Magma V2.23-9 Sat Jun 6 2020 13:17:10 on hegel [Seed = 1777134281]
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| This copy of Magma has been made available through a |
| generous initiative of the |
| |
| Simons Foundation |
| |
| covering U.S. Colleges, Universities, Nonprofit Research entities,|
| and their students, faculty, and staff |
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Type ? for help. Type -D to quit.
##########################
begin first computation
the first part of this code computes the action of G=PSp_4(F_3)
on M = H^2(X,Z) simeq Z^61. The explicit matrices x and y giving
this action are printed below
[Warning! matrices in Magma act on the right!]
[-4 2 2 -1 2 -1 -4 5 2 -5 2 2 5 2 -5 -2 8 -1 -4 2 -1 -1 3 -1 1 -4 -4 -1 -1 1 3 1
-1 1 -1 -1 0 0 -3 1 1 1 -1 2 -2 -2 1 -3 3 0 5 -1 -1 3 2 -1 0 -2 -1 -4 2]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-3 2 2 -1 2 0 -3 4 1 -3 1 1 3 3 -4 -1 7 -1 -3 2 -2 -1 2 -1 1 -4 -4 -1 -1 1 3 1
-1 1 -1 -1 0 0 -3 1 1 1 -1 2 -2 -2 1 -2 2 0 4 0 -1 3 2 -1 -1 -1 -1 -3 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-6 -3 6 -3 3 9 0 -6 -3 6 -6 3 -3 3 6 3 -3 0 -3 0 3 -1 -3 -2 0 3 -6 2 -3 1 -3 3
0 -2 -3 -2 3 0 0 1 3 2 -1 6 4 0 3 0 -2 0 -4 2 -3 -2 0 -3 0 7 -3 -1 -1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 -1 -1 1 -1 0 -1 -1 2 1 -2 1 0 -1 1 0 0 0 0 1 1 0 0 0 -1 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0 0 -1 0 -1 0 0 -1 -1 0 0 1 0 1 0]
[-6 6 3 0 3 -9 -12 18 9 -18 12 0 15 3 -18 -9 24 0 -6 3 -6 -2 9 -1 3 -12 -6 -4 -3
3 9 1 -3 4 0 -1 -3 3 -9 2 0 1 -2 0 -8 -5 -1 -8 11 -2 16 -3 0 9 5 1 -1 -10 2
-11 5]
[-6 0 6 -3 3 6 -3 -3 -3 3 -3 3 0 3 3 3 3 0 -6 0 0 -1 0 -2 0 0 -6 1 -3 2 0 3 -2 0
-3 -2 3 0 -3 1 3 2 -1 6 2 -1 3 -2 0 0 0 1 -3 0 1 -3 -1 5 -3 -2 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 3 0 0 0 -3 -3 6 3 -6 3 0 3 3 -6 -3 9 0 -3 3 -3 -1 3 0 1 -6 -3 -2 0 1 3 0 -1 2
0 -1 0 0 -3 1 0 1 0 0 -3 -2 0 -2 3 0 5 -1 0 4 3 0 -1 -4 0 -3 1]
[0 3 0 1 1 -3 -3 5 2 -5 3 -1 4 1 -5 -1 8 -1 -2 2 -3 -1 3 0 1 -5 -2 -2 0 1 3 0 -1
2 0 0 -1 0 -3 0 0 0 0 0 -3 -2 0 -2 3 0 5 -1 0 3 2 0 -1 -3 0 -2 1]
[0 0 0 0 0 1 1 -1 -1 1 -2 1 -1 0 1 2 -1 -1 -1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 1 0 0 1 0 -1 1 -1 0 0 0 0 -1 0 1 -1 1 0]
[3 3 -3 2 -1 -7 -1 7 4 -7 5 -2 4 -1 -7 -3 6 0 1 1 -3 0 3 1 1 -4 2 -2 2 0 3 -2 0
2 2 1 -3 0 -1 0 -2 -1 0 -4 -4 -1 -2 -1 3 0 5 -2 2 3 1 2 0 -6 2 -1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 -3 0 -3 0 6 3 -6 -3 6 -6 3 -6 0 6 3 -9 0 0 0 3 1 -3 0 -1 6 0 2 0 -1 -3 0 1 -2
0 -1 3 -3 3 0 1 1 0 3 4 1 2 2 -5 1 -6 1 0 -3 -1 -1 1 5 -2 2 -1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[3 -6 0 0 -3 9 9 -15 -6 15 -9 0 -12 -3 15 6 -21 3 6 -6 6 2 -9 0 -2 12 6 4 0 -2
-9 0 2 -4 0 1 3 0 6 -1 0 0 1 0 8 5 0 6 -8 0 -14 3 0 -9 -5 0 1 9 0 8 -4]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[-3 2 2 -1 2 0 -3 4 1 -3 1 1 3 3 -4 -1 7 -1 -3 2 -2 -1 2 -1 1 -4 -4 -1 -1 1 3 1
-1 1 -1 -1 0 0 -3 1 1 1 -1 2 -2 -2 1 -2 2 0 4 0 -1 3 2 -1 -1 -1 -1 -3 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 -1 -1 1 -1 0 -1 -1 2 1 -2 1 0 -1 1 0 0 0 0 1 1 0 0 0 -1 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0 0 -1 0 -1 0 0 -1 -1 0 0 1 0 1 0]
[-4 1 3 -1 2 1 -3 3 1 -2 1 2 3 2 -3 -1 5 -1 -3 1 -1 -1 1 -1 1 -2 -4 0 -1 1 2 1
-1 0 -1 -1 0 0 -2 1 1 1 -1 2 -1 -2 1 -2 2 0 3 0 -1 2 1 -1 0 0 -1 -3 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-2 4 0 1 1 -8 -6 12 7 -12 8 -1 10 2 -12 -7 14 -1 -2 2 -4 -1 5 0 2 -8 -2 -3 0 1
6 0 -1 2 1 0 -3 2 -4 1 -1 0 -1 -2 -6 -3 -2 -4 7 -1 10 -2 1 6 3 1 0 -8 2 -6
3]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-4 2 2 -1 2 -1 -4 5 2 -5 2 2 5 2 -5 -2 8 -1 -4 2 -1 -1 3 -1 1 -4 -4 -1 -1 1 3 1
-1 1 -1 -1 0 0 -3 1 1 1 -1 2 -2 -2 1 -3 3 0 5 -1 -1 3 2 -1 0 -2 -1 -4 2]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-6 -3 6 -3 3 9 0 -6 -3 6 -6 3 -3 3 6 3 -3 0 -3 0 3 -1 -3 -2 0 3 -6 2 -3 1 -3 3
0 -2 -3 -2 3 0 0 1 3 2 -1 6 4 0 3 0 -2 0 -4 2 -3 -2 0 -3 0 7 -3 -1 -1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
[3 3 -3 2 -1 -7 -1 7 4 -7 5 -2 4 -1 -7 -3 6 0 1 1 -3 0 3 1 1 -4 2 -2 2 0 3 -2 0
2 2 1 -3 0 -1 0 -2 -1 0 -4 -4 -1 -2 -1 3 0 5 -2 2 3 1 2 0 -6 2 -1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 -3 3 0 0 9 6 -12 -6 12 -6 0 -9 0 12 6 -12 3 3 -3 3 0 -6 -1 -1 6 0 3 -3 0 -6 1
1 -2 -3 0 3 0 3 0 1 1 1 0 6 3 1 4 -5 0 -9 3 -3 -6 -3 -1 -1 8 -1 5 -4]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 -1 1 1 0 0 -1 1 -2 1 -1 1 0 1 1 -2 -2 2 0 0 0 0 0 0 -2 0 1 0 1 0 0 0 0 -1
1 -2 0 0 1 0 0 2 0 -1 1 0 -1 1 0 0 0 1 1 -1 0 1 -2 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 3 0 0 0 -3 -3 6 3 -6 3 0 3 3 -6 -3 9 0 -3 3 -3 -1 3 0 1 -6 -3 -2 0 1 3 0 -1 2
0 -1 0 0 -3 1 0 1 0 0 -3 -2 0 -2 3 0 5 -1 0 4 3 0 -1 -4 0 -3 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 -3 -3 3 3 -3 3 0 3 0 -3 -3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 -1 -1 -1 -1 2 -1 2 -1 1 1 1 1 1 -2 1 -2 1]
[0 -3 0 -1 0 5 3 -7 -3 7 -5 1 -5 -2 7 3 -9 0 1 -2 4 1 -3 0 -1 6 2 2 0 -1 -4 0 1
-2 0 0 2 -1 3 -1 1 0 0 2 4 2 1 2 -4 0 -6 1 0 -4 -2 -1 1 5 -1 3 -1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-6 6 3 0 3 -9 -12 18 9 -18 12 0 15 3 -18 -9 24 0 -6 3 -6 -2 9 -1 3 -12 -6 -4 -3
3 9 1 -3 4 0 -1 -3 3 -9 2 0 1 -2 0 -8 -5 -1 -8 11 -2 16 -3 0 9 5 1 -1 -10 2
-11 5]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-6 0 6 -3 3 6 -3 -3 -3 3 -3 3 0 3 3 3 3 0 -6 0 0 -1 0 -2 0 0 -6 1 -3 2 0 3 -2 0
-3 -2 3 0 -3 1 3 2 -1 6 2 -1 3 -2 0 0 0 1 -3 0 1 -3 -1 5 -3 -2 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[3 -6 0 0 -3 9 9 -15 -6 15 -9 0 -12 -3 15 6 -21 3 6 -6 6 2 -9 0 -2 12 6 4 0 -2
-9 0 2 -4 0 1 3 0 6 -1 0 0 1 0 8 5 0 6 -8 0 -14 3 0 -9 -5 0 1 9 0 8 -4]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
Here are some representations of G
[Q]=[V_1]
( 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 )
[V_15]
( 15, -1, -1, 6, 6, 3, 0, 3, -1, 0, 2, 2, -1, -1, 2, -1, 0, 0, 0, 0 )
[V_20]
( 20, 4, 4, 2, 2, 5, -1, 0, 0, 0, -2, -2, 1, 1, 1, 1, -1, -1, 0, 0 )
[chi_24]
( 24, 8, 0, 6, 6, 0, 3, 0, 0, -1, 2, 2, 2, 2, -1, 0, 0, 0, 0, 0 )
The permutation representation Q[G/G40]=[Q]+[chi_24]+[V_15]
( 40, 8, 0, 13, 13, 4, 4, 4, 0, 0, 5, 5, 2, 2, 2, 0, 1, 1, 1, 1 )
The permutation representation Q[G/G45]=[Q]+[chi_24]+[V_20]
( 45, 13, 5, 9, 9, 6, 3, 1, 1, 0, 1, 1, 4, 4, 1, 2, 0, 0, 1, 1 )
The representation Q[G/G45] + Q[G/G40] - [chi_24]
( 61, 13, 5, 16, 16, 10, 4, 5, 1, 1, 4, 4, 4, 4, 4, 2, 1, 1, 2, 2 )
This should agree with [M tensor Q] which is
( 61, 13, 5, 16, 16, 10, 4, 5, 1, 1, 4, 4, 4, 4, 4, 2, 1, 1, 2, 2 )
##########################
In this computation, we determine for which subgroups P of G
One has H^1(P,M) =/= 1
##########################
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 6, 3, 8640 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 10, 4, 6480 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 2 over Integer Ring
Column moduli:
[ 2, 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 11, 4, 6480 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 14, 6, 4320 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 16, 6, 4320 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 21, 9, 2880 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 2 over Integer Ring
Column moduli:
[ 3, 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 22, 9, 2880 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 2 over Integer Ring
Column moduli:
[ 3, 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 27, 8, 3240 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 2 over Integer Ring
Column moduli:
[ 2, 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 28, 8, 3240 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 2 over Integer Ring
Column moduli:
[ 2, 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 31, 8, 3240 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 32, 8, 3240 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 2 ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 34, 8, 3240 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 36, 12, 2160 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 42, 18, 1440 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 2 over Integer Ring
Column moduli:
[ 3, 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 46, 18, 1440 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 50, 27, 960 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 51, 27, 960 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 2 over Integer Ring
Column moduli:
[ 3, 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 52, 27, 960 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 55, 16, 1620 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 2 over Integer Ring
Column moduli:
[ 2, 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 56, 16, 1620 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 58, 16, 1620 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 65, 24, 1080 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 6 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 68, 24, 1080 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 71, 36, 720 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 72, 36, 720 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 75, 54, 480 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 78, 60, 432 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 79, 81, 320 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 81, 32, 810 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 83, 48, 540 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 2 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 91, 108, 240 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 106, 324, 80 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
********************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 107, 360, 72 ]
the group H^1(H,M) is equal to
Full Quotient RSpace of degree 1 over Integer Ring
Column moduli:
[ 3 ]
the group H^1(H,M^vee) is equal to
Full Quotient RSpace of degree 0 over Integer Ring
Column moduli:
[ ]
##########################
In this second computation, for all H in G, find lcm of H^1(P,M) for
P inside H, and lcm of H^1(P,M^vee) for P inside H
##########################
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 2, 2, 12960 ]
<2, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 3, 2, 12960 ]
<2, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 4, 3, 8640 ]
<3, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 5, 3, 8640 ]
<3, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 6, 3, 8640 ]
<3, 1>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 7, 5, 5184 ]
<5, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 8, 4, 6480 ]
<4, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 9, 4, 6480 ]
<4, 2>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 10, 4, 6480 ]
<4, 2>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 11, 4, 6480 ]
<4, 2>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 12, 4, 6480 ]
<4, 2>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 13, 4, 6480 ]
<4, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 14, 6, 4320 ]
<6, 1>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 15, 6, 4320 ]
<6, 2>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 16, 6, 4320 ]
<6, 1>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 17, 6, 4320 ]
<6, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 18, 6, 4320 ]
<6, 2>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 19, 6, 4320 ]
<6, 2>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 20, 6, 4320 ]
<6, 2>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 21, 9, 2880 ]
<9, 2>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 22, 9, 2880 ]
<9, 2>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 23, 9, 2880 ]
<9, 2>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 24, 9, 2880 ]
<9, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 25, 10, 2592 ]
<10, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 26, 8, 3240 ]
<8, 4>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 27, 8, 3240 ]
<8, 5>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 28, 8, 3240 ]
<8, 5>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 29, 8, 3240 ]
<8, 5>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 30, 8, 3240 ]
<8, 2>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 31, 8, 3240 ]
<8, 3>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 32, 8, 3240 ]
<8, 2>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 33, 8, 3240 ]
<8, 3>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 34, 8, 3240 ]
<8, 3>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 35, 12, 2160 ]
<12, 3>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 36, 12, 2160 ]
<12, 3>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 37, 12, 2160 ]
<12, 4>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 38, 12, 2160 ]
<12, 5>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 39, 12, 2160 ]
<12, 1>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 40, 12, 2160 ]
<12, 2>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 41, 12, 2160 ]
<12, 4>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 42, 18, 1440 ]
<18, 4>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 43, 18, 1440 ]
<18, 3>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 44, 18, 1440 ]
<18, 3>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 45, 18, 1440 ]
<18, 3>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 46, 18, 1440 ]
<18, 3>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 47, 18, 1440 ]
<18, 3>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 48, 18, 1440 ]
<18, 5>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 49, 20, 1296 ]
<20, 3>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 50, 27, 960 ]
<27, 5>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 51, 27, 960 ]
<27, 3>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 52, 27, 960 ]
<27, 4>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 53, 16, 1620 ]
<16, 14>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 54, 16, 1620 ]
<16, 13>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 55, 16, 1620 ]
<16, 3>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 56, 16, 1620 ]
<16, 11>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 57, 16, 1620 ]
<16, 3>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 58, 16, 1620 ]
<16, 11>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 59, 24, 1080 ]
<24, 3>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 60, 24, 1080 ]
<24, 13>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 61, 24, 1080 ]
<24, 3>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 62, 24, 1080 ]
<24, 3>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 63, 24, 1080 ]
<24, 11>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 64, 24, 1080 ]
<24, 13>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 65, 24, 1080 ]
<24, 12>
[ 6, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 66, 24, 1080 ]
<24, 12>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 67, 24, 1080 ]
<24, 13>
[ 6, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 68, 24, 1080 ]
<24, 12>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 69, 24, 1080 ]
<24, 8>
[ 1, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 70, 36, 720 ]
<36, 10>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 71, 36, 720 ]
<36, 10>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 72, 36, 720 ]
<36, 9>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 73, 36, 720 ]
<36, 12>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 74, 54, 480 ]
<54, 8>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 75, 54, 480 ]
<54, 13>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 76, 54, 480 ]
<54, 12>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 77, 60, 432 ]
<60, 5>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 78, 60, 432 ]
<60, 5>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 79, 81, 320 ]
<81, 7>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 80, 32, 810 ]
<32, 49>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 81, 32, 810 ]
<32, 6>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 82, 32, 810 ]
<32, 27>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 83, 48, 540 ]
<48, 48>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 84, 48, 540 ]
<48, 49>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 85, 48, 540 ]
<48, 33>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 86, 48, 540 ]
<48, 30>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 87, 48, 540 ]
<48, 48>
[ 6, 6 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 88, 72, 360 ]
<72, 40>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 89, 72, 360 ]
<72, 25>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 90, 80, 324 ]
<80, 49>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 91, 108, 240 ]
<108, 40>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 92, 108, 240 ]
<108, 15>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 93, 108, 240 ]
<108, 38>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 94, 108, 240 ]
<108, 37>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 95, 120, 216 ]
<120, 34>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 96, 120, 216 ]
<120, 34>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 97, 162, 160 ]
<162, 10>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 98, 64, 405 ]
<64, 138>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 99, 96, 270 ]
<96, 204>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 100, 96, 270 ]
<96, 204>
[ 6, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 101, 96, 270 ]
<96, 201>
[ 2, 1 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 102, 96, 270 ]
<96, 195>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 103, 160, 162 ]
<160, 234>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 104, 216, 120 ]
<216, 88>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 105, 216, 120 ]
<216, 158>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 106, 324, 80 ]
<324, 160>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 107, 360, 72 ]
<360, 118>
[ 6, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 108, 192, 135 ]
<192, 1493>
[ 6, 6 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 109, 192, 135 ]
<192, 201>
[ 2, 2 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 110, 288, 90 ]
<288, 860>
[ 6, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 111, 648, 40 ]
<648, 533>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 112, 648, 40 ]
<648, 704>
[ 3, 3 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 113, 720, 36 ]
<720, 763>
[ 6, 6 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 114, 576, 45 ]
<576, 8277>
[ 6, 6 ]
*******************
for the subgroup H of label n, with [n,|H|,[G;H]] equal to
[ 115, 960, 27 ]
<960, 11358>
[ 2, 2 ]
##########################
list the lattice of subgroups of G = PSp_4(F_3)
##########################
Partially ordered set of subgroup classes
-----------------------------------------
[116] Order 25920 Length 1 Maximal Subgroups: 111 112 113 114 115
---
[115] Order 960 Length 27 Maximal Subgroups: 77 102 103 109
[114] Order 576 Length 45 Maximal Subgroups: 73 108 109 110
---
[113] Order 720 Length 36 Maximal Subgroups: 83 87 88 95 96 107
[112] Order 648 Length 40 Maximal Subgroups: 68 97 105 106
[111] Order 648 Length 40 Maximal Subgroups: 89 97 104
[110] Order 288 Length 45 Maximal Subgroups: 89 99 100 101
[109] Order 192 Length 135 Maximal Subgroups: 84 98 99
[108] Order 192 Length 45 Maximal Subgroups: 87 98 100
---
[107] Order 360 Length 36 Maximal Subgroups: 65 66 72 77 78
[106] Order 324 Length 40 Maximal Subgroups: 36 79 91
[105] Order 216 Length 120 Maximal Subgroups: 69 88 91 93 94
[104] Order 216 Length 40 Maximal Subgroups: 63 92
[103] Order 160 Length 162 Maximal Subgroups: 25 82 90
[102] Order 96 Length 270 Maximal Subgroups: 69 82 83 84 86
[101] Order 96 Length 90 Maximal Subgroups: 63 80 85
[100] Order 96 Length 45 Maximal Subgroups: 62 67 80
[ 99] Order 96 Length 45 Maximal Subgroups: 61 64 80
[ 98] Order 64 Length 135 Maximal Subgroups: 80 81 82
---
[ 97] Order 162 Length 160 Maximal Subgroups: 74 76 79
[ 96] Order 120 Length 216 Maximal Subgroups: 37 49 68 78
[ 95] Order 120 Length 216 Maximal Subgroups: 41 49 66 77
[ 94] Order 108 Length 120 Maximal Subgroups: 39 72 75
[ 93] Order 108 Length 120 Maximal Subgroups: 70 73 75 76
[ 92] Order 108 Length 120 Maximal Subgroups: 40 74
[ 91] Order 108 Length 40 Maximal Subgroups: 71 75
[ 90] Order 80 Length 162 Maximal Subgroups: 7 53
[ 89] Order 72 Length 360 Maximal Subgroups: 48 59 61 62 63
[ 88] Order 72 Length 360 Maximal Subgroups: 33 70 71 72
[ 87] Order 48 Length 540 Maximal Subgroups: 37 58 65 67 68
[ 86] Order 48 Length 270 Maximal Subgroups: 39 57 60
[ 85] Order 48 Length 270 Maximal Subgroups: 40 54 59
[ 84] Order 48 Length 270 Maximal Subgroups: 38 53 60 64
[ 83] Order 48 Length 270 Maximal Subgroups: 41 58 60 66
[ 82] Order 32 Length 405 Maximal Subgroups: 53 55 56 57 58
[ 81] Order 32 Length 405 Maximal Subgroups: 55 56
[ 80] Order 32 Length 45 Maximal Subgroups: 54 56
---
[ 79] Order 81 Length 160 Maximal Subgroups: 50 51 52
[ 78] Order 60 Length 216 Maximal Subgroups: 16 25 36
[ 77] Order 60 Length 216 Maximal Subgroups: 17 25 35
[ 76] Order 54 Length 240 Maximal Subgroups: 43 44 45 48 50
[ 75] Order 54 Length 120 Maximal Subgroups: 42 46 47 50
[ 74] Order 54 Length 40 Maximal Subgroups: 45 51
[ 73] Order 36 Length 720 Maximal Subgroups: 37 38 44 47 48
[ 72] Order 36 Length 360 Maximal Subgroups: 13 42
[ 71] Order 36 Length 360 Maximal Subgroups: 41 42 46
[ 70] Order 36 Length 120 Maximal Subgroups: 37 42 43
[ 69] Order 24 Length 1080 Maximal Subgroups: 33 38 39 41
[ 68] Order 24 Length 540 Maximal Subgroups: 14 33 36
[ 67] Order 24 Length 540 Maximal Subgroups: 18 28 36
[ 66] Order 24 Length 540 Maximal Subgroups: 17 34 35
[ 65] Order 24 Length 540 Maximal Subgroups: 16 34 36
[ 64] Order 24 Length 540 Maximal Subgroups: 19 27 35
[ 63] Order 24 Length 360 Maximal Subgroups: 26 40
[ 62] Order 24 Length 360 Maximal Subgroups: 18 26
[ 61] Order 24 Length 360 Maximal Subgroups: 19 26
[ 60] Order 24 Length 270 Maximal Subgroups: 20 29 35
[ 59] Order 24 Length 90 Maximal Subgroups: 15 26
[ 58] Order 16 Length 810 Maximal Subgroups: 28 29 32 33 34
[ 57] Order 16 Length 810 Maximal Subgroups: 29 30 32
[ 56] Order 16 Length 405 Maximal Subgroups: 27 28 30 31
[ 55] Order 16 Length 405 Maximal Subgroups: 27 32
[ 54] Order 16 Length 270 Maximal Subgroups: 26 30 31
[ 53] Order 16 Length 27 Maximal Subgroups: 27 29
---
[ 52] Order 27 Length 320 Maximal Subgroups: 22 24
[ 51] Order 27 Length 40 Maximal Subgroups: 22
[ 50] Order 27 Length 40 Maximal Subgroups: 21 22 23
[ 49] Order 20 Length 1296 Maximal Subgroups: 13 25
[ 48] Order 18 Length 720 Maximal Subgroups: 15 18 19 23
[ 47] Order 18 Length 720 Maximal Subgroups: 16 20 23
[ 46] Order 18 Length 720 Maximal Subgroups: 17 20 21
[ 45] Order 18 Length 480 Maximal Subgroups: 14 15 22
[ 44] Order 18 Length 240 Maximal Subgroups: 14 19 23
[ 43] Order 18 Length 240 Maximal Subgroups: 14 18 21
[ 42] Order 18 Length 120 Maximal Subgroups: 16 17 21
[ 41] Order 12 Length 1080 Maximal Subgroups: 12 17 20
[ 40] Order 12 Length 1080 Maximal Subgroups: 8 15
[ 39] Order 12 Length 1080 Maximal Subgroups: 13 20
[ 38] Order 12 Length 1080 Maximal Subgroups: 9 19 20
[ 37] Order 12 Length 720 Maximal Subgroups: 9 14 16 18
[ 36] Order 12 Length 540 Maximal Subgroups: 6 12
[ 35] Order 12 Length 270 Maximal Subgroups: 5 10
[ 34] Order 8 Length 1620 Maximal Subgroups: 10 12 13
[ 33] Order 8 Length 1620 Maximal Subgroups: 9 12 13
[ 32] Order 8 Length 810 Maximal Subgroups: 11 13
[ 31] Order 8 Length 810 Maximal Subgroups: 8 11
[ 30] Order 8 Length 405 Maximal Subgroups: 8 11
[ 29] Order 8 Length 270 Maximal Subgroups: 9 10 11
[ 28] Order 8 Length 135 Maximal Subgroups: 11 12
[ 27] Order 8 Length 135 Maximal Subgroups: 10 11
[ 26] Order 8 Length 90 Maximal Subgroups: 8
---
[ 25] Order 10 Length 1296 Maximal Subgroups: 3 7
[ 24] Order 9 Length 960 Maximal Subgroups: 4
[ 23] Order 9 Length 240 Maximal Subgroups: 4 5 6
[ 22] Order 9 Length 160 Maximal Subgroups: 4 6
[ 21] Order 9 Length 120 Maximal Subgroups: 5 6
[ 20] Order 6 Length 1080 Maximal Subgroups: 3 5
[ 19] Order 6 Length 720 Maximal Subgroups: 2 5
[ 18] Order 6 Length 720 Maximal Subgroups: 2 6
[ 17] Order 6 Length 720 Maximal Subgroups: 3 5
[ 16] Order 6 Length 720 Maximal Subgroups: 3 6
[ 15] Order 6 Length 360 Maximal Subgroups: 2 4
[ 14] Order 6 Length 240 Maximal Subgroups: 2 6
[ 13] Order 4 Length 1620 Maximal Subgroups: 3
[ 12] Order 4 Length 540 Maximal Subgroups: 3
[ 11] Order 4 Length 405 Maximal Subgroups: 2 3
[ 10] Order 4 Length 270 Maximal Subgroups: 3
[ 9] Order 4 Length 270 Maximal Subgroups: 2 3
[ 8] Order 4 Length 270 Maximal Subgroups: 2
---
[ 7] Order 5 Length 1296 Maximal Subgroups: 1
[ 6] Order 3 Length 240 Maximal Subgroups: 1
[ 5] Order 3 Length 120 Maximal Subgroups: 1
[ 4] Order 3 Length 40 Maximal Subgroups: 1
[ 3] Order 2 Length 270 Maximal Subgroups: 1
[ 2] Order 2 Length 45 Maximal Subgroups: 1
---
[ 1] Order 1 Length 1 Maximal Subgroups:
##########################
For every H in G, compute the Burnside Cokernel which is
R_H(G) modulo permutation representations. Then determine
if V_H where V=[M tensor Q] is non-trivial in this group,
equivalently, determine if V_H is a virtual sum of permutation
representations of H. If not, then print a message
##########################
V has dimension
61
G has Burnside Cokernel
Abelian Group isomorphic to Z/2
Defined on 1 generator
Relations:
2*$.1 = 0
function(rho) ... end function [
[ 0, 1/2, 1/2, 1/2, 1/2, 0, 1/2, 1/2, 1/2, 0, 1/2, 0, 1/2, 0, 1/2 ]
]
************************
For the subgroup H of label n then [n,[G:H]] equals
[ 116, 1 ]
X_H is not rational if the following is false
false
the order of V_H in the Burnside cokernel is as follows
2
************************
For the subgroup H of label n then [n,[G:H]] equals
[ 114, 45 ]
<576, 8277>
X_H is not rational if the following is false
false
the order of V_H in the Burnside cokernel is as follows
2
************************
For the subgroup H of label n then [n,[G:H]] equals
[ 111, 40 ]
<648, 533>
X_H is not rational if the following is false
false
the order of V_H in the Burnside cokernel is as follows
2
************************
For the subgroup H of label n then [n,[G:H]] equals
[ 110, 90 ]
<288, 860>
X_H is not rational if the following is false
false
the order of V_H in the Burnside cokernel is as follows
2
************************
For the subgroup H of label n then [n,[G:H]] equals
[ 104, 120 ]
<216, 88>
X_H is not rational if the following is false
false
the order of V_H in the Burnside cokernel is as follows
2
************************
For the subgroup H of label n then [n,[G:H]] equals
[ 101, 270 ]
<96, 201>
X_H is not rational if the following is false
false
the order of V_H in the Burnside cokernel is as follows
2
************************
For the subgroup H of label n then [n,[G:H]] equals
[ 89, 360 ]
<72, 25>
X_H is not rational if the following is false
false
the order of V_H in the Burnside cokernel is as follows
2
Total time: 1260.009 seconds, Total memory usage: 320.38MB