>
<id>3</id>
<group>first</group>
</element>
...
<root>

How I can group my elements by the group name in xslt 1.0. the output:

<root>
<group name="first">
 <element>
    <id>1</id>
    <group>first</group>
 </element>
 <element>
    <id>3</id>
    <group>first</group>
 </element>
</group>
<group name="second">
 <element>
    <id>2</id>
    <group>second</group>
    </element>
</group>
</root>

Any ideas?