To check if at least one is checked:
$(".classname:checked", container).length > 0
"container" is the (optional) container element.
If you want to avoid using class names for grouping, you should simply give each checkbox the same name:
<input type="checkbox" name="group1" value="1" />
<input type="checkbox" name="group1" value="2" />
<input type="checkbox" name="group1" value="3" />
Then you can change the test code to:
$("[name=group1]:checked").length > 0
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