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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

560922 views
#g3 f4 z1

5x5
0 1 0 0 0
-1 1 0 0 0
0 0 0 1 0
0 0 -1 1 0
0 0 0 0 1

5x5
0 1 0 0 0
1 0 0 0 0
0 0 0 -1 0
0 0 -1 0 0
0 0 0 0 1

5x5
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 -1

5x5
2 -1 0 0 0
-1 2 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0

5x5
0 0 0 0 0
0 0 0 0 0
0 0 2 -1 0
0 0 -1 2 0
0 0 0 0 0

5x5
0 0 0 1 0
0 0 -1 0 0
0 -1 0 0 0
1 0 0 0 0
0 0 0 0 0

5x5
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

5x5
0 0 0 1 1
0 0 -1 0 1
1 0 0 0 0
0 1 0 0 0
0 0 1 -1 1

2^3*3=24