Do not use a group! It will mess things up in your case.
Fist, set the default values of the check boxes in the property window.
Then go to the code window in the class module of the form.
Find in the left drop-down the first check box. Once clicked, the event code will be placed in the code window. Add to that code and IF statement, checking the value of the check box and then the names of the other 2 check boxes with their vale properties. Set the value properties to what you want.
Something like:
Private Sub CheckBox1_Click()
If CheckBox1.Value = True Then
CheckBox2.Value = False
CheckBox3.Value = True
End If
End Sub
Which also could be written like:
Private Sub CheckBox1_Click()
CheckBox2.Value =Not CheckBox1.Value
CheckBox3.Value = CheckBox1.Value
End Sub
Do the same thing for the other 2 check boxes, setting the values accordingly.
Now, what you will have to do is decide what happens to the check boxes when you change records. You can add the Form_Current event to the code window as well and set the values of the check boxes according, based on the value(s) of the other check box(es). Normally, if these are bound controls, the values in the fields should already reflect the business rules, and therefore the checkboxes should already have the correct values, but as an extra safe guard you can set the values in the Form_Current event.