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This follows a similar pattern to how tabs are moved left/right: https://cs.chromium.org/chromium/src/chrome/browser/ui/views/tabs/tab_strip.cc?l=1591&rcl=3e23198594e08a63cc5e091e1eefe79e3dd48454

I deliberately chose not to support MoveGroupFirst() and MoveGroupLast(), since the implementation seemed too finicky and the feature seemed very niche. We can return to it if we decide it's higher priority for accessibility.

Bug: 1039921
Change-Id: Ifcd078d640a84fe96f15c41a38daa82a5090641c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2006219
Commit-Queue: Connie Wan <connily@chromium.org>
Reviewed-by: Taylor Bergquist <tbergquist@chromium.org>
Cr-Commit-Position: refs/heads/master@{#734224}