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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
  1  0
  0 -1

  2x  2
  0 -1
  1  0

  2x  2
  1  0
  0  1
2x2 %zentr
-1 0
0 -1
2x2 %centralizer
-1 0
0 -1
 2^3 = 8;