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 ?