/*
www-ATLAS of Group Representations.
U4(3):D8 represented as permutations on 112 points.
*/

G<x,y>:=PermutationGroup<112|\[
1,4,5,2,3,10,11,12,9,6,7,8,13,22,23,16,26,18,29,25,21,14,15,35,20,
17,39,41,19,44,46,47,40,34,24,36,52,38,27,33,28,58,60,30,63,31,32,50,69,48,
64,37,53,75,55,56,57,42,59,43,61,62,45,51,65,66,84,68,49,87,71,88,73,74,54,
91,77,78,79,80,96,92,98,67,85,86,70,72,102,100,76,82,93,94,95,81,97,83,99,90,
103,89,101,110,105,106,107,108,109,104,111,112]
,\[
2,4,1,7,8,3,6,13,5,15,17,19,21,9,24,10,27,11,30,12,14,32,34,36,16,
37,40,18,42,45,20,48,22,23,50,25,53,26,55,28,43,59,29,61,31,64,66,68,33,70,
35,72,74,38,65,39,41,76,57,78,79,44,81,56,46,83,47,49,86,87,51,89,52,54,60,
92,58,94,95,62,69,63,99,73,67,97,71,101,100,75,104,105,77,103,80,98,82,88,85,84,
107,108,90,91,93,96,106,111,102,112,110,109]
>;
print "Group G is U4(3):D8 < Sym(112)";