
print "The simple group of McLaughlin represented";
print "as a permutation group of degree 275. This is a";
print "rank 3 representation with subdegrees 112 and 162.";
print "The stabilizer of a point is U( 4, 3 ). ";
print "Order is 898 128 000 = 2^7 * 3^6 * 5^3 * 7 * 11";
print "Group: G";

G := PermutationGroup< 275  |
    \[2,5,6,3,8,9,10,14,15,16,17,18,19,25,26,27,28,29,30,31,32,33,34,35,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,11,65,82,83,
84,85,22,86,37,87,88,89,90,91,44,92,93,94,43,95,96,97,98,42,99,100,
101,102,4,103,104,105,106,107,108,109,110,111,140,141,142,20,143,23,
144,145,134,146,36,125,147,148,149,150,151,152,130,153,154,155,120,
12,156,127,13,76,157,158,159,38,119,160,161,162,163,133,164,116,165,
166,45,167,69,7,168,169,170,171,126,70,172,173,118,174,175,129,191,200,
197,73,75,201,202,203,189,204,205,182,128,206,207,78,208,209,183,210,
194,211,138,212,213,81,214,80,74,198,215,216,217,181,113,218,219,220,
221,131,222,79,223,71,224,24,187,193,121,115,225,226,227,228,190,188,
186,77,229,230,72,240,137,233,177,241,242,243,244,245,246,247,248,249,
235,250,136,251,252,253,237,124,254,184,255,67,1,66,256,257,258,259,
260,261,262,40,41,236,232,263,21,271,270,122,272,265,273,238,231,68,
199,234,112,268,196,269,239,274,132,179,264,123,185,180,195,39,114,266,
139,192,267,275,135,117,176,178],
    \[3,4,1,2,7,6,5,11,12,13,8,9,10,14,20,21,22,23,24,15,16,17,18,19,36,
37,38,39,40,41,42,32,43,44,45,25,26,27,28,29,30,31,33,34,35,66,67,52,
68,69,70,48,71,72,73,74,75,58,76,77,78,62,79,80,81,46,47,49,50,51,53,
54,55,56,57,59,60,61,63,64,65,91,112,113,114,115,116,117,118,119,82,
120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,
137,138,139,83,84,85,86,87,88,89,90,92,93,94,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,109,110,111,176,177,178,179,150,180,181,
182,183,184,144,167,152,185,186,187,188,189,190,159,191,192,193,163,
194,195,166,151,196,197,172,171,170,198,199,175,140,141,142,143,145,
146,147,148,149,153,154,155,156,157,158,160,161,162,164,165,168,169,
173,174,210,201,231,209,218,205,206,216,208,203,200,220,232,223,233,234,
207,235,204,219,211,221,236,213,237,238,226,227,228,229,239,202,212,
214,215,217,222,224,225,230,240,260,242,243,244,264,265,247,250,266,
248,251,256,267,268,257,252,255,269,259,241,261,262,270,245,246,249,
253,254,258,263,271,272,273,274,275]>;
AssertAttribute(G, "Order", 2^7 * 3^6 * 5^3 * 7 * 11);
