//Standard generators of L3(4) are a and b where a has order 2, b has
//order 4, ab has order 7 and abb has order 5.
//Standard generators of 3.L3(4) are preimages A, B where A has order 2
//and B has order 4.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [ a, b^2*a*b^2*a*b*a*b*a*b^-1*a*b^2*a*b^2 ],
       //L34.2_1 = field x duality - order 2 - not same as in Online ATLAS.
            [ a, b^-1*a*b^2*a*b^-1*a*b^2*a*b*a*b^2*a*b^-1],
       //L34.3 = diagonal - order 3
            [ a, b^-1 ] ]
       //L34.2_3 = duality  - order 2
                  where a is (_LR`F).1 where b is (_LR`F).2;

//four constituents, AI[2], cycled by AI[1],AI[3].
_LR`G :=
/*
Original group: c9Group("3l34p")
Direct induction from degree 2
Schur index: 1
Character: ( 252, -4, -126, -126, 0, -4, -4, -4, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 
2, 2, -1, -1, -1, -1, 0, 0, 0, 0 )
*/

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

return _LR;
