/*
www-ATLAS of Group Representations.
2.PGL2(7) represented as permutations on 224 points.
*/

G<x,y>:=PermutationGroup<224|\[
2,4,1,3,9,11,10,12,7,5,8,6,21,23,22,24,25,27,26,28,15,13,16,14,19,
17,20,18,45,47,46,48,49,51,50,52,53,55,54,56,57,59,58,60,31,29,32,30,35,33,
36,34,39,37,40,38,43,41,44,42,81,82,83,85,84,86,87,88,89,91,90,92,93,95,94,
96,97,99,98,100,62,61,65,63,66,64,68,67,71,69,72,70,75,73,76,74,79,77,80,78,
129,131,130,132,133,134,135,137,136,138,139,141,140,142,143,145,144,146,147,148,149,151,150,152,153,
155,154,156,103,101,104,102,106,105,109,107,110,108,113,111,114,112,117,115,118,116,120,119,123,121,
124,122,127,125,128,126,177,178,179,180,181,183,182,184,185,186,187,188,189,190,191,192,193,195,194,
196,158,157,160,159,163,161,164,162,166,165,168,167,170,169,172,171,175,173,176,174,205,206,207,208,
209,210,211,212,198,197,200,199,202,201,204,203,217,218,219,220,214,213,216,215,223,224,222,221]
,\[
1,5,7,4,6,2,8,3,13,15,17,19,14,9,16,10,18,11,20,12,29,31,33,35,37,
39,41,43,30,21,32,22,34,23,36,24,38,25,40,26,42,27,44,28,60,59,63,65,67,68,
69,71,73,75,50,49,77,79,62,61,45,46,64,47,66,48,56,55,70,51,72,52,74,53,76,
54,78,57,80,58,101,103,105,106,107,109,111,113,115,117,119,120,92,91,121,123,125,127,84,83,
102,81,104,82,100,99,108,85,110,86,112,87,114,88,116,89,118,90,94,93,122,95,124,96,126,
97,128,98,157,158,149,150,161,163,165,166,167,168,138,137,169,170,151,152,130,129,173,175,159,160,
171,172,141,142,135,136,146,145,131,132,162,133,164,134,155,156,140,139,153,154,143,144,174,147,176,
148,184,183,199,200,180,179,198,197,185,186,193,194,203,204,191,192,201,202,190,189,177,178,182,181,
187,188,196,195,213,214,212,211,205,206,216,215,209,210,207,208,221,222,218,217,220,219,223,224]
>;
print "Group G is 2.PGL2(7) < Sym(224)";