23edo and set types

I was actually working with 22edo, 23edo, and 24edo in conjunction with the Mathieu Groups, and discovered some things about isometric sets in 23-tET. My approach is to look at C(23,7) down to C(23,4) which play into Steiner S(4,7,23) in M23 finite simple sporadic group. Of course, I am most interested in M24, and next M22, but I was surpirsed by the fact that almost all set type counts here, and the isometric reductions, and final set types based on interval vectors are divisible by 11. Now this might not be surprising because the vectors in 23-edo have 11 slots (1 through 11 and 12 through 22)

But it was still kind of fun to find. Here is the table:

Div/11 Div/11 Div/11 C(23,4) 220 220 0 20 20 0 C(23,5) 759 759 0 69 69 0 C(23,6) 2244 2277 33 204 207 3 C(23,7) 5302 5412 110 482 492 10 C(23,8) 10395 10824 429 945 984 39 C(23,9) 17105 17930 825 1555 1630 75 C(23,10) 23958 25102 1144 2178 2282 104 C(23,11) 28216 29624 1408 2565.091 2693.091 128

Delta Div/11 Div/11 Div/11 220 220 0 20 20 0 759 759 0 69 69 0 2244 2277 33 204 207 3 C(23,7) 5302 5412 110 482 492 10 C(23,8) 10395 10824 429 945 984 39 C(23,9) 17105 17930 825 1555 1630 75 C(23,10) 23958 25102 1144 2178 2282 104 C(23,11) 28216 29624 1408 2565.091 2693.091 128

I could not delete the second paste. These yahoo groups are absolutely horrid now, what in the hell did they do to this site? Anyway, the reason 23-tET sets divide by 11 is due to the fact that the Affine(23) group or Z/23x group has 22 elements, the way Z/22x has 10. So in the first case division by 11 or 22 is common and in 22 by 5 or 10