/*
www-ATLAS of Group Representations.
S4(4) represented as permutations on 85 points.
*/

G<x,y>:=PermutationGroup<85|\[
2,1,3,6,8,4,11,5,14,16,7,12,18,9,15,10,22,13,25,26,21,17,30,24,19,
20,32,36,29,23,39,27,41,43,45,28,47,38,31,40,33,52,34,55,35,46,37,57,49,60,
62,42,54,53,44,58,48,56,59,50,68,51,70,64,65,74,73,61,69,63,71,75,67,66,72,
78,80,76,79,77,81,82,83,84,85]
,\[
3,4,5,7,9,10,12,13,15,17,18,19,16,20,1,21,23,24,2,27,28,29,31,32,33,
34,35,8,37,38,6,40,42,44,46,26,48,49,50,11,51,53,54,47,56,14,36,58,59,61,
63,64,57,65,30,66,25,22,55,67,69,45,71,72,73,75,76,77,74,68,78,79,80,39,62,
81,82,41,83,43,84,85,52,60,70]
>;
print "Group G is S4(4) < Sym(85)";