//Standard generators of the Mathieu group M22 are a and b where a has order 2,
//b is in class 4A, ab has order 11 and ababb has order 11.
//Standard generators of 6.M22 are preimages A, B where A is in class +2A and
//B is in class -4A. Alternatively: A has order 2, B has order 4, AB has
//order 33 and ABABB has order 33. 

_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [ a, a*b^-1*a ] ]
                  where a is (_LR`F).1 where b is (_LR`F).2;
//four constituents

_LR`G :=
/*
Original group: c9Group("6m22p")
Direct induction from degree 12
Schur index: 1
Character: ( 264, -264, 24, -24, -132, -132, 0, 8, -8, 0, 4, 132, 132, -12, 12, 
-12, 12, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, -4, 0, 0, -4, 4, 4, -4, 0, 0, 2, 2, 
-2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0,
0 )
*/

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

return _LR;
