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

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#g2 f1 z1 c1
  2x  2
  0  1
 -1  1

  2x  2
  0  1
  1  0

  2x  2
  2 -1
 -1  2

2x2
-1 0
0 -1
2x2
-1 0
0 -1

 2^2 *3= 12 %order of the group;