All 15 aluminum windows in my house appear to be the same manufacture except for size and weight. Twelve windows are marked 27C and your S770-27 has worked in those. I have two windows that are marked 23b which I have not replaced but it appears that your S770 series will work there too.
My confusion is with one window that weighs 26lbs. The stamp is C2340 with a "k" spaced before the C2340. It looks like a heavier duty version of your S770 series.
I'm thinking your S770-23E will work but I'm not sure.
