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

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G:=Group(
(2,8,13,17,20,22,7)(3,9,14,18,21,6,12)(4,10,15,19,5,11,16)(24,77,99,72,64,82,
40)(25,92,49,88,28,65,90)(26,41,70,98,91,38,75)(27,55,43,78,86,87,45)(29,69,
59,79,76,35,67)(30,39,42,81,36,57,89)(31,93,62,44,73,71,50)(32,53,85,60,51,96,
83)(33,37,58,46,84,100,56)(34,94,80,61,97,48,68)(47,95,66,74,52,54,63),
(1,35)(3,81)(4,92)(6,60)(7,59)(8,46)(9,70)(10,91)(11,18)(12,66)(13,55)(14,85)
(15,90)(17,53)(19,45)(20,68)(21,69)(23,84)(24,34)(25,31)(26,32)(37,39)(38,42)
(40,41)(43,44)(49,64)(50,63)(51,52)(54,95)(56,96)(57,100)(58,97)(61,62)(65,82)
(67,83)(71,98)(72,99)(74,77)(76,78)(87,89)
);