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Sep 4, 2014 at 1:09 comment added mme I checked, and unfortunately the reference you've listed only seems to compute the 2-primary part as well.
May 17, 2013 at 11:04 comment added Trimok @Mark : Yes, I understand this is not the final answer...
May 17, 2013 at 11:01 comment added Mark Grant @Trimok: Good find! Note that this is only supposed to be the $2$_primary part; there may be other summands of the form $\mathbb{Z}_{p^n}$ with $p$ an odd prime.
May 17, 2013 at 10:29 comment added Trimok I don't know if it is the correct result, but it seems that the answer should be $Z_2 + Z_2 + Z_2 + Z_2$ (Found page 204, in 1st paper reference below) Nobuyuki Oda, On the 2.Components of the Unstable Homotopy Groups of Spheres I. Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 53, Number 7 (1977), 215-218. 1st paper
May 17, 2013 at 9:34 comment added Trimok The beginning of the article can apparently be read on Google Books
May 17, 2013 at 9:04 history answered Mark Grant CC BY-SA 3.0