A minimal set of generators for the cohomology is:
w
2
(r
6
) of degree 2
w
2
(r
8
) of degree 2
w
1
(r
3
) of degree 1
w
1
(r
8
) of degree 1
The Steenrod operations are as follows:
Sq
1
(w
2
(r
6
)) = 0
Sq
1
(w
2
(r
8
)) = w
2
(r
8
)w
1
(r
8
)
Here is a minimal system of equations:
(1) w
1
(r
8
)
2
= 0
(2) w
1
(r
3
)
2
+ w
1
(r
3
)w
1
(r
8
) = 0
Stiefel-Whitney classes:
w
1
(r
1
) = w
1
(r
8
)
w
1
(r
2
) = w
1
(r
3
) + w
1
(r
8
)
w
1
(r
3
) = w
1
(r
3
)
w
2
(r
4
) = w
2
(r
6
) + w
1
(r
3
)
2
w
2
(r
6
) = w
2
(r
6
)
w
1
(r
8
) = w
1
(r
8
)
w
2
(r
8
) = w
2
(r
8
)
w
4
(r
9
) = w
2
(r
6
)
2
+ w
2
(r
8
)
2
Chern classes:
c
1
(r
1
) = 0
c
1
(r
2
) = w
1
(r
3
)
2
c
1
(r
3
) = w
1
(r
3
)
2
c
1
(r
4
) = w
2
(r
6
) + w
1
(r
3
)
2
c
1
(r
5
) = w
2
(r
6
) + w
1
(r
3
)
2
c
1
(r
6
) = w
2
(r
6
)
c
1
(r
7
) = w
2
(r
6
)
c
1
(r
8
) = 0
c
2
(r
8
) = w
2
(r
8
)
2
c
2
(r
9
) = w
2
(r
6
)
2
+ w
2
(r
8
)
2
The algebra of Milnor constants is generated by:
c
1
(r
2
) + c
1
(r
4
)
c
1
(r
2
)
c
2
(r
8
)
w
2
(r
8
)w
1
(r
3
)w
1
(r
8
) which is not a combination of Chern classes; it is nilpotent of order 2
The results above have been produced during the second run in April, 2008.