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So the Problem Computer (the Lenovo 580) only has a FAST ETHERNET NIC (network INterface Card) .....correct?
YOu do realize, that FAST ETHERNET is only a theoretical maximum of 100Mbps.....and is typically notated as 10/100 Mbps. YOu will never get the maximum, its only the theoratical, under 100% perfect ideal conditions......and thats not possible outside of a laboratory.....you will expect 25-50% of the max......so you getting 56Mbps....is actually good.
So.....you getting 56Mbps.....is very normal. Matter of fact is pretty good for a 10/100 NIC.
If you want a faster transfer...upgrade the NIC to a 10/100/1000 NIC.....typically called Gigabit
Then you can exceed the 100 Mbps barrior.
Unless im not understanding somethign.......but.....I can do a remote session with you....so i can take a very EXACT look at the type of hardware you are using....and run some tests......do you have some time now to do this?