I am running a core2duo
That could be a problem. It's not a very capable processor for this kind of media. (Though I wouldn't necessarily expect it to cause a crash.)
What exactly do you mean by "move the clips in the timeline as a group"? Do you mean a nested sequence, as you image suggests? Or do you mean grouped clips, which is something very different? Or do you mean a bunch of selected clips?
The CPU hasnt been too much of an issue before, I shot a 1hr30min documentary last year at it only lagged at the final export stage.
In saying that it isnt the best, thank God my upgrade is coming soon!
What I mean by "moving the clips in a group is..."
using the tool (right facing arrow and shift - sorry I cant remember the tool's name) and selecting every clip to the right of it, for the purposes of moving to an earlier point in the timeline to close a gap, moving clips individually is out of the question and there are too many and loads are specifically sync'd and have intricate sequencing and timings.
I havent tried 'grouping' the clips but I shouldnt need to for a simple move like this.
All I need to do is close a few gaps in the timeline.
I can't think of any reason for the crash, but to get the job done have you tried just performing a Ripple Delete?