radio button with no option

HTML

<input type="radio" name="group" class="no_option" value="0">option 0<br>
<input type="radio" name="group" class="no_option" value="1">option 1<br>
<input type="radio" name="group" class="no_option" value="2">option 2<br>
<input type="radio" name="group" class="no_option" value="3">option 3<br>
<input type="radio" name="group" class="no_option" value="4">option 4<br>
<input type="radio" name="group" class="no_option" value="5">option 5<br>
<input type="radio" name="group" class="no_option" value="6">option 6<br>
<input type="radio" name="group" class="no_option" value="null" style="display:none">

JavaScript

var checked_val = "null";
$(".no_option").on("click", function(){
  if($(this).val() == checked_val){
  	$('input[name=group][value=null]').prop("checked",true);
    checked_val = "null";
  }else{
  	checked_val = $(this).val();
    $('input[name=group][value=null]').propRemove("checked");
  }
});