Number of groups of order $512$ with exponent $2,4,8,16,...$

Question

I want to determine the number of groups of order $512$ with exponent $2,4,8,16,32,64,128,256$ and $512$

The first $500,000$ groups in GAP give the following result :

500000  4:90031  8:366214  16:41085  32:2425  64:212  128:27  256:5  512:1

But the calculation took several hours. It is a long way to go through the $10,494,213$ groups.

Is there a method to determine the numbers faster, or does someone know an internet link, where the numbers are given ?

Answer 1

I have these data, computed for the same project that I've mentioned in another question of yours:

gap> Length(exponent512);
10494213
gap> Collected(exponent512{[1..500000]});
[ [ 4, 90031 ], [ 8, 366214 ], [ 16, 41085 ], [ 32, 2425 ], [ 64, 212 ], 
  [ 128, 27 ], [ 256, 5 ], [ 512, 1 ] ]

so exactly as in your question. Now the numbers for the full list:

gap> Collected(exponent512);
[ [ 2, 1 ], [ 4, 8791062 ], [ 8, 1656695 ], [ 16, 43767 ], [ 32, 2443 ], 
  [ 64, 212 ], [ 128, 27 ], [ 256, 5 ], [ 512, 1 ] ]