If G is a finite group and H, K are subgroups of G, then how many H\G/K double cosets are there?
this is a good question! the only formula for the number of double cosets of i know is in terms of the conjugacy classes of that is if are the conjugacy classes of
then the number of double cosets of is equal to: you should check this formula for the special case when or is normal. note that if, for example
is normal, then thus: