insol5_3:= [ MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 1, 1, 0, 1, 1, 1 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 2, 0, 1, 2, 0, 1 ] /* order = 660 = 2^2 * 3 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 1, 2, 1, 0, 0, 2, 1 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 2, 2, 2, 1, 2, 1, 0, 0, 0, 0 ] /* order = 960 = 2^6 * 3 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 0, 1, 2, 2, 0 ], \[ 0, 0, 1, 0, 0, 1, 0, 2, 1, 0, 2, 2, 2, 0, 1, 2, 0, 2, 1, 0, 1, 0, 1, 2, 2 ] /* order = 1320 = 2^3 * 3 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 1 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 1, 0, 2, 1, 0, 0, 1, 0, 2, 2, 1 ] /* order = 1920 = 2^7 * 3 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, 2, 2, 1, 2, 2, 2, 1, 1, 1 ] /* order = 1920 = 2^7 * 3 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 1, 2, 1 ], \[ 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 1, 1, 1, 1, 1, 2, 2, 1, 0 ] /* order = 1920 = 2^7 * 3 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 1, 0, 0, 2, 1, 2, 1, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 1, 0, 1, 2, 0, 0, 2, 1, 2, 1, 2 ] /* order = 3840 = 2^8 * 3 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 1, 1, 1, 1 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 0, 2, 1, 0 ] /* order = 7920 = 2^4 * 3^2 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2, 2, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 1, 1, 2 ] /* order = 7920 = 2^4 * 3^2 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 1, 0, 1, 1 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 2, 2 ] /* order = 15840 = 2^5 * 3^2 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 1, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2 ] /* order = 15840 = 2^5 * 3^2 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 1, 1, 1, 2, 2 ] /* order = 25920 = 2^6 * 3^4 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0, 2, 1, 2, 2, 0, 0 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 1, 2, 1, 2, 0, 2, 0, 1, 0, 0 ] /* order = 51840 = 2^7 * 3^4 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 1, 1, 1, 0, 0, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 0, 0 ] /* order = 51840 = 2^7 * 3^4 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2 ], \[ 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 2, 2, 2, 0, 1 ] /* order = 51840 = 2^7 * 3^4 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0 ], \[ 0, 0, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 2, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1 ] /* order = 103680 = 2^8 * 3^4 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 0, 2, 0, 0, 2, 1, 1, 0 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 0, 2, 2, 0, 1, 2, 0, 1, 0 ] /* order = 2^9 * 3^10 * 5 * 11^2 * 13 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 1, 2, 1, 0, 2, 2, 2, 2, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 2, 0 ] /* order = 2^10 * 3^10 * 5 * 11^2 * 13 */ > ] [ PowerStructure(GrpMat) | MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 2, 0, 1, 2, 2, 0, 0, 2, 1, 2, 0 ] /* order = 660 = 2^2 * 3 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 1, 2, 1, 0, 0, 2, 1 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 2, 2, 2, 1, 2, 1, 0, 0, 0, 0 ] /* order = 960 = 2^6 * 3 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 0, 1, 2, 2, 0 ], \[ 0, 0, 1, 0, 0, 1, 0, 2, 1, 0, 2, 2, 2, 0, 1, 2, 0, 2, 1, 0, 1, 0, 1, 2, 2 ] /* order = 1320 = 2^3 * 3 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 1 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 1, 0, 2, 1, 0, 0, 1, 0, 2, 2, 1 ] /* order = 1920 = 2^7 * 3 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, 2, 2, 1, 2, 2, 2, 1, 1, 1 ] /* order = 1920 = 2^7 * 3 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 1, 2, 1 ], \[ 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2, 2, 0, 1, 1, 1, 1, 1, 2, 2, 1, 0 ] /* order = 1920 = 2^7 * 3 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0 ] /* order = 3840 = 2^8 * 3 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 1, 0, 1, 1, 2, 1, 2, 1, 1 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 2, 2, 1, 2 ] /* order = 7920 = 2^4 * 3^2 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2, 2, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 1, 1, 2 ] /* order = 7920 = 2^4 * 3^2 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 1, 0, 1, 1 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 2, 2 ] /* order = 15840 = 2^5 * 3^2 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 1, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2 ] /* order = 15840 = 2^5 * 3^2 * 5 * 11 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 1, 1, 1, 2, 2 ] /* order = 25920 = 2^6 * 3^4 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0, 2, 1, 2, 2, 0, 0 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 1, 2, 1, 2, 0, 2, 0, 1, 0, 0 ] /* order = 51840 = 2^7 * 3^4 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 1, 1, 1, 0, 0, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 0, 0 ] /* order = 51840 = 2^7 * 3^4 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2 ], \[ 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 2, 2, 2, 0, 1 ] /* order = 51840 = 2^7 * 3^4 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0 ], \[ 0, 0, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 2, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1 ] /* order = 103680 = 2^8 * 3^4 * 5 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 0, 2, 0, 0, 2, 1, 1, 0 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 0, 2, 2, 0, 1, 2, 0, 1, 0 ] /* order = 2^9 * 3^10 * 5 * 11^2 * 13 */ >, MatrixGroup<5, GF(3) | \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 1, 2, 1, 0, 2, 2, 2, 2, 2 ], \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 2, 0 ] /* order = 2^10 * 3^10 * 5 * 11^2 * 13 */ > ];