/*
www-ATLAS of Group Representations.
S4(4) represented as permutations on 120 points.
*/

G<x,y>:=PermutationGroup<120|\[
2,1,4,3,7,9,5,12,6,14,16,8,19,10,22,11,25,27,13,30,32,15,35,36,17,
39,18,40,42,20,45,21,47,49,23,24,52,51,26,28,57,29,59,61,31,63,33,66,34,69,
38,37,73,68,74,76,41,79,43,81,44,84,46,86,88,48,90,54,50,92,83,94,53,55,96,
56,99,101,58,103,60,93,71,62,105,64,107,65,109,67,111,70,82,72,112,75,114,115,77,106,
78,113,80,117,85,100,87,118,89,119,91,95,102,97,98,120,104,108,110,116]
,\[
3,1,5,6,8,10,11,2,13,15,17,18,20,21,23,24,26,28,29,31,33,34,4,37,38,
36,9,41,43,44,27,46,48,50,51,7,53,54,55,56,58,16,60,62,39,64,65,67,68,70,
71,72,42,47,75,77,78,12,80,82,83,61,85,87,25,89,14,91,63,93,94,76,95,81,97,
98,100,102,35,104,69,19,30,99,74,106,108,105,73,110,90,84,22,79,113,107,45,103,109,116,
111,96,52,118,86,115,57,32,112,49,114,92,66,120,88,40,101,119,59,117]
>;
print "Group G is S4(4) < Sym(120)";