You can use the :checkbox and :checked pseudo-selectors and the .class
selector, with that you will make sure that you are getting the right elements, only checked checkboxes with the class you specify.
Then you can easily use the Traversing/map method to get an array of values:
var values = $('input:checkbox:checked.group1').map(function () {
return this.value;
}).get(); // ["18", "55", "10"]