/*
www-ATLAS of Group Representations.
S4(4):4 represented as permutations on 170 points.
*/

G<x,y>:=PermutationGroup<170|\[
2,1,7,8,5,9,3,4,6,10,19,20,21,14,22,23,24,18,11,12,13,15,16,17,41,
42,27,43,44,45,31,46,47,48,35,49,50,51,52,53,25,26,28,29,30,32,33,34,36,37,
38,39,40,81,62,77,82,76,59,83,75,55,84,85,65,86,87,88,89,70,90,91,92,93,61,
58,56,94,95,96,54,57,60,63,64,66,67,68,69,71,72,73,74,78,79,80,97,127,128,100,
112,109,103,104,129,106,120,130,102,131,132,101,117,133,134,135,113,123,136,107,121,137,118,138,139,
140,98,99,105,108,110,111,114,115,116,119,122,124,125,126,142,141,165,148,145,166,147,144,149,162,
167,152,153,155,154,168,164,158,159,160,161,150,169,157,143,146,151,156,163,170]
,\[
3,4,5,2,6,1,10,11,12,13,14,15,16,17,18,7,8,9,25,26,27,28,29,30,31,
20,32,33,34,35,36,37,38,39,40,19,21,22,23,24,54,55,56,57,58,59,60,61,62,63,
64,65,66,41,67,68,69,45,47,46,70,71,50,51,72,73,74,75,76,77,78,79,80,42,43,
44,48,49,52,53,97,98,99,100,101,102,103,92,104,105,106,88,107,108,109,110,111,112,83,84,
85,113,114,115,90,116,96,117,118,93,119,120,121,122,123,124,125,126,81,82,86,87,89,91,94,
95,141,142,143,144,145,146,147,138,148,149,150,135,151,152,139,153,129,154,155,156,133,134,136,157,
127,158,159,160,161,162,163,164,128,130,131,132,137,140,168,167,169,165,170,166]
>;
print "Group G is S4(4):4 < Sym(170)";