| 10 ! style="width:5%" | 11 ! style="width:5%" | 12 ! style="width:5%" | 13 ! style="width:5%" | 14 ! style="width:5%" | 15 ! style="width:5%" | 16 ! style="width:5%" | 17 |- ! style="text-align:right" | | 1 || 2 || 1 || || 1 || 1 || 1 || || 2 || 2 || 1 || || 1 || 1 || 1 || || 2 || 2 |- ! style="text-align:right" | | 1 || 2 || 1 || 24 || 1 || 1 || 1 || 240 || 2 || 2 || 1 || 504 || 1 || 1 || 1 || 480 || 2 || 2 |- ! style="text-align:right" | | || 2 || 2 || 24 || 1 || 1 || 2 || 240 || 22 || 23 || 6 || 504 || 1 || 3 || 22 || 480×2 || 22 || 24 |- ! style="text-align:right" | | || || || 1⁄6 || || || || −1⁄30 || || || || 1⁄42 || || || || −1⁄30 || || |} Applications introduced the group J(X) of a space X, which for X a sphere is the image of the J-homomorphism in a suitable dimension. The cokernel of the J-homomorphism appears in the group Θn of h-cobordism classes of oriented homotopy n-spheres (). References . Homotopy theory Topology of Lie groups