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

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#g3 f6 z3
    
6x6
0 -1 0 0 0 0
1 0 0 0 0 0
0 0 0 -1 0 0
0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 0 0 1

6x6
-1 0 0 0 0 0
0 1 0 0 0 0 
0 0 0 1 0 0
0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 0 0 1

6x6
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 -1 0
0 0 0 0 0 -1

6x6
1 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

6x6
0 0 0 0 0 0
0 0 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 0 0
0 0 0 0 0 0

6x6
0 0 1 -1 0 0
0 0 1 1 0 0
1 1 0 0 0 0
-1 1 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0

6x6
0 0 0 0 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

6x6
0 0 0 0 0 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

6x6
0 0 0 0 0 0
0 0 0 0 0 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

6x6
0 0 0 0 1 0
0 0 0 1 1 1
1 0 0 0 0 0
0 1 0 0 0 0
0 0 0 -1 0 1
0 0 1 0 0 0

6x6
0 0 0 0 1 0 
0 1 0 0 1 0
0 -1 1 0 0 0
0 0 -1 1 0 1
0 0 0 -1 0 1
1 0 0 0 0 0

6x6
1 0 0 0 0 0
1 1 0 0 1 0
0 0 1 0 0 -1
0 0 0 1 0 0
0 -1 0 0 1 0
0 0 1 -1 0 1
 
2^4=16

dim6/2-1,2-1;1,1b