CompleteDatabase:= [ rec( name := "M11", sbgname := "A6.2_3", degree := 11, rank := 2, permchar := "1a + 10a", charnmbs := [ 1, 2 ], ctbl := [ [ 1, 10 ], [ 1, -1 ] ], mats := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 10 ], [ 1, 9 ] ] ] ), rec( name := "M11", sbgname := "L2(11)", filename := "L211", degree := 12, rank := 2, permchar := "1a + 11a", charnmbs := [ 1, 5 ], ctbl := [ [ 1, 11 ], [ 1, -1 ] ], mats := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 11 ], [ 1, 10 ] ] ] ), rec( name := "M11", sbgname := "3^2:8 leq 3^2:Q8.2", filename := "3^2:8", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 110, rank := 4, permchar := "1a + 10a + 44a + 55a", charnmbs := [ 1, 2, 8, 10 ], ctbl := [ [ 1, 1, 36, 72 ], [ 1, 1, 14, -16 ], [ 1, 1, -4, 2 ], [ 1, -1, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 0, 36, 0 ], [ 0, 0, 36, 0 ], [ 1, 1, 18, 16 ], [ 0, 0, 8, 28 ] ], [ [ 0, 0, 0, 72 ], [ 0, 0, 0, 72 ], [ 0, 0, 16, 56 ], [ 1, 1, 28, 42 ] ] ] ), rec( name := "M11", sbgname := "3^2:Q8.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 55, rank := 3, permchar := "1a + 10a + 44a", charnmbs := [ 1, 2, 8 ], ctbl := [ [ 1, 18, 36 ], [ 1, 7, -8 ], [ 1, -2, 1 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 18, 0 ], [ 1, 9, 8 ], [ 0, 4, 14 ] ], [ [ 0, 0, 36 ], [ 0, 8, 28 ], [ 1, 14, 21 ] ] ] ), rec( name := "M11", sbgname := "A5.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 66, rank := 4, permchar := "1a + 10a + 11a + 44a", charnmbs := [ 1, 2, 5, 8 ], ctbl := [ [ 1, 15, 20, 30 ], [ 1, -7, -2, 8 ], [ 1, -3, 8, -6 ], [ 1, 2, -2, -1 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 15, 0, 0 ], [ 1, 0, 4, 10 ], [ 0, 3, 3, 9 ], [ 0, 5, 6, 4 ] ], [ [ 0, 0, 20, 0 ], [ 0, 4, 4, 12 ], [ 1, 3, 10, 6 ], [ 0, 6, 4, 10 ] ], [ [ 0, 0, 0, 30 ], [ 0, 10, 12, 8 ], [ 0, 9, 6, 15 ], [ 1, 4, 10, 15 ] ] ] ), rec( name := "M11", sbgname := "A6 leq A6.2_3", filename := "A6", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 22, rank := 3, permchar := "1a + 10a + 11a", charnmbs := [ 1, 2, 5 ], ctbl := [ [ 1, 1, 20 ], [ 1, 1, -2 ], [ 1, -1, 0 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 1, 0 ], [ 1, 0, 0 ], [ 0, 0, 1 ] ], [ [ 0, 0, 20 ], [ 0, 0, 20 ], [ 1, 1, 18 ] ] ] ), rec( name := "M11", sbgname := "11:5 leq L2(11)", filename := "11:5", degree := 144, rank := 6, permchar := "1a + 11a + 16ab + 45a + 55a", charnmbs := [ 1, 5, 6, 7, 9, 10 ], ctbl := [ [ 1, 11, 11, 11, 55, 55 ], [ 1, -1, -1, 11, -5, -5 ], [ 1, E(11)+4*E(11)^2+E(11)^3+E(11)^4+E(11)^5+4*E(11)^6+4*E(11)^7+4*E(11)^8+E(11)^9+4*E(11)^10, 4*E(11)+E(11)^2+4*E(11)^3+4*E(11)^4+4*E(11)^5+E(11)^6+E(11)^7+E(11)^8+4*E(11)^9+E(11)^10, -1, -5, 10 ], [ 1, 4*E(11)+E(11)^2+4*E(11)^3+4*E(11)^4+4*E(11)^5+E(11)^6+E(11)^7+E(11)^8+4*E(11)^9+E(11)^10, E(11)+4*E(11)^2+E(11)^3+E(11)^4+E(11)^5+4*E(11)^6+4*E(11)^7+4*E(11)^8+E(11)^9+4*E(11)^10, -1, -5, 10 ], [ 1, 3, 3, -1, -5, -1 ], [ 1, -1, -1, -1, 7, -5 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 11, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 10 ], [ 0, 5, 0, 1, 5, 0 ], [ 0, 1, 0, 0, 5, 5 ], [ 0, 1, 0, 1, 4, 5 ], [ 0, 0, 2, 1, 5, 3 ] ], [ [ 0, 11, 0, 0, 0, 0 ], [ 0, 0, 5, 1, 5, 0 ], [ 1, 0, 0, 0, 0, 10 ], [ 0, 0, 1, 0, 5, 5 ], [ 0, 0, 1, 1, 4, 5 ], [ 0, 2, 0, 1, 5, 3 ] ], [ [ 0, 0, 0, 11, 0, 0 ], [ 0, 0, 1, 0, 5, 5 ], [ 0, 1, 0, 0, 5, 5 ], [ 1, 0, 0, 10, 0, 0 ], [ 0, 1, 1, 0, 4, 5 ], [ 0, 1, 1, 0, 5, 4 ] ], [ [ 0, 0, 0, 0, 55, 0 ], [ 0, 0, 5, 5, 20, 25 ], [ 0, 5, 0, 5, 20, 25 ], [ 0, 5, 5, 0, 20, 25 ], [ 1, 4, 4, 4, 22, 20 ], [ 0, 5, 5, 5, 20, 20 ] ], [ [ 0, 0, 0, 0, 0, 55 ], [ 0, 10, 0, 5, 25, 15 ], [ 0, 0, 10, 5, 25, 15 ], [ 0, 5, 5, 0, 25, 20 ], [ 0, 5, 5, 5, 20, 20 ], [ 1, 3, 3, 4, 20, 24 ] ] ] ), rec( name := "M12", sbgname := "M11", degree := 12, rank := 2, permchar := "1a + 11a", permchar2 := "1a + 11b", charnmbs := [ 1, 2 ], charnmbs2 := [ 1, 3 ], ctbl := [ [ 1, 11 ], [ 1, -1 ] ], mats := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 11 ], [ 1, 10 ] ] ] ), rec( name := "M12", sbgname := "3^2.2.S4", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 220, rank := 5, permchar := "1a + 11a + 54a + 55a + 99a", permchar2 := "1a + 11b + 54a + 55a + 99a", charnmbs := [ 1, 2, 7, 8, 12 ], charnmbs2 := [ 1, 3, 7, 8, 12 ], ctbl := [ [ 1, 12, 27, 72, 108 ], [ 1, -4, 15, -24, 12 ], [ 1, 1, 5, 6, -13 ], [ 1, 5, -3, -6, 3 ], [ 1, -3, -3, 2, 3 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 12, 0, 0, 0 ], [ 1, 2, 0, 0, 9 ], [ 0, 0, 0, 8, 4 ], [ 0, 0, 3, 3, 6 ], [ 0, 1, 1, 4, 6 ] ], [ [ 0, 0, 27, 0, 0 ], [ 0, 0, 0, 18, 9 ], [ 1, 0, 10, 0, 16 ], [ 0, 3, 0, 15, 9 ], [ 0, 1, 4, 6, 16 ] ], [ [ 0, 0, 0, 72, 0 ], [ 0, 0, 18, 18, 36 ], [ 0, 8, 0, 40, 24 ], [ 1, 3, 15, 14, 39 ], [ 0, 4, 6, 26, 36 ] ], [ [ 0, 0, 0, 0, 108 ], [ 0, 9, 9, 36, 54 ], [ 0, 4, 16, 24, 64 ], [ 0, 6, 9, 39, 54 ], [ 1, 6, 16, 36, 49 ] ] ] ), rec( name := "M12", sbgname := "A6.2^2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 66, rank := 3, permchar := "1a + 11a + 54a", permchar2 := "1a + 11b + 54a", charnmbs := [ 1, 2, 7 ], charnmbs2 := [ 1, 3, 7 ], ctbl := [ [ 1, 20, 45 ], [ 1, 8, -9 ], [ 1, -2, 1 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 20, 0 ], [ 1, 10, 9 ], [ 0, 4, 16 ] ], [ [ 0, 0, 45 ], [ 0, 9, 36 ], [ 1, 16, 28 ] ] ] ), rec( name := "M12", sbgname := "A6.2_1", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 132, rank := 5, permchar := "1a + 11ab + 54a + 55a", permchar2 := "1a + 11ab + 54a + 55a", charnmbs := [ 1, 2, 3, 7, 8 ], charnmbs2 := [ 1, 2, 3, 7, 8 ], ctbl := [ [ 1, 1, 40, 45, 45 ], [ 1, -1, 0, 15, -15 ], [ 1, 1, 16, -9, -9 ], [ 1, 1, -4, 1, 1 ], [ 1, -1, 0, -3, 3 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 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 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ], [ 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 40, 0, 0 ], [ 0, 0, 40, 0, 0 ], [ 1, 1, 20, 9, 9 ], [ 0, 0, 8, 16, 16 ], [ 0, 0, 8, 16, 16 ] ], [ [ 0, 0, 0, 45, 0 ], [ 0, 0, 0, 0, 45 ], [ 0, 0, 9, 18, 18 ], [ 1, 0, 16, 20, 8 ], [ 0, 1, 16, 8, 20 ] ], [ [ 0, 0, 0, 0, 45 ], [ 0, 0, 0, 45, 0 ], [ 0, 0, 9, 18, 18 ], [ 0, 1, 16, 8, 20 ], [ 1, 0, 16, 20, 8 ] ] ] ), rec( name := "M12", sbgname := "A6.2_2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 132, rank := 4, permchar := "1a + 11a + 54a + 66a", permchar2 := "1a + 11b + 54a + 66a", charnmbs := [ 1, 2, 7, 11 ], charnmbs2 := [ 1, 3, 7, 11 ], ctbl := [ [ 1, 1, 40, 90 ], [ 1, 1, 16, -18 ], [ 1, 1, -4, 2 ], [ 1, -1, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 0, 40, 0 ], [ 0, 0, 40, 0 ], [ 1, 1, 20, 18 ], [ 0, 0, 8, 32 ] ], [ [ 0, 0, 0, 90 ], [ 0, 0, 0, 90 ], [ 0, 0, 18, 72 ], [ 1, 1, 32, 56 ] ] ] ), rec( name := "M12", sbgname := "L2(11)", filename := "L211", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 144, rank := 5, permchar := "1a + 16ab + 45a + 66a", charnmbs := [ 1, 4, 5, 6, 11 ], ctbl := [ [ 1, 11, 11, 55, 66 ], [ 1, E(11)+4*E(11)^2+E(11)^3+E(11)^4+E(11)^5+4*E(11)^6+4*E(11)^7+4*E(11)^8+E(11)^9+4*E(11)^10, 4*E(11)+E(11)^2+4*E(11)^3+4*E(11)^4+4*E(11)^5+E(11)^6+E(11)^7+E(11)^8+4*E(11)^9+E(11)^10, 10, -6 ], [ 1, 4*E(11)+E(11)^2+4*E(11)^3+4*E(11)^4+4*E(11)^5+E(11)^6+E(11)^7+E(11)^8+4*E(11)^9+E(11)^10, E(11)+4*E(11)^2+E(11)^3+E(11)^4+E(11)^5+4*E(11)^6+4*E(11)^7+4*E(11)^8+E(11)^9+4*E(11)^10, 10, -6 ], [ 1, 3, 3, -1, -6 ], [ 1, -1, -1, -5, 6 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 11, 0, 0 ], [ 1, 0, 0, 10, 0 ], [ 0, 5, 0, 0, 6 ], [ 0, 0, 2, 3, 6 ], [ 0, 1, 0, 5, 5 ] ], [ [ 0, 11, 0, 0, 0 ], [ 0, 0, 5, 0, 6 ], [ 1, 0, 0, 10, 0 ], [ 0, 2, 0, 3, 6 ], [ 0, 0, 1, 5, 5 ] ], [ [ 0, 0, 0, 55, 0 ], [ 0, 10, 0, 15, 30 ], [ 0, 0, 10, 15, 30 ], [ 1, 3, 3, 24, 24 ], [ 0, 5, 5, 20, 25 ] ], [ [ 0, 0, 0, 0, 66 ], [ 0, 0, 6, 30, 30 ], [ 0, 6, 0, 30, 30 ], [ 0, 6, 6, 24, 30 ], [ 1, 5, 5, 25, 30 ] ] ] ), rec( name := "M12", sbgname := "L2(11) leq M11", filename := "L211inM11", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 144, rank := 5, permchar := "1a + 11ab + 55a + 66a", charnmbs := [ 1, 2, 3, 8, 11 ], ctbl := [ [ 1, 11, 11, 55, 66 ], [ 1, -1, 11, -5, -6 ], [ 1, 11, -1, -5, -6 ], [ 1, -1, -1, 7, -6 ], [ 1, -1, -1, -5, 6 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 11, 0, 0, 0 ], [ 1, 10, 0, 0, 0 ], [ 0, 0, 0, 5, 6 ], [ 0, 0, 1, 4, 6 ], [ 0, 0, 1, 5, 5 ] ], [ [ 0, 0, 11, 0, 0 ], [ 0, 0, 0, 5, 6 ], [ 1, 0, 10, 0, 0 ], [ 0, 1, 0, 4, 6 ], [ 0, 1, 0, 5, 5 ] ], [ [ 0, 0, 0, 55, 0 ], [ 0, 0, 5, 20, 30 ], [ 0, 5, 0, 20, 30 ], [ 1, 4, 4, 22, 24 ], [ 0, 5, 5, 20, 25 ] ], [ [ 0, 0, 0, 0, 66 ], [ 0, 0, 6, 30, 30 ], [ 0, 6, 0, 30, 30 ], [ 0, 6, 6, 24, 30 ], [ 1, 5, 5, 25, 30 ] ] ] ), rec( name := "M12", sbgname := "3^2:2.A4 leq 3^2.2.S4", filename := "3^2.2.A4", degree := 440, rank := 8, permchar := "1a + 11a + 45a + 54a + 55ac + 99a + 120a", permchar2 := "1a + 11b + 45a + 54a + 55ab + 99a + 120a", charnmbs := [ 1, 2, 6, 7, 8, 10, 12, 13 ], charnmbs2 := [ 1, 3, 6, 7, 8, 9, 12, 13 ], ctbl := [ [ 1, 1, 24, 27, 27, 72, 72, 216 ], [ 1, 1, -8, 15, 15, -24, -24, 24 ], [ 1, -1, 0, 3, -3, 16, -16, 0 ], [ 1, 1, 2, 5, 5, 6, 6, -26 ], [ 1, 1, 10, -3, -3, -6, -6, 6 ], [ 1, -1, 0, -9, 9, 0, 0, 0 ], [ 1, 1, -6, -3, -3, 2, 2, 6 ], [ 1, -1, 0, 3, -3, -6, 6, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 24, 0, 0, 0, 0, 0 ], [ 0, 0, 24, 0, 0, 0, 0, 0 ], [ 1, 1, 4, 0, 0, 0, 0, 18 ], [ 0, 0, 0, 0, 0, 8, 8, 8 ], [ 0, 0, 0, 0, 0, 8, 8, 8 ], [ 0, 0, 0, 3, 3, 3, 3, 12 ], [ 0, 0, 0, 3, 3, 3, 3, 12 ], [ 0, 0, 2, 1, 1, 4, 4, 12 ] ], [ [ 0, 0, 0, 27, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 27, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 9, 9, 9 ], [ 1, 0, 0, 2, 8, 0, 0, 16 ], [ 0, 1, 0, 8, 2, 0, 0, 16 ], [ 0, 0, 3, 0, 0, 9, 6, 9 ], [ 0, 0, 3, 0, 0, 6, 9, 9 ], [ 0, 0, 1, 2, 2, 3, 3, 16 ] ], [ [ 0, 0, 0, 0, 27, 0, 0, 0 ], [ 0, 0, 0, 27, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 9, 9, 9 ], [ 0, 1, 0, 8, 2, 0, 0, 16 ], [ 1, 0, 0, 2, 8, 0, 0, 16 ], [ 0, 0, 3, 0, 0, 6, 9, 9 ], [ 0, 0, 3, 0, 0, 9, 6, 9 ], [ 0, 0, 1, 2, 2, 3, 3, 16 ] ], [ [ 0, 0, 0, 0, 0, 72, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 72, 0 ], [ 0, 0, 0, 9, 9, 9, 9, 36 ], [ 0, 0, 8, 0, 0, 24, 16, 24 ], [ 0, 0, 8, 0, 0, 16, 24, 24 ], [ 1, 0, 3, 9, 6, 12, 2, 39 ], [ 0, 1, 3, 6, 9, 2, 12, 39 ], [ 0, 0, 4, 3, 3, 13, 13, 36 ] ], [ [ 0, 0, 0, 0, 0, 0, 72, 0 ], [ 0, 0, 0, 0, 0, 72, 0, 0 ], [ 0, 0, 0, 9, 9, 9, 9, 36 ], [ 0, 0, 8, 0, 0, 16, 24, 24 ], [ 0, 0, 8, 0, 0, 24, 16, 24 ], [ 0, 1, 3, 6, 9, 2, 12, 39 ], [ 1, 0, 3, 9, 6, 12, 2, 39 ], [ 0, 0, 4, 3, 3, 13, 13, 36 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 216 ], [ 0, 0, 0, 0, 0, 0, 0, 216 ], [ 0, 0, 18, 9, 9, 36, 36, 108 ], [ 0, 0, 8, 16, 16, 24, 24, 128 ], [ 0, 0, 8, 16, 16, 24, 24, 128 ], [ 0, 0, 12, 9, 9, 39, 39, 108 ], [ 0, 0, 12, 9, 9, 39, 39, 108 ], [ 1, 1, 12, 16, 16, 36, 36, 98 ] ] ] ), rec( name := "M12.2", sbgname := "3^2:2.A4 leq 3^2.2.S4", filename := "3^2.2.A4", degree := 880, rank := 14, permchar := "1a^{+-} + 11ab + 45a^{+-} + 54a^{+-} + 55a^{+-}bc + 99a^{+-} + 120a^{+-}", charnmbs := [ 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17 ], ctbl := [ [ 1, 1, 8, 24, 27, 27, 36, 36, 72, 72, 72, 72, 216, 216 ], [ 1, 1, -8, 24, 27, 27, -36, -36, 72, 72, -72, -72, -216, 216 ], [ 1, 1, 0, -8, 15, 15, 0, 0, -24, -24, 0, 0, 0, 24 ], [ 1, -1, 0, 0, 3, -3, 12, -12, 16, -16, 8, -8, 0, 0 ], [ 1, -1, 0, 0, 3, -3, -12, 12, 16, -16, -8, 8, 0, 0 ], [ 1, 1, 2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4, 2, 5, 5, -2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4, -2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4, 6, 6, -4*E(5)+4*E(5)^2+4*E(5)^3-4*E(5)^4, -4*E(5)+4*E(5)^2+4*E(5)^3-4*E(5)^4, 10*E(5)-10*E(5)^2-10*E(5)^3+10*E(5)^4, -26 ], [ 1, 1, -2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4, 2, 5, 5, 2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4, 2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4, 6, 6, 4*E(5)-4*E(5)^2-4*E(5)^3+4*E(5)^4, 4*E(5)-4*E(5)^2-4*E(5)^3+4*E(5)^4, -10*E(5)+10*E(5)^2+10*E(5)^3-10*E(5)^4, -26 ], [ 1, 1, 6, 10, -3, -3, 6, 6, -6, -6, 0, 0, -18, 6 ], [ 1, 1, -6, 10, -3, -3, -6, -6, -6, -6, 0, 0, 18, 6 ], [ 1, -1, 0, 0, -9, 9, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 2, -6, -3, -3, -6, -6, 2, 2, 8, 8, -6, 6 ], [ 1, 1, -2, -6, -3, -3, 6, 6, 2, 2, -8, -8, 6, 6 ], [ 1, -1, 0, 0, 3, -3, -2*E(12)^7+2*E(12)^11, 2*E(12)^7-2*E(12)^11, -6, 6, 6*E(12)^7-6*E(12)^11, -6*E(12)^7+6*E(12)^11, 0, 0 ], [ 1, -1, 0, 0, 3, -3, 2*E(12)^7-2*E(12)^11, -2*E(12)^7+2*E(12)^11, -6, 6, -6*E(12)^7+6*E(12)^11, 6*E(12)^7-6*E(12)^11, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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36, 36, 126, 0 ], [ 0, 0, 8, 0, 0, 0, 16, 16, 0, 0, 32, 32, 112, 0 ], [ 0, 0, 8, 0, 0, 0, 16, 16, 0, 0, 32, 32, 112, 0 ], [ 0, 0, 0, 6, 12, 12, 0, 0, 36, 36, 0, 0, 0, 114 ], [ 0, 0, 0, 6, 12, 12, 0, 0, 36, 36, 0, 0, 0, 114 ], [ 0, 0, 6, 0, 0, 0, 18, 18, 0, 0, 33, 33, 108, 0 ], [ 0, 0, 6, 0, 0, 0, 18, 18, 0, 0, 33, 33, 108, 0 ], [ 0, 0, 0, 12, 12, 12, 0, 0, 33, 33, 0, 0, 0, 114 ], [ 0, 0, 0, 12, 12, 12, 0, 0, 33, 33, 0, 0, 0, 114 ], [ 1, 1, 0, 14, 14, 14, 0, 0, 36, 36, 0, 0, 0, 100 ], [ 0, 0, 2, 0, 0, 0, 19, 19, 0, 0, 38, 38, 100, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216 ], [ 0, 0, 0, 0, 0, 0, 27, 27, 0, 0, 54, 54, 54, 0 ], [ 0, 0, 0, 18, 9, 9, 0, 0, 36, 36, 0, 0, 0, 108 ], [ 0, 0, 0, 8, 16, 16, 0, 0, 24, 24, 0, 0, 0, 128 ], [ 0, 0, 0, 8, 16, 16, 0, 0, 24, 24, 0, 0, 0, 128 ], [ 0, 0, 6, 0, 0, 0, 18, 18, 0, 0, 30, 30, 114, 0 ], [ 0, 0, 6, 0, 0, 0, 18, 18, 0, 0, 30, 30, 114, 0 ], [ 0, 0, 0, 12, 9, 9, 0, 0, 39, 39, 0, 0, 0, 108 ], [ 0, 0, 0, 12, 9, 9, 0, 0, 39, 39, 0, 0, 0, 108 ], [ 0, 0, 6, 0, 0, 0, 15, 15, 0, 0, 33, 33, 114, 0 ], [ 0, 0, 6, 0, 0, 0, 15, 15, 0, 0, 33, 33, 114, 0 ], [ 0, 0, 2, 0, 0, 0, 19, 19, 0, 0, 38, 38, 100, 0 ], [ 1, 1, 0, 12, 16, 16, 0, 0, 36, 36, 0, 0, 0, 98 ] ] ] ), rec( name := "M12.2", sbgname := "(2^2xA5).2", filename := "2^2xA5.2", degree := 396, rank := 7, permchar := "1a^+ + 16ab + 45a^+ + 54a^{+-} + 66a^+ + 144a^+", charnmbs := [ 1, 4, 5, 7, 8, 12, 18 ], ctbl := [ [ 1, 15, 20, 60, 60, 120, 120 ], [ 1, 6, -7, 15, -12, 3, -6 ], [ 1, -5, 4, 4, -12, -8, 16 ], [ 1, E(5)-3*E(5)^2-3*E(5)^3+E(5)^4, -2, -4*E(5)+4*E(5)^2+4*E(5)^3-4*E(5)^4, -10*E(5)-6*E(5)^2-6*E(5)^3-10*E(5)^4, -12, -8*E(5)^2-8*E(5)^3 ], [ 1, -3*E(5)+E(5)^2+E(5)^3-3*E(5)^4, -2, 4*E(5)-4*E(5)^2-4*E(5)^3+4*E(5)^4, -6*E(5)-10*E(5)^2-10*E(5)^3-6*E(5)^4, -12, -8*E(5)-8*E(5)^4 ], [ 1, 3, 8, 0, 0, 0, -12 ], [ 1, -2, -2, -5, 0, 10, -2 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 15, 0, 0, 0, 0, 0 ], [ 1, 2, 0, 4, 0, 0, 8 ], [ 0, 0, 3, 0, 6, 6, 0 ], [ 0, 1, 0, 4, 0, 8, 2 ], [ 0, 0, 2, 0, 1, 4, 8 ], [ 0, 0, 1, 4, 2, 4, 4 ], [ 0, 1, 0, 1, 4, 4, 5 ] ], [ [ 0, 0, 20, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 8, 8, 0 ], [ 1, 3, 4, 6, 0, 6, 0 ], [ 0, 0, 2, 0, 4, 6, 8 ], [ 0, 2, 0, 4, 2, 8, 4 ], [ 0, 1, 1, 3, 4, 5, 6 ], [ 0, 0, 0, 4, 2, 6, 8 ] ], [ [ 0, 0, 0, 60, 0, 0, 0 ], [ 0, 4, 0, 16, 0, 32, 8 ], [ 0, 0, 6, 0, 12, 18, 24 ], [ 1, 4, 0, 13, 8, 16, 18 ], [ 0, 0, 4, 8, 16, 16, 16 ], [ 0, 4, 3, 8, 8, 17, 20 ], [ 0, 1, 4, 9, 8, 20, 18 ] ], [ [ 0, 0, 0, 0, 60, 0, 0 ], [ 0, 0, 8, 0, 4, 16, 32 ], [ 0, 6, 0, 12, 6, 24, 12 ], [ 0, 0, 4, 8, 16, 16, 16 ], [ 1, 1, 2, 16, 8, 12, 20 ], [ 0, 2, 4, 8, 6, 20, 20 ], [ 0, 4, 2, 8, 10, 20, 16 ] ], [ [ 0, 0, 0, 0, 0, 120, 0 ], [ 0, 0, 8, 32, 16, 32, 32 ], [ 0, 6, 6, 18, 24, 30, 36 ], [ 0, 8, 6, 16, 16, 34, 40 ], [ 0, 4, 8, 16, 12, 40, 40 ], [ 1, 4, 5, 17, 20, 35, 38 ], [ 0, 4, 6, 20, 20, 38, 32 ] ], [ [ 0, 0, 0, 0, 0, 0, 120 ], [ 0, 8, 0, 8, 32, 32, 40 ], [ 0, 0, 0, 24, 12, 36, 48 ], [ 0, 2, 8, 18, 16, 40, 36 ], [ 0, 8, 4, 16, 20, 40, 32 ], [ 0, 4, 6, 20, 20, 38, 32 ], [ 1, 5, 8, 18, 16, 32, 40 ] ] ] ), rec( name := "M12.2", sbgname := "(2xA5).2 leq (2^2xA5).2", filename := "2xA5.2", degree := 792, rank := 11, permchar := "1a^+ + 16ab + 45a^+ + 54a^{+-} + 55a^- + 66a^{+-} + 99a^- + 144a^+ + 176a^-", charnmbs := [ 1, 4, 5, 7, 8, 10, 12, 13, 15, 18, 21 ], ctbl := [ [ 1, 1, 15, 15, 40, 60, 60, 120, 120, 120, 240 ], [ 1, 1, 6, 6, -14, 15, 15, -6, -6, -24, 6 ], [ 1, 1, -5, -5, 8, 4, 4, 16, 16, -24, -16 ], [ 1, 1, -3*E(5)+E(5)^2+E(5)^3-3*E(5)^4, -3*E(5)+E(5)^2+E(5)^3-3*E(5)^4, -4, 4*E(5)-4*E(5)^2-4*E(5)^3+4*E(5)^4, 4*E(5)-4*E(5)^2-4*E(5)^3+4*E(5)^4, -8*E(5)-8*E(5)^4, -8*E(5)-8*E(5)^4, -12*E(5)-20*E(5)^2-20*E(5)^3-12*E(5)^4, -24 ], [ 1, 1, E(5)-3*E(5)^2-3*E(5)^3+E(5)^4, E(5)-3*E(5)^2-3*E(5)^3+E(5)^4, -4, -4*E(5)+4*E(5)^2+4*E(5)^3-4*E(5)^4, -4*E(5)+4*E(5)^2+4*E(5)^3-4*E(5)^4, -8*E(5)^2-8*E(5)^3, -8*E(5)^2-8*E(5)^3, -20*E(5)-12*E(5)^2-12*E(5)^3-20*E(5)^4, -24 ], [ 1, -1, 7, -7, 0, 12, -12, 8, -8, 0, 0 ], [ 1, 1, 3, 3, 16, 0, 0, -12, -12, 0, 0 ], [ 1, -1, -5, 5, 0, 0, 0, 20, -20, 0, 0 ], [ 1, -1, 3, -3, 0, -12, 12, 0, 0, 0, 0 ], [ 1, 1, -2, -2, -4, -5, -5, -2, -2, 0, 20 ], [ 1, -1, -2, 2, 0, 3, -3, -10, 10, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 2, 0, 0, 4, 0, 8, 0, 0, 0 ], [ 0, 1, 0, 2, 0, 0, 4, 0, 8, 0, 0 ], [ 0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 6 ], [ 0, 0, 1, 0, 0, 4, 0, 2, 0, 0, 8 ], [ 0, 0, 0, 1, 0, 0, 4, 0, 2, 0, 8 ], [ 0, 0, 1, 0, 0, 1, 0, 1, 4, 4, 4 ], [ 0, 0, 0, 1, 0, 0, 1, 4, 1, 4, 4 ], [ 0, 0, 0, 0, 2, 0, 0, 4, 4, 1, 4 ], [ 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 4 ] ], [ [ 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 2, 0, 0, 4, 0, 8, 0, 0 ], [ 1, 0, 2, 0, 0, 4, 0, 8, 0, 0, 0 ], [ 0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 6 ], [ 0, 0, 0, 1, 0, 0, 4, 0, 2, 0, 8 ], [ 0, 0, 1, 0, 0, 4, 0, 2, 0, 0, 8 ], [ 0, 0, 0, 1, 0, 0, 1, 4, 1, 4, 4 ], [ 0, 0, 1, 0, 0, 1, 0, 1, 4, 4, 4 ], [ 0, 0, 0, 0, 2, 0, 0, 4, 4, 1, 4 ], [ 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 4 ] ], [ [ 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 8, 0, 0, 0, 0, 16, 16 ], [ 0, 0, 0, 0, 8, 0, 0, 0, 0, 16, 16 ], [ 1, 1, 3, 3, 8, 6, 6, 0, 0, 0, 12 ], [ 0, 0, 0, 0, 4, 0, 0, 8, 8, 8, 12 ], [ 0, 0, 0, 0, 4, 0, 0, 8, 8, 8, 12 ], [ 0, 0, 0, 0, 0, 4, 4, 8, 8, 4, 12 ], [ 0, 0, 0, 0, 0, 4, 4, 8, 8, 4, 12 ], [ 0, 0, 2, 2, 0, 4, 4, 4, 4, 4, 16 ], [ 0, 0, 1, 1, 2, 3, 3, 6, 6, 8, 10 ] ], [ [ 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 16, 0, 8, 0, 0, 32 ], [ 0, 0, 0, 4, 0, 0, 16, 0, 8, 0, 32 ], [ 0, 0, 0, 0, 6, 0, 0, 12, 12, 12, 18 ], [ 1, 0, 4, 0, 0, 5, 8, 10, 8, 8, 16 ], [ 0, 1, 0, 4, 0, 8, 5, 8, 10, 8, 16 ], [ 0, 0, 1, 0, 4, 5, 4, 10, 8, 8, 20 ], [ 0, 0, 0, 1, 4, 4, 5, 8, 10, 8, 20 ], [ 0, 0, 0, 0, 4, 4, 4, 8, 8, 16, 16 ], [ 0, 0, 2, 2, 3, 4, 4, 10, 10, 8, 17 ] ], [ [ 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 4, 0, 0, 16, 0, 8, 0, 32 ], [ 0, 0, 4, 0, 0, 16, 0, 8, 0, 0, 32 ], [ 0, 0, 0, 0, 6, 0, 0, 12, 12, 12, 18 ], [ 0, 1, 0, 4, 0, 8, 5, 8, 10, 8, 16 ], [ 1, 0, 4, 0, 0, 5, 8, 10, 8, 8, 16 ], [ 0, 0, 0, 1, 4, 4, 5, 8, 10, 8, 20 ], [ 0, 0, 1, 0, 4, 5, 4, 10, 8, 8, 20 ], [ 0, 0, 0, 0, 4, 4, 4, 8, 8, 16, 16 ], [ 0, 0, 2, 2, 3, 4, 4, 10, 10, 8, 17 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0 ], [ 0, 0, 8, 0, 0, 8, 0, 8, 32, 32, 32 ], [ 0, 0, 0, 8, 0, 0, 8, 32, 8, 32, 32 ], [ 0, 0, 0, 0, 0, 12, 12, 24, 24, 12, 36 ], [ 0, 0, 2, 0, 8, 10, 8, 20, 16, 16, 40 ], [ 0, 0, 0, 2, 8, 8, 10, 16, 20, 16, 40 ], [ 1, 0, 1, 4, 8, 10, 8, 24, 16, 16, 32 ], [ 0, 1, 4, 1, 8, 8, 10, 16, 24, 16, 32 ], [ 0, 0, 4, 4, 4, 8, 8, 16, 16, 20, 40 ], [ 0, 0, 2, 2, 6, 10, 10, 16, 16, 20, 38 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0 ], [ 0, 0, 0, 8, 0, 0, 8, 32, 8, 32, 32 ], [ 0, 0, 8, 0, 0, 8, 0, 8, 32, 32, 32 ], [ 0, 0, 0, 0, 0, 12, 12, 24, 24, 12, 36 ], [ 0, 0, 0, 2, 8, 8, 10, 16, 20, 16, 40 ], [ 0, 0, 2, 0, 8, 10, 8, 20, 16, 16, 40 ], [ 0, 1, 4, 1, 8, 8, 10, 16, 24, 16, 32 ], [ 1, 0, 1, 4, 8, 10, 8, 24, 16, 16, 32 ], [ 0, 0, 4, 4, 4, 8, 8, 16, 16, 20, 40 ], [ 0, 0, 2, 2, 6, 10, 10, 16, 16, 20, 38 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0 ], [ 0, 0, 0, 0, 16, 0, 0, 32, 32, 8, 32 ], [ 0, 0, 0, 0, 16, 0, 0, 32, 32, 8, 32 ], [ 0, 0, 6, 6, 0, 12, 12, 12, 12, 12, 48 ], [ 0, 0, 0, 0, 8, 8, 8, 16, 16, 32, 32 ] , [ 0, 0, 0, 0, 8, 8, 8, 16, 16, 32, 32 ], [ 0, 0, 4, 4, 4, 8, 8, 16, 16, 20, 40 ], [ 0, 0, 4, 4, 4, 8, 8, 16, 16, 20, 40 ], [ 1, 1, 1, 1, 4, 16, 16, 20, 20, 16, 24 ], [ 0, 0, 2, 2, 8, 8, 8, 20, 20, 12, 40 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240 ], [ 0, 0, 0, 0, 16, 32, 32, 32, 32, 32, 64 ], [ 0, 0, 0, 0, 16, 32, 32, 32, 32, 32, 64 ], [ 0, 0, 6, 6, 12, 18, 18, 36, 36, 48, 60 ], [ 0, 0, 8, 8, 12, 16, 16, 40, 40, 32, 68 ], [ 0, 0, 8, 8, 12, 16, 16, 40, 40, 32, 68 ], [ 0, 0, 4, 4, 12, 20, 20, 32, 32, 40, 76 ], [ 0, 0, 4, 4, 12, 20, 20, 32, 32, 40, 76 ], [ 0, 0, 4, 4, 16, 16, 16, 40, 40, 24, 80 ], [ 1, 1, 4, 4, 10, 17, 17, 38, 38, 40, 70 ] ] ] ), rec( name := "M12.2", sbgname := "4^2:D12.2", degree := 495, rank := 8, permchar := "1a^+ + 16ab + 45a^- + 54a^{+-} + 66a^+ + 99a^- + 144a^+", charnmbs := [ 1, 4, 6, 7, 8, 12, 15, 18 ], ctbl := [ [ 1, 6, 16, 24, 64, 96, 96, 192 ], [ 1, -3, 7, 6, 10, -21, -12, 12 ], [ 1, -3, -4, 6, -12, 12, -12, 12 ], [ 1, -E(5)-3*E(5)^2-3*E(5)^3-E(5)^4, -4*E(5)-4*E(5)^4, 2*E(5)-4*E(5)^2-4*E(5)^3+2*E(5)^4, 12*E(5)+8*E(5)^2+8*E(5)^3+12*E(5)^4, 4*E(5)+8*E(5)^2+8*E(5)^3+4*E(5)^4, 8, -4*E(5)-4*E(5)^4 ], [ 1, -3*E(5)-E(5)^2-E(5)^3-3*E(5)^4, -4*E(5)^2-4*E(5)^3, -4*E(5)+2*E(5)^2+2*E(5)^3-4*E(5)^4, 8*E(5)+12*E(5)^2+12*E(5)^3+8*E(5)^4, 8*E(5)+4*E(5)^2+4*E(5)^3+8*E(5)^4, 8, -4*E(5)^2-4*E(5)^3 ], [ 1, 3, 4, 0, 4, 12, -12, -12 ], [ 1, 1, -4, -6, 4, -4, -4, 12 ], [ 1, -2, -1, 0, 4, 2, 8, -12 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 6, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 6, 0, 0 ], [ 0, 1, 0, 1, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 0, 3, 0, 3 ], [ 0, 0, 1, 0, 2, 1, 0, 2 ], [ 0, 0, 0, 1, 0, 0, 1, 4 ], [ 0, 0, 0, 0, 1, 1, 2, 2 ] ], [ [ 0, 0, 16, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 16, 0, 0 ], [ 1, 0, 3, 0, 0, 0, 0, 12 ], [ 0, 0, 0, 0, 8, 0, 0, 8 ], [ 0, 0, 0, 3, 4, 3, 0, 6 ], [ 0, 1, 0, 0, 2, 5, 4, 4 ], [ 0, 0, 0, 0, 0, 4, 4, 8 ], [ 0, 0, 1, 1, 2, 2, 4, 6 ] ], [ [ 0, 0, 0, 24, 0, 0, 0, 0 ], [ 0, 4, 0, 4, 0, 0, 16, 0 ], [ 0, 0, 0, 0, 12, 0, 0, 12 ], [ 1, 1, 0, 2, 0, 0, 4, 16 ], [ 0, 0, 3, 0, 3, 3, 6, 9 ], [ 0, 0, 0, 0, 2, 8, 4, 10 ], [ 0, 1, 0, 1, 4, 4, 6, 8 ], [ 0, 0, 1, 2, 3, 5, 4, 9 ] ], [ [ 0, 0, 0, 0, 64, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 32, 0, 32 ], [ 0, 0, 0, 12, 16, 12, 0, 24 ], [ 0, 0, 8, 0, 8, 8, 16, 24 ], [ 1, 0, 4, 3, 2, 12, 12, 30 ], [ 0, 2, 2, 2, 8, 14, 16, 20 ], [ 0, 0, 0, 4, 8, 16, 12, 24 ], [ 0, 1, 2, 3, 10, 10, 12, 26 ] ], [ [ 0, 0, 0, 0, 0, 96, 0, 0 ], [ 0, 0, 16, 0, 32, 16, 0, 32 ], [ 0, 6, 0, 0, 12, 30, 24, 24 ], [ 0, 0, 0, 0, 8, 32, 16, 40 ], [ 0, 3, 3, 3, 12, 21, 24, 30 ], [ 1, 1, 5, 8, 14, 15, 12, 40 ], [ 0, 0, 4, 4, 16, 12, 20, 40 ], [ 0, 1, 2, 5, 10, 20, 20, 38 ] ], [ [ 0, 0, 0, 0, 0, 0, 96, 0 ], [ 0, 0, 0, 16, 0, 0, 16, 64 ], [ 0, 0, 0, 0, 0, 24, 24, 48 ], [ 0, 4, 0, 4, 16, 16, 24, 32 ], [ 0, 0, 0, 6, 12, 24, 18, 36 ], [ 0, 0, 4, 4, 16, 12, 20, 40 ], [ 1, 1, 4, 6, 12, 20, 16, 36 ], [ 0, 2, 4, 4, 12, 20, 18, 36 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 192 ], [ 0, 0, 0, 0, 32, 32, 64, 64 ], [ 0, 0, 12, 12, 24, 24, 48, 72 ], [ 0, 0, 8, 16, 24, 40, 32, 72 ], [ 0, 3, 6, 9, 30, 30, 36, 78 ], [ 0, 2, 4, 10, 20, 40, 40, 76 ], [ 0, 4, 8, 8, 24, 40, 36, 72 ], [ 1, 2, 6, 9, 26, 38, 36, 74 ] ] ] ), rec( name := "M12.2", sbgname := "A6.2^2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 132, rank := 5, permchar := "1a^{+-} + 11ab + 54a^{+-}", charnmbs := [ 1, 2, 3, 7, 8 ], ctbl := [ [ 1, 20, 30, 36, 45 ], [ 1, 20, -30, -36, 45 ], [ 1, 8, 0, 0, -9 ], [ 1, -2, -2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4, 2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4, 1 ], [ 1, -2, 2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4, -2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4, 1 ] ] , mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 20, 0, 0, 0 ], [ 1, 10, 0, 0, 9 ], [ 0, 0, 8, 12, 0 ], [ 0, 0, 10, 10, 0 ], [ 0, 4, 0, 0, 16 ] ], [ [ 0, 0, 30, 0, 0 ], [ 0, 0, 12, 18, 0 ], [ 1, 8, 0, 0, 21 ], [ 0, 10, 0, 0, 20 ], [ 0, 0, 14, 16, 0 ] ], [ [ 0, 0, 0, 36, 0 ], [ 0, 0, 18, 18, 0 ], [ 0, 12, 0, 0, 24 ], [ 1, 10, 0, 0, 25 ], [ 0, 0, 16, 20, 0 ] ], [ [ 0, 0, 0, 0, 45 ], [ 0, 9, 0, 0, 36 ], [ 0, 0, 21, 24, 0 ], [ 0, 0, 20, 25, 0 ], [ 1, 16, 0, 0, 28 ] ] ] ), rec( name := "M12.2", sbgname := "A6.2_2 leq A6.2^2", filename := "A6.2_2", degree := 264, rank := 7, permchar := "1a^{+-} + 11ab + 54a^{+-} + 66a^{+-}", charnmbs := [ 1, 2, 3, 7, 8, 12, 13 ], ctbl := [ [ 1, 1, 36, 36, 40, 60, 90 ], [ 1, 1, -36, -36, 40, -60, 90 ], [ 1, 1, 0, 0, 16, 0, -18 ], [ 1, 1, -2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4, -2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4, -4, 4*E(5)-4*E(5)^2-4*E(5)^3+4*E(5)^4, 2 ], [ 1, 1, 2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4, 2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4, -4, -4*E(5)+4*E(5)^2+4*E(5)^3-4*E(5)^4, 2 ], [ 1, -1, -6, 6, 0, 0, 0 ], [ 1, -1, 6, -6, 0, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 36, 0, 0, 0, 0 ], [ 0, 0, 0, 36, 0, 0, 0 ], [ 1, 0, 0, 0, 10, 0, 25 ], [ 0, 1, 0, 0, 10, 0, 25 ], [ 0, 0, 9, 9, 0, 18, 0 ], [ 0, 0, 0, 0, 12, 0, 24 ], [ 0, 0, 10, 10, 0, 16, 0 ] ], [ [ 0, 0, 0, 36, 0, 0, 0 ], [ 0, 0, 36, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 10, 0, 25 ], [ 1, 0, 0, 0, 10, 0, 25 ], [ 0, 0, 9, 9, 0, 18, 0 ], [ 0, 0, 0, 0, 12, 0, 24 ], [ 0, 0, 10, 10, 0, 16, 0 ] ], [ [ 0, 0, 0, 0, 40, 0, 0 ], [ 0, 0, 0, 0, 40, 0, 0 ], [ 0, 0, 10, 10, 0, 20, 0 ], [ 0, 0, 10, 10, 0, 20, 0 ], [ 1, 1, 0, 0, 20, 0, 18 ], [ 0, 0, 12, 12, 0, 16, 0 ], [ 0, 0, 0, 0, 8, 0, 32 ] ], [ [ 0, 0, 0, 0, 0, 60, 0 ], [ 0, 0, 0, 0, 0, 60, 0 ], [ 0, 0, 0, 0, 20, 0, 40 ], [ 0, 0, 0, 0, 20, 0, 40 ], [ 0, 0, 18, 18, 0, 24, 0 ], [ 1, 1, 0, 0, 16, 0, 42 ], [ 0, 0, 16, 16, 0, 28, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 90 ], [ 0, 0, 0, 0, 0, 0, 90 ], [ 0, 0, 25, 25, 0, 40, 0 ], [ 0, 0, 25, 25, 0, 40, 0 ], [ 0, 0, 0, 0, 18, 0, 72 ], [ 0, 0, 24, 24, 0, 42, 0 ], [ 1, 1, 0, 0, 32, 0, 56 ] ] ] ), rec( name := "M12.2", sbgname := "3^2.2.S4", degree := 440, rank := 9, permchar := "1a^{+-} + 11ab + 54a^{+-} + 55a^{+-} + 99a^{+-}", charnmbs := [ 1, 2, 3, 7, 8, 9, 10, 14, 15 ], ctbl := [ [ 1, 4, 12, 27, 36, 72, 72, 108, 108 ], [ 1, -4, 12, 27, -36, -72, 72, -108, 108 ], [ 1, 0, -4, 15, 0, 0, -24, 0, 12 ], [ 1, -E(5)+E(5)^2+E(5)^3-E(5)^4, 1, 5, 2*E(5)-2*E(5)^2-2*E(5)^3+2*E(5)^4, 4*E(5)-4*E(5)^2-4*E(5)^3+4*E(5)^4, 6, -5*E(5)+5*E(5)^2+5*E(5)^3-5*E(5)^4, -13 ], [ 1, E(5)-E(5)^2-E(5)^3+E(5)^4, 1, 5, -2*E(5)+2*E(5)^2+2*E(5)^3-2*E(5)^4, -4*E(5)+4*E(5)^2+4*E(5)^3-4*E(5)^4, 6, 5*E(5)-5*E(5)^2-5*E(5)^3+5*E(5)^4, -13 ], [ 1, 3, 5, -3, 6, 0, -6, -9, 3 ], [ 1, -3, 5, -3, -6, 0, -6, 9, 3 ], [ 1, 1, -3, -3, -6, 8, 2, -3, 3 ], [ 1, -1, -3, -3, 6, -8, 2, 3, 3 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 4, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 3, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 3, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 4, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 3 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 3 ], [ 0, 0, 0, 0, 0, 1, 0, 3, 0 ], [ 0, 0, 0, 1, 0, 0, 2, 0, 1 ], [ 0, 0, 0, 0, 1, 2, 0, 1, 0 ] ], [ [ 0, 0, 12, 0, 0, 0, 0, 0, 0 ], [ 0, 3, 0, 0, 9, 0, 0, 0, 0 ], [ 1, 0, 2, 0, 0, 0, 0, 0, 9 ], [ 0, 0, 0, 0, 0, 0, 8, 0, 4 ], [ 0, 1, 0, 0, 2, 6, 0, 3, 0 ], [ 0, 0, 0, 0, 3, 3, 0, 6, 0 ], [ 0, 0, 0, 3, 0, 0, 3, 0, 6 ], [ 0, 0, 0, 0, 1, 4, 0, 7, 0 ], [ 0, 0, 1, 1, 0, 0, 4, 0, 6 ] ], [ [ 0, 0, 0, 27, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 27, 0 ], [ 0, 0, 0, 0, 0, 0, 18, 0, 9 ], [ 1, 0, 0, 10, 0, 0, 0, 0, 16 ], [ 0, 0, 0, 0, 3, 12, 0, 12, 0 ], [ 0, 0, 0, 0, 6, 9, 0, 12, 0 ], [ 0, 0, 3, 0, 0, 0, 15, 0, 9 ], [ 0, 1, 0, 0, 4, 8, 0, 14, 0 ], [ 0, 0, 1, 4, 0, 0, 6, 0, 16 ] ], [ [ 0, 0, 0, 0, 36, 0, 0, 0, 0 ], [ 0, 0, 9, 0, 0, 0, 0, 0, 27 ], [ 0, 3, 0, 0, 6, 18, 0, 9, 0 ], [ 0, 0, 0, 0, 4, 16, 0, 16, 0 ], [ 1, 0, 2, 3, 0, 0, 12, 0, 18 ], [ 0, 0, 3, 6, 0, 0, 12, 0, 15 ], [ 0, 0, 0, 0, 6, 12, 0, 18, 0 ], [ 0, 0, 1, 4, 0, 0, 12, 0, 19 ], [ 0, 1, 0, 0, 6, 10, 0, 19, 0 ] ], [ [ 0, 0, 0, 0, 0, 72, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 18, 0, 54 ], [ 0, 0, 0, 0, 18, 18, 0, 36, 0 ], [ 0, 0, 0, 0, 16, 24, 0, 32, 0 ], [ 0, 0, 6, 12, 0, 0, 24, 0, 30 ], [ 1, 0, 3, 9, 0, 0, 26, 0, 33 ], [ 0, 1, 0, 0, 12, 26, 0, 33, 0 ], [ 0, 0, 4, 8, 0, 0, 22, 0, 38 ], [ 0, 2, 0, 0, 10, 22, 0, 38, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 72, 0, 0 ], [ 0, 0, 0, 0, 0, 18, 0, 54, 0 ], [ 0, 0, 0, 18, 0, 0, 18, 0, 36 ], [ 0, 0, 8, 0, 0, 0, 40, 0, 24 ], [ 0, 0, 0, 0, 12, 24, 0, 36, 0 ], [ 0, 1, 0, 0, 12, 26, 0, 33, 0 ], [ 1, 0, 3, 15, 0, 0, 14, 0, 39 ], [ 0, 2, 0, 0, 12, 22, 0, 36, 0 ], [ 0, 0, 4, 6, 0, 0, 26, 0, 36 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 108, 0 ], [ 0, 0, 0, 27, 0, 0, 54, 0, 27 ], [ 0, 0, 0, 0, 9, 36, 0, 63, 0 ], [ 0, 4, 0, 0, 16, 32, 0, 56, 0 ], [ 0, 0, 3, 12, 0, 0, 36, 0, 57 ], [ 0, 0, 6, 12, 0, 0, 33, 0, 57 ], [ 0, 3, 0, 0, 18, 33, 0, 54, 0 ], [ 1, 0, 7, 14, 0, 0, 36, 0, 50 ], [ 0, 1, 0, 0, 19, 38, 0, 50, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 108 ], [ 0, 0, 0, 0, 27, 54, 0, 27, 0 ], [ 0, 0, 9, 9, 0, 0, 36, 0, 54 ], [ 0, 0, 4, 16, 0, 0, 24, 0, 64 ], [ 0, 3, 0, 0, 18, 30, 0, 57, 0 ], [ 0, 3, 0, 0, 15, 33, 0, 57, 0 ], [ 0, 0, 6, 9, 0, 0, 39, 0, 54 ], [ 0, 1, 0, 0, 19, 38, 0, 50, 0 ], [ 1, 0, 6, 16, 0, 0, 36, 0, 49 ] ] ] ), rec( name := "M12.2", sbgname := "L2(11).2", filename := "L_211.2-1", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 144, rank := 4, permchar := "1a^+ + 11ab + 55a^+ + 66a^+", charnmbs := [ 1, 3, 9, 12 ], ctbl := [ [ 1, 22, 55, 66 ], [ 1, 10, -5, -6 ], [ 1, -2, 7, -6 ], [ 1, -2, -5, 6 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 22, 0, 0 ], [ 1, 10, 5, 6 ], [ 0, 2, 8, 12 ], [ 0, 2, 10, 10 ] ], [ [ 0, 0, 55, 0 ], [ 0, 5, 20, 30 ], [ 1, 8, 22, 24 ], [ 0, 10, 20, 25 ] ], [ [ 0, 0, 0, 66 ], [ 0, 6, 30, 30 ], [ 0, 12, 24, 30 ], [ 1, 10, 25, 30 ] ] ] ), rec( name := "M12.2", sbgname := "L2(11).2", filename := "L_211.2-2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 144, rank := 4, permchar := "1a^+ + 16ab + 45a^+ + 66a^+", charnmbs := [ 1, 4, 5, 12 ], ctbl := [ [ 1, 22, 55, 66 ], [ 1, -5, 10, -6 ], [ 1, 6, -1, -6 ], [ 1, -2, -5, 6 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 22, 0, 0 ], [ 1, 5, 10, 6 ], [ 0, 4, 6, 12 ], [ 0, 2, 10, 10 ] ], [ [ 0, 0, 55, 0 ], [ 0, 10, 15, 30 ], [ 1, 6, 24, 24 ], [ 0, 10, 20, 25 ] ], [ [ 0, 0, 0, 66 ], [ 0, 6, 30, 30 ], [ 0, 12, 24, 30 ], [ 1, 10, 25, 30 ] ] ] ), rec( name := "M12.2", sbgname := "M11", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 24, rank := 3, permchar := "1a^{+-} + 11ab", charnmbs := [ 1, 2, 3 ], ctbl := [ [ 1, 11, 12 ], [ 1, 11, -12 ], [ 1, -1, 0 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 11, 0 ], [ 1, 10, 0 ], [ 0, 0, 11 ] ], [ [ 0, 0, 12 ], [ 0, 0, 12 ], [ 1, 11, 0 ] ] ] ), rec( name := "M12.2", sbgname := "M8.(S4x2)", filename := "M8.S4x2", degree := 495, rank := 8, permchar := "1a^+ + 11ab + 54a^{+-} + 55a^+ + 66a^+ + 99a^- + 144a^+", charnmbs := [ 1, 3, 7, 8, 9, 12, 15, 18 ], ctbl := [ [ 1, 6, 16, 24, 64, 96, 96, 192 ], [ 1, -3, -8, 6, 16, -12, 24, -24 ], [ 1, -3*E(5)-E(5)^2-E(5)^3-3*E(5)^4, -4*E(5)^2-4*E(5)^3, -4*E(5)+2*E(5)^2+2*E(5)^3-4*E(5)^4, -4*E(5)-8*E(5)^2-8*E(5)^3-4*E(5)^4, 8, 8*E(5)+4*E(5)^2+4*E(5)^3+8*E(5)^4, 12*E(5)+16*E(5)^2+16*E(5)^3+12*E(5)^4 ], [ 1, -E(5)-3*E(5)^2-3*E(5)^3-E(5)^4, -4*E(5)-4*E(5)^4, 2*E(5)-4*E(5)^2-4*E(5)^3+2*E(5)^4, -8*E(5)-4*E(5)^2-4*E(5)^3-8*E(5)^4, 8, 4*E(5)+8*E(5)^2+8*E(5)^3+4*E(5)^4, 16*E(5)+12*E(5)^2+12*E(5)^3+16*E(5)^4 ], [ 1, -3, 4, 6, 4, -12, -12, 12 ], [ 1, 3, 4, 0, -8, -12, 12, 0 ], [ 1, 1, -4, -6, 4, -4, -4, 12 ], [ 1, -2, -1, 0, -8, 8, 2, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 6, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 4, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 6, 0 ], [ 0, 1, 0, 1, 0, 4, 0, 0 ], [ 0, 0, 0, 0, 0, 3, 0, 3 ], [ 0, 0, 0, 1, 2, 1, 0, 2 ], [ 0, 0, 1, 0, 0, 0, 1, 4 ], [ 0, 0, 0, 0, 1, 1, 2, 2 ] ], [ [ 0, 0, 16, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 16, 0 ], [ 1, 0, 1, 0, 8, 0, 6, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 16 ], [ 0, 0, 2, 0, 2, 6, 0, 6 ], [ 0, 0, 0, 0, 4, 4, 4, 4 ], [ 0, 1, 1, 0, 0, 4, 2, 8 ], [ 0, 0, 0, 2, 2, 2, 4, 6 ] ], [ [ 0, 0, 0, 24, 0, 0, 0, 0 ], [ 0, 4, 0, 4, 0, 16, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 24 ], [ 1, 1, 0, 2, 8, 4, 0, 8 ], [ 0, 0, 0, 3, 3, 3, 6, 9 ], [ 0, 1, 0, 1, 2, 6, 4, 10 ], [ 0, 0, 0, 0, 4, 4, 8, 8 ], [ 0, 0, 2, 1, 3, 5, 4, 9 ] ], [ [ 0, 0, 0, 0, 64, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 32, 0, 32 ], [ 0, 0, 8, 0, 8, 24, 0, 24 ], [ 0, 0, 0, 8, 8, 8, 16, 24 ], [ 1, 0, 2, 3, 10, 12, 18, 18 ], [ 0, 2, 4, 2, 8, 12, 12, 24 ], [ 0, 0, 0, 4, 12, 12, 16, 20 ], [ 0, 1, 2, 3, 6, 12, 10, 30 ] ], [ [ 0, 0, 0, 0, 0, 96, 0, 0 ], [ 0, 0, 0, 16, 32, 16, 0, 32 ], [ 0, 0, 0, 0, 24, 24, 24, 24 ], [ 0, 4, 0, 4, 8, 24, 16, 40 ], [ 0, 3, 6, 3, 12, 18, 18, 36 ], [ 1, 1, 4, 6, 12, 16, 20, 36 ], [ 0, 0, 4, 4, 12, 20, 12, 44 ], [ 0, 1, 2, 5, 12, 18, 22, 36 ] ], [ [ 0, 0, 0, 0, 0, 0, 96, 0 ], [ 0, 0, 16, 0, 0, 0, 16, 64 ], [ 0, 6, 6, 0, 0, 24, 12, 48 ], [ 0, 0, 0, 0, 16, 16, 32, 32 ], [ 0, 0, 0, 6, 18, 18, 24, 30 ], [ 0, 0, 4, 4, 12, 20, 12, 44 ], [ 1, 1, 2, 8, 16, 12, 24, 32 ], [ 0, 2, 4, 4, 10, 22, 16, 38 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 192 ], [ 0, 0, 0, 0, 32, 32, 64, 64 ], [ 0, 0, 0, 24, 24, 24, 48, 72 ], [ 0, 0, 16, 8, 24, 40, 32, 72 ], [ 0, 3, 6, 9, 18, 36, 30, 90 ], [ 0, 2, 4, 10, 24, 36, 44, 72 ], [ 0, 4, 8, 8, 20, 44, 32, 76 ], [ 1, 2, 6, 9, 30, 36, 38, 70 ] ] ] ), rec( name := "M12.2", sbgname := "M8.(A4x2)leq M8.(S4x2)", filename := "M8.A4x2", degree := 990, rank := 13, permchar := "1a^+ + 11ab + 45a^- + 54a^{+-} + 55a^+ + 66a^{+-} + 99a^- + 120a^{+-} + 144a^{+-}", charnmbs := [ 1, 3, 6, 7, 8, 9, 12, 13, 15, 16, 17, 18, 19 ], ctbl := [ [ 1, 1, 12, 16, 16, 48, 64, 64, 96, 96, 192, 192, 192 ], [ 1, 1, -6, -8, -8, 12, 16, 16, 24, 24, -24, -24, -24 ], [ 1, -1, 0, 8, -8, 0, 16, -16, 8, -8, 16, 0, -16 ], [ 1, 1, -6*E(5)-2*E(5)^2-2*E(5)^3-6*E(5)^4, -4*E(5)^2-4*E(5)^3, -4*E(5)^2-4*E(5)^3, -8*E(5)+4*E(5)^2+4*E(5)^3-8*E(5)^4, -4*E(5)-8*E(5)^2-8*E(5)^3-4*E(5)^4, -4*E(5)-8*E(5)^2-8*E(5)^3-4*E(5)^4, 8*E(5)+4*E(5)^2+4*E(5)^3+8*E(5)^4, 8*E(5)+4*E(5)^2+4*E(5)^3+8*E(5)^4, 12*E(5)+16*E(5)^2+16*E(5)^3+12*E(5)^4, 16, 12*E(5)+16*E(5)^2+16*E(5)^3+12*E(5)^4 ], [ 1, 1, -2*E(5)-6*E(5)^2-6*E(5)^3-2*E(5)^4, -4*E(5)-4*E(5)^4, -4*E(5)-4*E(5)^4, 4*E(5)-8*E(5)^2-8*E(5)^3+4*E(5)^4, -8*E(5)-4*E(5)^2-4*E(5)^3-8*E(5)^4, -8*E(5)-4*E(5)^2-4*E(5)^3-8*E(5)^4, 4*E(5)+8*E(5)^2+8*E(5)^3+4*E(5)^4, 4*E(5)+8*E(5)^2+8*E(5)^3+4*E(5)^4, 16*E(5)+12*E(5)^2+12*E(5)^3+16*E(5)^4, 16, 16*E(5)+12*E(5)^2+12*E(5)^3+16*E(5)^4 ], [ 1, 1, -6, 4, 4, 12, 4, 4, -12, -12, 12, -24, 12 ], [ 1, 1, 6, 4, 4, 0, -8, -8, 12, 12, 0, -24, 0 ], [ 1, -1, 0, 4, -4, 0, -8, 8, 12, -12, -24, 0, 24 ], [ 1, 1, 2, -4, -4, -12, 4, 4, -4, -4, 12, -8, 12 ], [ 1, -1, 0, 2*E(12)^4+2*E(12)^7+2*E(12)^8-2*E(12)^11, -2*E(12)^4-2*E(12)^7-2*E(12)^8+2*E(12)^11, 0, -4*E(12)^4-2*E(12)^7-4*E(12)^8+2*E(12)^11, 4*E(12)^4+2*E(12)^7+4*E(12)^8-2*E(12)^11, 6*E(12)^4-6*E(12)^7+6*E(12)^8+6*E(12)^11, -6*E(12)^4+6*E(12)^7-6*E(12)^8-6*E(12)^11, -6, 0, 6 ], [ 1, -1, 0, 2*E(12)^4-2*E(12)^7+2*E(12)^8+2*E(12)^11, -2*E(12)^4+2*E(12)^7-2*E(12)^8-2*E(12)^11, 0, -4*E(12)^4+2*E(12)^7-4*E(12)^8-2*E(12)^11, 4*E(12)^4-2*E(12)^7+4*E(12)^8+2*E(12)^11, 6*E(12)^4+6*E(12)^7+6*E(12)^8-6*E(12)^11, -6*E(12)^4-6*E(12)^7-6*E(12)^8+6*E(12)^11, -6, 0, 6 ], [ 1, 1, -4, -1, -1, 0, -8, -8, 2, 2, 0, 16, 0 ], [ 1, -1, 0, -1, 1, 0, -8, 8, 2, -2, 16, 0, -16 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 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4, 8, 12, 12, 12, 12, 44, 40, 44 ], [ 0, 0, 2, 2, 2, 10, 12, 12, 22, 22, 36, 36, 36 ], [ 1, 1, 2, 4, 4, 12, 12, 12, 20, 20, 36, 32, 36 ], [ 0, 0, 2, 2, 2, 10, 12, 12, 22, 22, 36, 36, 36 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 16, 16, 32, 32, 32, 32, 32 ], [ 0, 0, 0, 0, 0, 24, 0, 24, 24, 24, 24, 24, 48 ], [ 0, 0, 0, 0, 0, 24, 24, 0, 24, 24, 48, 24, 24 ], [ 0, 0, 0, 8, 8, 8, 12, 12, 16, 16, 36, 40, 36 ], [ 0, 0, 3, 0, 6, 9, 6, 12, 12, 18, 51, 36, 39 ], [ 0, 0, 3, 6, 0, 9, 12, 6, 18, 12, 39, 36, 51 ], [ 0, 0, 4, 4, 4, 8, 8, 12, 20, 12, 32, 44, 44 ], [ 0, 0, 4, 4, 4, 8, 12, 8, 12, 20, 44, 44, 32 ], [ 0, 1, 2, 2, 4, 9, 17, 13, 16, 22, 36, 36, 34 ], [ 0, 0, 2, 2, 2, 10, 12, 12, 22, 22, 36, 36, 36 ], [ 1, 0, 2, 4, 2, 9, 13, 17, 22, 16, 34, 36, 36 ] ] ] ), rec( name := "M12.2", sbgname := "4^2:(6x2) leq 4^2:D12.2", filename := "4^2:6x2", degree := 990, rank := 13, permchar := "1a^+ + 16ab + 45a^- + 54a^{+-} + 55a^{+-}bc + 66a^+ + 99a^{+-} + 144a^+ + 176a^+", charnmbs := [ 1, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20 ], ctbl := [ [ 1, 1, 12, 16, 16, 48, 64, 64, 96, 96, 192, 192, 192 ], [ 1, 1, -6, 7, 7, 12, 10, 10, -12, -12, 12, -42, 12 ], [ 1, 1, -6, -4, -4, 12, -12, -12, -12, -12, 12, 24, 12 ], [ 1, 1, -2*E(5)-6*E(5)^2-6*E(5)^3-2*E(5)^4, -4*E(5)-4*E(5)^4, -4*E(5)-4*E(5)^4, 4*E(5)-8*E(5)^2-8*E(5)^3+4*E(5)^4, 12*E(5)+8*E(5)^2+8*E(5)^3+12*E(5)^4, 12*E(5)+8*E(5)^2+8*E(5)^3+12*E(5)^4, 8, 8, -4*E(5)-4*E(5)^4, 8*E(5)+16*E(5)^2+16*E(5)^3+8*E(5)^4, -4*E(5)-4*E(5)^4 ], [ 1, 1, -6*E(5)-2*E(5)^2-2*E(5)^3-6*E(5)^4, -4*E(5)^2-4*E(5)^3, -4*E(5)^2-4*E(5)^3, -8*E(5)+4*E(5)^2+4*E(5)^3-8*E(5)^4, 8*E(5)+12*E(5)^2+12*E(5)^3+8*E(5)^4, 8*E(5)+12*E(5)^2+12*E(5)^3+8*E(5)^4, 8, 8, -4*E(5)^2-4*E(5)^3, 16*E(5)+8*E(5)^2+8*E(5)^3+16*E(5)^4, -4*E(5)^2-4*E(5)^3 ], [ 1, -1, 0, 8, -8, 0, 8, -8, 0, 0, 24, 0, -24 ], [ 1, -1, 0, -4, 4, 0, -4, 4, -24, 24, 12, 0, -12 ], [ 1, -1, 0, -4, 4, 0, -4, 4, 12, -12, 12, 0, -12 ], [ 1, 1, 6, 4, 4, 0, 4, 4, -12, -12, -12, 24, -12 ], [ 1, -1, 0, 4, -4, 0, -12, 12, 0, 0, -12, 0, 12 ], [ 1, 1, 2, -4, -4, -12, 4, 4, -4, -4, 12, -8, 12 ], [ 1, 1, -4, -1, -1, 0, 4, 4, 8, 8, -12, 4, -12 ], [ 1, -1, 0, -1, 1, 0, 8, -8, 0, 0, -12, 0, 12 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 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], [ 0, 0, 1, 0, 0, 0, 1, 1, 2, 2, 2, 5, 2 ], [ 0, 0, 0, 1, 0, 1, 2, 0, 2, 2, 4, 2, 2 ] ], [ [ 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 8, 0, 0, 8, 0, 0, 16, 16, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 12, 12, 0, 0, 12, 0, 12 ], [ 0, 0, 0, 0, 0, 0, 12, 12, 0, 0, 12, 0, 12 ], [ 1, 1, 2, 0, 0, 4, 0, 0, 4, 4, 16, 0, 16 ], [ 0, 0, 0, 3, 3, 0, 3, 3, 6, 6, 9, 6, 9 ], [ 0, 0, 0, 3, 3, 0, 3, 3, 6, 6, 9, 6, 9 ], [ 0, 0, 2, 0, 0, 2, 4, 4, 6, 6, 8, 8, 8 ], [ 0, 0, 2, 0, 0, 2, 4, 4, 6, 6, 8, 8, 8 ], [ 0, 0, 0, 1, 1, 4, 3, 3, 4, 4, 9, 10, 9 ], [ 0, 0, 0, 0, 0, 0, 2, 2, 4, 4, 10, 16, 10 ], [ 0, 0, 0, 1, 1, 4, 3, 3, 4, 4, 9, 10, 9 ] ], [ [ 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 32, 16 ], [ 0, 0, 0, 0, 0, 12, 12, 4, 0, 0, 24, 12, 0 ], [ 0, 0, 0, 0, 0, 12, 4, 12, 0, 0, 0, 12, 24 ], [ 0, 0, 0, 4, 4, 0, 4, 4, 8, 8, 12, 8, 12 ], [ 1, 0, 0, 3, 1, 3, 0, 2, 6, 6, 12, 12, 18 ], [ 0, 1, 0, 1, 3, 3, 2, 0, 6, 6, 18, 12, 12 ], [ 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, 12, 16, 12 ], [ 0, 0, 0, 0, 0, 4, 4, 4, 8, 4, 12, 16, 12 ], [ 0, 0, 1, 2, 0, 3, 4, 6, 6, 6, 14, 10, 12 ], [ 0, 0, 2, 1, 1, 2, 4, 4, 8, 8, 10, 14, 10 ], [ 0, 0, 1, 0, 2, 3, 6, 4, 6, 6, 12, 10, 14 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 32, 16 ], [ 0, 0, 0, 0, 0, 12, 4, 12, 0, 0, 0, 12, 24 ], [ 0, 0, 0, 0, 0, 12, 12, 4, 0, 0, 24, 12, 0 ], [ 0, 0, 0, 4, 4, 0, 4, 4, 8, 8, 12, 8, 12 ], [ 0, 1, 0, 1, 3, 3, 2, 0, 6, 6, 18, 12, 12 ], [ 1, 0, 0, 3, 1, 3, 0, 2, 6, 6, 12, 12, 18 ], [ 0, 0, 0, 0, 0, 4, 4, 4, 8, 4, 12, 16, 12 ], [ 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, 12, 16, 12 ], [ 0, 0, 1, 0, 2, 3, 6, 4, 6, 6, 12, 10, 14 ], [ 0, 0, 2, 1, 1, 2, 4, 4, 8, 8, 10, 14, 10 ], [ 0, 0, 1, 2, 0, 3, 4, 6, 6, 6, 14, 10, 12 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 16, 0, 0, 8, 8, 32, 0, 32 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 24, 24, 24 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 24, 24, 24 ], [ 0, 0, 4, 0, 0, 4, 8, 8, 12, 12, 16, 16, 16 ], [ 0, 0, 0, 0, 0, 6, 6, 6, 6, 12, 18, 24, 18 ], [ 0, 0, 0, 0, 0, 6, 6, 6, 12, 6, 18, 24, 18 ], [ 1, 0, 1, 0, 4, 6, 4, 8, 2, 14, 24, 20, 12 ], [ 0, 1, 1, 4, 0, 6, 8, 4, 14, 2, 12, 20, 24 ], [ 0, 0, 2, 2, 2, 4, 6, 6, 12, 6, 18, 20, 18 ], [ 0, 0, 0, 2, 2, 4, 8, 8, 10, 10, 20, 12, 20 ], [ 0, 0, 2, 2, 2, 4, 6, 6, 6, 12, 18, 20, 18 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 16, 0, 0, 8, 8, 32, 0, 32 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 24, 24, 24 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 24, 24, 24 ], [ 0, 0, 4, 0, 0, 4, 8, 8, 12, 12, 16, 16, 16 ], [ 0, 0, 0, 0, 0, 6, 6, 6, 12, 6, 18, 24, 18 ], [ 0, 0, 0, 0, 0, 6, 6, 6, 6, 12, 18, 24, 18 ], [ 0, 1, 1, 4, 0, 6, 8, 4, 14, 2, 12, 20, 24 ], [ 1, 0, 1, 0, 4, 6, 4, 8, 2, 14, 24, 20, 12 ], [ 0, 0, 2, 2, 2, 4, 6, 6, 6, 12, 18, 20, 18 ], [ 0, 0, 0, 2, 2, 4, 8, 8, 10, 10, 20, 12, 20 ], [ 0, 0, 2, 2, 2, 4, 6, 6, 12, 6, 18, 20, 18 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192 ], [ 0, 0, 0, 0, 0, 0, 16, 16, 32, 32, 32, 32, 32 ], [ 0, 0, 0, 12, 0, 12, 24, 0, 24, 24, 48, 24, 24 ], [ 0, 0, 0, 0, 12, 12, 0, 24, 24, 24, 24, 24, 48 ], [ 0, 0, 0, 4, 4, 16, 12, 12, 16, 16, 36, 40, 36 ], [ 0, 0, 3, 6, 0, 9, 12, 18, 18, 18, 42, 30, 36 ], [ 0, 0, 3, 0, 6, 9, 18, 12, 18, 18, 36, 30, 42 ], [ 0, 0, 4, 4, 4, 8, 12, 12, 24, 12, 36, 40, 36 ], [ 0, 0, 4, 4, 4, 8, 12, 12, 12, 24, 36, 40, 36 ], [ 1, 0, 2, 4, 2, 9, 14, 12, 18, 18, 40, 38, 34 ], [ 0, 0, 2, 2, 2, 10, 10, 10, 20, 20, 38, 40, 38 ], [ 0, 1, 2, 2, 4, 9, 12, 14, 18, 18, 34, 38, 40 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0 ], [ 0, 0, 0, 16, 16, 0, 32, 32, 0, 0, 32, 32, 32 ], [ 0, 0, 12, 0, 0, 0, 12, 12, 24, 24, 24, 60, 24 ], [ 0, 0, 12, 0, 0, 0, 12, 12, 24, 24, 24, 60, 24 ], [ 0, 0, 0, 0, 0, 0, 8, 8, 16, 16, 40, 64, 40 ], [ 0, 0, 6, 3, 3, 6, 12, 12, 24, 24, 30, 42, 30 ], [ 0, 0, 6, 3, 3, 6, 12, 12, 24, 24, 30, 42, 30 ], [ 0, 0, 0, 4, 4, 8, 16, 16, 20, 20, 40, 24, 40 ], [ 0, 0, 0, 4, 4, 8, 16, 16, 20, 20, 40, 24, 40 ], [ 0, 0, 2, 2, 2, 10, 10, 10, 20, 20, 38, 40, 38 ], [ 1, 1, 2, 5, 5, 16, 14, 14, 12, 12, 40, 30, 40 ], [ 0, 0, 2, 2, 2, 10, 10, 10, 20, 20, 38, 40, 38 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 16, 16, 32, 32, 32, 32, 32 ], [ 0, 0, 0, 0, 12, 12, 0, 24, 24, 24, 24, 24, 48 ], [ 0, 0, 0, 12, 0, 12, 24, 0, 24, 24, 48, 24, 24 ], [ 0, 0, 0, 4, 4, 16, 12, 12, 16, 16, 36, 40, 36 ], [ 0, 0, 3, 0, 6, 9, 18, 12, 18, 18, 36, 30, 42 ], [ 0, 0, 3, 6, 0, 9, 12, 18, 18, 18, 42, 30, 36 ], [ 0, 0, 4, 4, 4, 8, 12, 12, 12, 24, 36, 40, 36 ], [ 0, 0, 4, 4, 4, 8, 12, 12, 24, 12, 36, 40, 36 ], [ 0, 1, 2, 2, 4, 9, 12, 14, 18, 18, 34, 38, 40 ], [ 0, 0, 2, 2, 2, 10, 10, 10, 20, 20, 38, 40, 38 ], [ 1, 0, 2, 4, 2, 9, 14, 12, 18, 18, 40, 38, 34 ] ] ] ), rec( name := "J1", sbgname := "L2(11)", filename := "L_211", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 266, rank := 5, permchar := "1a + 56ab + 76a + 77a", charnmbs := [ 1, 2, 3, 4, 6 ], ctbl := [ [ 1, 11, 12, 110, 132 ], [ 1, 3*E(5)+4*E(5)^2+4*E(5)^3+3*E(5)^4, 3*E(5)+3*E(5)^4, E(5)-6*E(5)^2-6*E(5)^3+E(5)^4, -6*E(5)+3*E(5)^2+3*E(5)^3-6*E(5)^4 ], [ 1, 4*E(5)+3*E(5)^2+3*E(5)^3+4*E(5)^4, 3*E(5)^2+3*E(5)^3, -6*E(5)+E(5)^2+E(5)^3-6*E(5)^4, 3*E(5)-6*E(5)^2-6*E(5)^3+3*E(5)^4 ], [ 1, 4, -2, 5, -8 ], [ 1, 1, 4, -10, 4 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 11, 0, 0, 0 ], [ 1, 0, 0, 10, 0 ], [ 0, 0, 0, 0, 11 ], [ 0, 1, 0, 4, 6 ], [ 0, 0, 1, 5, 5 ] ], [ [ 0, 0, 12, 0, 0 ], [ 0, 0, 0, 0, 12 ], [ 1, 0, 0, 0, 11 ], [ 0, 0, 0, 6, 6 ], [ 0, 1, 1, 5, 5 ] ], [ [ 0, 0, 0, 110, 0 ], [ 0, 10, 0, 40, 60 ], [ 0, 0, 0, 55, 55 ], [ 1, 4, 6, 45, 54 ], [ 0, 5, 5, 45, 55 ] ], [ [ 0, 0, 0, 0, 132 ], [ 0, 0, 12, 60, 60 ], [ 0, 11, 11, 55, 55 ], [ 0, 6, 6, 54, 66 ], [ 1, 5, 5, 55, 66 ] ] ] ), rec( name := "J1", sbgname := "2^3.7.3", degree := 1045, rank := 11, permchar := "1a + 56ab + 76a + 77bc + 120abc + 133a + 209a", charnmbs := [ 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 15 ], ctbl := [ [ 1, 8, 28, 56, 56, 56, 168, 168, 168, 168, 168 ], [ 1, 3*E(5)+E(5)^2+E(5)^3+3*E(5)^4, -4*E(5)+2*E(5)^2+2*E(5)^3-4*E(5)^4, -5*E(5)+3*E(5)^2+3*E(5)^3-5*E(5)^4, 12*E(5)+10*E(5)^2+10*E(5)^3+12*E(5)^4, -8*E(5)-15*E(5)^2-15*E(5)^3-8*E(5)^4, -6*E(5)+6*E(5)^2+6*E(5)^3-6*E(5)^4, 15*E(5)+18*E(5)^2+18*E(5)^3+15*E(5)^4, -18*E(5)-9*E(5)^2-9*E(5)^3-18*E(5)^4, 12*E(5)+12*E(5)^4, -15*E(5)^2-15*E(5)^3 ], [ 1, E(5)+3*E(5)^2+3*E(5)^3+E(5)^4, 2*E(5)-4*E(5)^2-4*E(5)^3+2*E(5)^4, 3*E(5)-5*E(5)^2-5*E(5)^3+3*E(5)^4, 10*E(5)+12*E(5)^2+12*E(5)^3+10*E(5)^4, -15*E(5)-8*E(5)^2-8*E(5)^3-15*E(5)^4, 6*E(5)-6*E(5)^2-6*E(5)^3+6*E(5)^4, 18*E(5)+15*E(5)^2+15*E(5)^3+18*E(5)^4, -9*E(5)-18*E(5)^2-18*E(5)^3-9*E(5)^4, 12*E(5)^2+12*E(5)^3, -15*E(5)-15*E(5)^4 ], [ 1, 2, 11, -4, 4, -2, -24, -6, 12, 18, -12 ], [ 1, 3*E(5)+E(5)^2+E(5)^3+3*E(5)^4, -7, -5*E(5)+3*E(5)^2+3*E(5)^3-5*E(5)^4, 8*E(5)^2+8*E(5)^3, 5*E(5)+3*E(5)^2+3*E(5)^3+5*E(5)^4, 3, 6*E(5)-12*E(5)^2-12*E(5)^3+6*E(5)^4, -6*E(5)^2-6*E(5)^3, -21*E(5)-15*E(5)^2-15*E(5)^3-21*E(5)^4, 9*E(5)+15*E(5)^2+15*E(5)^3+9*E(5)^4 ], [ 1, E(5)+3*E(5)^2+3*E(5)^3+E(5)^4, -7, 3*E(5)-5*E(5)^2-5*E(5)^3+3*E(5)^4, 8*E(5)+8*E(5)^4, 3*E(5)+5*E(5)^2+5*E(5)^3+3*E(5)^4, 3, -12*E(5)+6*E(5)^2+6*E(5)^3-12*E(5)^4, -6*E(5)-6*E(5)^4, -15*E(5)-21*E(5)^2-21*E(5)^3-15*E(5)^4, 15*E(5)+9*E(5)^2+9*E(5)^3+15*E(5)^4 ], [ 1, -E(19)-2*E(19)^2-2*E(19)^3-2*E(19)^4-2*E(19)^5-2*E(19)^6-E(19)^7-E(19)^8-2*E(19)^9-2*E(19)^10-E(19)^11-E(19)^12-2*E(19)^13-2*E(19)^14-2*E(19)^15-2*E(19)^16-2*E(19)^17-E(19)^18, 2*E(19)^4+2*E(19)^6+2*E(19)^9+2*E(19)^10+2*E(19)^13+2*E(19)^15 , 4*E(19)-E(19)^2-E(19)^3-E(19)^5+4*E(19)^7+4*E(19)^8+4*E(19)^11+4*E(19)^12-E(19)^14-E(19)^16-E(19)^17+4*E(19)^18, -E(19)+2*E(19)^2+2*E(19)^3-2*E(19)^4+2*E(19)^5-2*E(19)^6-E(19)^7-E(19)^8-2*E(19)^9-2*E(19)^10-E(19)^11-E(19)^12-2*E(19)^13 +2*E(19)^14-2*E(19)^15+2*E(19)^16+2*E(19)^17-E(19)^18, 7*E(19)+7*E(19)^2+7*E(19)^3+6*E(19)^4+7*E(19)^5+6*E(19)^6+7*E(19)^7+7*E(19)^8+6*E(19)^9+6*E(19)^10+7*E(19)^11+7*E(19)^12+6*E(19)^13+7*E(19)^14+6*E(19)^15+7*E(19)^16+7*E(19)^17 +7*E(19)^18, -6*E(19)-2*E(19)^2-2*E(19)^3-E(19)^4-2*E(19)^5-E(19)^6-6*E(19)^7-6*E(19)^8-E(19)^9-E(19)^10-6*E(19)^11-6*E(19)^12-E(19)^13-2*E(19)^14-E(19)^15-2*E(19)^16-2*E(19)^17-6*E(19)^18, 3*E(19)+E(19)^2+E(19)^3+2*E(19)^4+E(19)^5+2*E(19)^6+3*E(19)^7+3*E(19)^8+2*E(19)^9+2*E(19)^10+3*E(19)^11+3*E(19)^12+2*E(19)^13+E(19)^14+2*E(19)^15+E(19)^16+E(19)^17+3*E(19)^18, -E(19)+2*E(19)^2+2*E(19)^3-5*E(19)^4+2*E(19)^5-5*E(19)^6-E(19)^7 -E(19)^8-5*E(19)^9-5*E(19)^10-E(19)^11-E(19)^12-5*E(19)^13+2*E(19)^14-5*E(19)^15+2*E(19)^16+2*E(19)^17-E(19)^18, 5*E(19)+4*E(19)^2+4*E(19)^3+8*E(19)^4+4*E(19)^5+8*E(19)^6+5*E(19)^7+5*E(19)^8+8*E(19)^9+8*E(19)^10+5*E(19)^11+5*E(19)^12 +8*E(19)^13+4*E(19)^14+8*E(19)^15+4*E(19)^16+4*E(19)^17+5*E(19)^18, -9*E(19)-10*E(19)^2-10*E(19)^3-7*E(19)^4-10*E(19)^5-7*E(19)^6-9*E(19)^7-9*E(19)^8-7*E(19)^9-7*E(19)^10-9*E(19)^11-9*E(19)^12-7*E(19)^13-10*E(19)^14-7*E(19)^15 -10*E(19)^16-10*E(19)^17-9*E(19)^18 ], [ 1, -2*E(19)-2*E(19)^2-2*E(19)^3-E(19)^4-2*E(19)^5-E(19)^6-2*E(19)^7-2*E(19)^8-E(19)^9-E(19)^10-2*E(19)^11-2*E(19)^12-E(19)^13-2*E(19)^14-E(19)^15-2*E(19)^16-2*E(19)^17-2*E(19)^18, 2*E(19)^2+2*E(19)^3+2*E(19)^5+2*E(19)^14+2*E(19)^16+2*E(19)^17, -E(19)+4*E(19)^4+4*E(19)^6-E(19)^7-E(19)^8+4*E(19)^9+4*E(19)^10-E(19)^11-E(19)^12+4*E(19)^13+4*E(19)^15-E(19)^18, 2*E(19)-2*E(19)^2-2*E(19)^3-E(19)^4-2*E(19)^5-E(19)^6 +2*E(19)^7+2*E(19)^8-E(19)^9-E(19)^10+2*E(19)^11+2*E(19)^12-E(19)^13-2*E(19)^14-E(19)^15-2*E(19)^16-2*E(19)^17+2*E(19)^18, 7*E(19)+6*E(19)^2+6*E(19)^3+7*E(19)^4+6*E(19)^5+7*E(19)^6+7*E(19)^7+7*E(19)^8+7*E(19)^9+7*E(19)^10+7*E(19)^11 +7*E(19)^12+7*E(19)^13+6*E(19)^14+7*E(19)^15+6*E(19)^16+6*E(19)^17+7*E(19)^18, -2*E(19)-E(19)^2-E(19)^3-6*E(19)^4-E(19)^5-6*E(19)^6-2*E(19)^7-2*E(19)^8-6*E(19)^9-6*E(19)^10-2*E(19)^11-2*E(19)^12-6*E(19)^13-E(19)^14-6*E(19)^15-E(19)^16 -E(19)^17-2*E(19)^18, E(19)+2*E(19)^2+2*E(19)^3+3*E(19)^4+2*E(19)^5+3*E(19)^6+E(19)^7+E(19)^8+3*E(19)^9+3*E(19)^10+E(19)^11+E(19)^12+3*E(19)^13+2*E(19)^14+3*E(19)^15+2*E(19)^16+2*E(19)^17+E(19)^18, 2*E(19)-5*E(19)^2-5*E(19)^3-E(19)^4-5*E(19)^5-E(19)^6+2*E(19)^7+2*E(19)^8-E(19)^9-E(19)^10+2*E(19)^11+2*E(19)^12-E(19)^13-5*E(19)^14-E(19)^15-5*E(19)^16-5*E(19)^17+2*E(19)^18, 4*E(19)+8*E(19)^2+8*E(19)^3+5*E(19)^4+8*E(19)^5+5*E(19)^6 +4*E(19)^7+4*E(19)^8+5*E(19)^9+5*E(19)^10+4*E(19)^11+4*E(19)^12+5*E(19)^13+8*E(19)^14+5*E(19)^15+8*E(19)^16+8*E(19)^17+4*E(19)^18, -10*E(19)-7*E(19)^2-7*E(19)^3-9*E(19)^4-7*E(19)^5-9*E(19)^6-10*E(19)^7-10*E(19)^8-9*E(19)^9-9*E(19)^10 -10*E(19)^11-10*E(19)^12-9*E(19)^13-7*E(19)^14-9*E(19)^15-7*E(19)^16-7*E(19)^17-10*E(19)^18 ], [ 1, -2*E(19)-E(19)^2-E(19)^3-2*E(19)^4-E(19)^5-2*E(19)^6-2*E(19)^7-2*E(19)^8-2*E(19)^9-2*E(19)^10-2*E(19)^11-2*E(19)^12-2*E(19)^13-E(19)^14 -2*E(19)^15-E(19)^16-E(19)^17-2*E(19)^18, 2*E(19)+2*E(19)^7+2*E(19)^8+2*E(19)^11+2*E(19)^12+2*E(19)^18, 4*E(19)^2+4*E(19)^3-E(19)^4+4*E(19)^5-E(19)^6-E(19)^9-E(19)^10-E(19)^13+4*E(19)^14-E(19)^15+4*E(19)^16+4*E(19)^17, -2*E(19)-E(19)^2-E(19)^3+2*E(19)^4-E(19)^5+2*E(19)^6-2*E(19)^7-2*E(19)^8+2*E(19)^9+2*E(19)^10-2*E(19)^11-2*E(19)^12+2*E(19)^13-E(19)^14+2*E(19)^15-E(19)^16-E(19)^17-2*E(19)^18, 6*E(19)+7*E(19)^2+7*E(19)^3+7*E(19)^4+7*E(19)^5+7*E(19)^6 +6*E(19)^7+6*E(19)^8+7*E(19)^9+7*E(19)^10+6*E(19)^11+6*E(19)^12+7*E(19)^13+7*E(19)^14+7*E(19)^15+7*E(19)^16+7*E(19)^17+6*E(19)^18, -E(19)-6*E(19)^2-6*E(19)^3-2*E(19)^4-6*E(19)^5-2*E(19)^6-E(19)^7-E(19)^8-2*E(19)^9-2*E(19)^10-E(19)^11 -E(19)^12-2*E(19)^13-6*E(19)^14-2*E(19)^15-6*E(19)^16-6*E(19)^17-E(19)^18, 2*E(19)+3*E(19)^2+3*E(19)^3+E(19)^4+3*E(19)^5+E(19)^6+2*E(19)^7+2*E(19)^8+E(19)^9+E(19)^10+2*E(19)^11+2*E(19)^12+E(19)^13+3*E(19)^14+E(19)^15+3*E(19)^16 +3*E(19)^17+2*E(19)^18, -5*E(19)-E(19)^2-E(19)^3+2*E(19)^4-E(19)^5+2*E(19)^6-5*E(19)^7-5*E(19)^8+2*E(19)^9+2*E(19)^10-5*E(19)^11-5*E(19)^12+2*E(19)^13-E(19)^14+2*E(19)^15-E(19)^16-E(19)^17-5*E(19)^18, 8*E(19)+5*E(19)^2+5*E(19)^3+4*E(19)^4+5*E(19)^5+4*E(19)^6+8*E(19)^7+8*E(19)^8+4*E(19)^9+4*E(19)^10+8*E(19)^11+8*E(19)^12+4*E(19)^13+5*E(19)^14+4*E(19)^15+5*E(19)^16+5*E(19)^17+8*E(19)^18, -7*E(19)-9*E(19)^2-9*E(19)^3-10*E(19)^4-9*E(19)^5 -10*E(19)^6-7*E(19)^7-7*E(19)^8-10*E(19)^9-10*E(19)^10-7*E(19)^11-7*E(19)^12-10*E(19)^13-9*E(19)^14-10*E(19)^15-9*E(19)^16-9*E(19)^17-7*E(19)^18 ], [ 1, 3, 1, 1, 4, 9, 15, -4, -14, -1, -15 ], [ 1, -3, 1, 1, 4, 3, -9, 14, -8, -7, 3 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0 ], [ 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 3 ], [ 0, 0, 1, 0, 0, 1, 3, 0, 3, 0, 0 ], [ 0, 0, 0, 0, 1, 1, 3, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 1, 1, 2, 2, 0, 1, 1 ], [ 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1 ], [ 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 2 ], [ 0, 0, 1, 0, 0, 1, 1, 2, 2, 0, 1 ], [ 0, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2 ] ], [ [ 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 7, 0, 0, 0, 0, 21, 0 ], [ 1, 0, 3, 0, 0, 0, 0, 0, 12, 12, 0 ], [ 0, 0, 0, 0, 0, 4, 6, 6, 9, 0, 3 ], [ 0, 1, 0, 0, 0, 3, 0, 9, 3, 9, 3 ], [ 0, 0, 0, 4, 3, 0, 6, 6, 6, 3, 0 ], [ 0, 0, 0, 2, 0, 2, 8, 4, 3, 2, 7 ], [ 0, 0, 0, 2, 3, 2, 4, 2, 3, 5, 7 ], [ 0, 0, 2, 3, 1, 2, 3, 3, 6, 5, 3 ], [ 0, 1, 2, 0, 3, 1, 2, 5, 5, 4, 5 ], [ 0, 0, 0, 1, 1, 0, 7, 7, 3, 5, 4 ] ], [ [ 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 7, 0, 7, 0, 0, 0, 21, 0, 0, 21 ], [ 0, 0, 0, 0, 0, 8, 12, 12, 18, 0, 6 ], [ 1, 1, 0, 6, 0, 0, 9, 6, 12, 9, 12 ], [ 0, 0, 0, 0, 1, 4, 9, 12, 3, 18, 9 ], [ 0, 0, 4, 0, 4, 0, 15, 12, 9, 6, 6 ], [ 0, 0, 2, 3, 3, 5, 8, 7, 11, 10, 7 ], [ 0, 1, 2, 2, 4, 4, 7, 8, 8, 7, 13 ], [ 0, 0, 3, 4, 1, 3, 11, 8, 8, 8, 10 ], [ 0, 0, 0, 3, 6, 2, 10, 7, 8, 11, 9 ], [ 0, 1, 1, 4, 3, 2, 7, 13, 10, 9, 6 ] ], [ [ 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 7, 0, 0, 7, 21, 0, 21, 0, 0 ], [ 0, 2, 0, 0, 0, 6, 0, 18, 6, 18, 6 ], [ 0, 0, 0, 0, 1, 4, 9, 12, 3, 18, 9 ], [ 1, 0, 0, 1, 0, 3, 12, 9, 18, 6, 6 ], [ 0, 1, 3, 4, 3, 0, 12, 15, 3, 9, 6 ], [ 0, 1, 0, 3, 4, 4, 9, 8, 8, 9, 10 ], [ 0, 0, 3, 4, 3, 5, 8, 6, 8, 6, 13 ], [ 0, 1, 1, 1, 6, 1, 8, 8, 9, 9, 12 ], [ 0, 0, 3, 6, 2, 3, 9, 6, 9, 10, 8 ], [ 0, 0, 1, 3, 2, 2, 10, 13, 12, 8, 5 ] ], [ [ 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 7, 7, 21, 0, 0, 21, 0 ], [ 0, 0, 0, 8, 6, 0, 12, 12, 12, 6, 0 ], [ 0, 0, 4, 0, 4, 0, 15, 12, 9, 6, 6 ], [ 0, 1, 3, 4, 3, 0, 12, 15, 3, 9, 6 ], [ 1, 1, 0, 0, 0, 9, 9, 0, 6, 12, 18 ], [ 0, 1, 2, 5, 4, 3, 10, 10, 9, 8, 4 ], [ 0, 0, 2, 4, 5, 0, 10, 11, 8, 9, 7 ], [ 0, 0, 2, 3, 1, 2, 9, 8, 9, 10, 12 ], [ 0, 1, 1, 2, 3, 4, 8, 9, 10, 7, 11 ], [ 0, 0, 0, 2, 2, 6, 4, 7, 12, 11, 12 ] ], [ [ 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 21, 21, 42, 42, 0, 21, 21 ], [ 0, 0, 0, 12, 0, 12, 48, 24, 18, 12, 42 ], [ 0, 0, 6, 9, 9, 15, 24, 21, 33, 30, 21 ], [ 0, 3, 0, 9, 12, 12, 27, 24, 24, 27, 30 ], [ 0, 3, 6, 15, 12, 9, 30, 30, 27, 24, 12 ], [ 1, 2, 8, 8, 9, 10, 24, 24, 27, 30, 25 ], [ 0, 2, 4, 7, 8, 10, 24, 25, 29, 31, 28 ], [ 0, 0, 3, 11, 8, 9, 27, 29, 32, 21, 28 ], [ 0, 1, 2, 10, 9, 8, 30, 31, 21, 26, 30 ], [ 0, 1, 7, 7, 10, 4, 25, 28, 28, 30, 28 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0 ], [ 0, 0, 0, 21, 0, 0, 42, 0, 42, 42, 21 ], [ 0, 0, 0, 12, 18, 12, 24, 12, 18, 30, 42 ], [ 0, 3, 6, 6, 12, 12, 21, 24, 24, 21, 39 ], [ 0, 0, 9, 12, 9, 15, 24, 18, 24, 18, 39 ], [ 0, 0, 6, 12, 15, 0, 30, 33, 24, 27, 21 ], [ 0, 2, 4, 7, 8, 10, 24, 25, 29, 31, 28 ], [ 1, 0, 2, 8, 6, 11, 25, 30, 29, 31, 25 ], [ 0, 2, 3, 8, 8, 8, 29, 29, 24, 32, 25 ], [ 0, 2, 5, 7, 6, 9, 31, 31, 32, 21, 24 ], [ 0, 1, 7, 13, 13, 7, 28, 25, 25, 24, 25 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0 ], [ 0, 0, 0, 0, 21, 0, 0, 42, 21, 42, 42 ], [ 0, 0, 12, 18, 6, 12, 18, 18, 36, 30, 18 ], [ 0, 0, 9, 12, 3, 9, 33, 24, 24, 24, 30 ], [ 0, 3, 3, 3, 18, 3, 24, 24, 27, 27, 36 ], [ 0, 0, 6, 9, 3, 6, 27, 24, 27, 30, 36 ], [ 0, 0, 3, 11, 8, 9, 27, 29, 32, 21, 28 ], [ 0, 2, 3, 8, 8, 8, 29, 29, 24, 32, 25 ], [ 1, 1, 6, 8, 9, 9, 32, 24, 32, 22, 24 ], [ 0, 2, 5, 8, 9, 10, 21, 32, 22, 33, 26 ], [ 0, 2, 3, 10, 12, 12, 28, 25, 24, 26, 26 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0 ], [ 0, 0, 21, 0, 0, 21, 21, 42, 42, 0, 21 ], [ 0, 6, 12, 0, 18, 6, 12, 30, 30, 24, 30 ], [ 0, 0, 0, 9, 18, 6, 30, 21, 24, 33, 27 ], [ 0, 0, 9, 18, 6, 9, 27, 18, 27, 30, 24 ], [ 0, 3, 3, 6, 9, 12, 24, 27, 30, 21, 33 ], [ 0, 1, 2, 10, 9, 8, 30, 31, 21, 26, 30 ], [ 0, 2, 5, 7, 6, 9, 31, 31, 32, 21, 24 ], [ 0, 2, 5, 8, 9, 10, 21, 32, 22, 33, 26 ], [ 1, 0, 4, 11, 10, 7, 26, 21, 33, 32, 23 ], [ 0, 1, 5, 9, 8, 11, 30, 24, 26, 23, 31 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168 ], [ 0, 0, 0, 21, 0, 0, 21, 21, 42, 21, 42 ], [ 0, 0, 0, 6, 6, 0, 42, 42, 18, 30, 24 ], [ 0, 3, 3, 12, 9, 6, 21, 39, 30, 27, 18 ], [ 0, 0, 3, 9, 6, 6, 30, 39, 36, 24, 15 ], [ 0, 0, 0, 6, 6, 18, 12, 21, 36, 33, 36 ], [ 0, 1, 7, 7, 10, 4, 25, 28, 28, 30, 28 ], [ 0, 1, 7, 13, 13, 7, 28, 25, 25, 24, 25 ], [ 0, 2, 3, 10, 12, 12, 28, 25, 24, 26, 26 ], [ 0, 1, 5, 9, 8, 11, 30, 24, 26, 23, 31 ], [ 1, 2, 4, 6, 5, 12, 28, 25, 26, 31, 28 ] ] ] ), rec( name := "M22", sbgname := "L3(4)", filename := "L34", degree := 22, rank := 2, permchar := "1a + 21a", charnmbs := [ 1, 2 ], ctbl := [ [ 1, 21 ], [ 1, -1 ] ], mats := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 21 ], [ 1, 20 ] ] ] ), rec( name := "M22", sbgname := "2^3:L3(2)", filename := "2^3:L32", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 330, rank := 5, permchar := "1a + 21a + 55a + 99a + 154a", charnmbs := [ 1, 2, 5, 6, 7 ], ctbl := [ [ 1, 7, 42, 112, 168 ], [ 1, -4, 9, 24, -30 ], [ 1, 4, 9, -8, -6 ], [ 1, -3, 2, -8, 8 ], [ 1, 1, -6, 4, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 7, 0, 0, 0 ], [ 1, 0, 6, 0, 0 ], [ 0, 1, 2, 0, 4 ], [ 0, 0, 0, 1, 6 ], [ 0, 0, 1, 4, 2 ] ], [ [ 0, 0, 42, 0, 0 ], [ 0, 6, 12, 0, 24 ], [ 1, 2, 7, 16, 16 ], [ 0, 0, 6, 18, 18 ], [ 0, 1, 4, 12, 25 ] ], [ [ 0, 0, 0, 112, 0 ], [ 0, 0, 0, 16, 96 ], [ 0, 0, 16, 48, 48 ], [ 1, 1, 18, 44, 48 ], [ 0, 4, 12, 32, 64 ] ], [ [ 0, 0, 0, 0, 168 ], [ 0, 0, 24, 96, 48 ], [ 0, 4, 16, 48, 100 ], [ 0, 6, 18, 48, 96 ], [ 1, 2, 25, 64, 76 ] ] ] ), rec( name := "M22", sbgname := "2^4:A5 leq 2^4:A6", filename := "2^4:A5", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 462, rank := 5, permchar := "1a + 21a + 55a + 154a + 231a", charnmbs := [ 1, 2, 5, 7, 9 ], ctbl := [ [ 1, 5, 96, 120, 240 ], [ 1, 5, -36, 10, 20 ], [ 1, 5, 12, -6, -12 ], [ 1, -1, 0, 12, -12 ], [ 1, -1, 0, -8, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 5, 0, 0, 0 ], [ 1, 4, 0, 0, 0 ], [ 0, 0, 5, 0, 0 ], [ 0, 0, 0, 1, 4 ], [ 0, 0, 0, 2, 3 ] ], [ [ 0, 0, 96, 0, 0 ], [ 0, 0, 96, 0, 0 ], [ 1, 5, 0, 30, 60 ], [ 0, 0, 24, 24, 48 ], [ 0, 0, 24, 24, 48 ] ], [ [ 0, 0, 0, 120, 0 ], [ 0, 0, 0, 24, 96 ], [ 0, 0, 30, 30, 60 ], [ 1, 1, 24, 34, 60 ], [ 0, 2, 24, 30, 64 ] ], [ [ 0, 0, 0, 0, 240 ], [ 0, 0, 0, 96, 144 ], [ 0, 0, 60, 60, 120 ], [ 0, 4, 48, 60, 128 ], [ 1, 3, 48, 64, 124 ] ] ] ), rec( name := "M22", sbgname := "2^4:A6", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 77, rank := 3, permchar := "1a + 21a + 55a", charnmbs := [ 1, 2, 5 ], ctbl := [ [ 1, 16, 60 ], [ 1, -6, 5 ], [ 1, 2, -3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 16, 0 ], [ 1, 0, 15 ], [ 0, 4, 12 ] ], [ [ 0, 0, 60 ], [ 0, 15, 45 ], [ 1, 12, 47 ] ] ] ), rec( name := "M22", sbgname := "2^4:S5", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 231, rank := 4, permchar := "1a + 21a + 55a + 154a", charnmbs := [ 1, 2, 5, 7 ], ctbl := [ [ 1, 30, 40, 160 ], [ 1, -3, 18, -16 ], [ 1, 9, -2, -8 ], [ 1, -3, -2, 4 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 30, 0, 0 ], [ 1, 9, 4, 16 ], [ 0, 3, 3, 24 ], [ 0, 3, 6, 21 ] ], [ [ 0, 0, 40, 0 ], [ 0, 4, 4, 32 ], [ 1, 3, 20, 16 ], [ 0, 6, 4, 30 ] ], [ [ 0, 0, 0, 160 ], [ 0, 16, 32, 112 ], [ 0, 24, 16, 120 ], [ 1, 21, 30, 108 ] ] ] ), rec( name := "M22", sbgname := "A6.2_3", filename := "A6.2^3", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 616, rank := 5, permchar := "1a + 21a + 55a + 154a + 385a", charnmbs := [ 1, 2, 5, 7, 12 ], ctbl := [ [ 1, 30, 45, 180, 360 ], [ 1, 8, -21, 48, -36 ], [ 1, 16, 3, -16, -4 ], [ 1, -2, 9, 8, -16 ], [ 1, -2, -3, -4, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 30, 0, 0, 0 ], [ 1, 14, 3, 0, 12 ], [ 0, 2, 4, 0, 24 ], [ 0, 0, 0, 14, 16 ], [ 0, 1, 3, 8, 18 ] ], [ [ 0, 0, 45, 0, 0 ], [ 0, 3, 6, 0, 36 ], [ 1, 4, 0, 32, 8 ], [ 0, 0, 8, 5, 32 ], [ 0, 3, 1, 16, 25 ] ], [ [ 0, 0, 0, 180, 0 ], [ 0, 0, 0, 84, 96 ], [ 0, 0, 32, 20, 128 ], [ 1, 14, 5, 72, 88 ], [ 0, 8, 16, 44, 112 ] ], [ [ 0, 0, 0, 0, 360 ], [ 0, 12, 36, 96, 216 ], [ 0, 24, 8, 128, 200 ], [ 0, 16, 32, 88, 224 ], [ 1, 18, 25, 112, 204 ] ] ] ), rec( name := "M22", sbgname := "A7", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 176, rank := 3, permchar := "1a + 21a + 154a", permchar2 := "1a + 21a + 154a", charnmbs := [ 1, 2, 7 ], charnmbs2 := [ 1, 2, 7 ], ctbl := [ [ 1, 70, 105 ], [ 1, -18, 17 ], [ 1, 2, -3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 70, 0 ], [ 1, 18, 51 ], [ 0, 34, 36 ] ], [ [ 0, 0, 105 ], [ 0, 51, 54 ], [ 1, 36, 68 ] ] ] ), rec( name := "M22", sbgname := "L2(11)", filename := "L211", degree := 672, rank := 6, permchar := "1a + 21a + 55a + 154a + 210a + 231a", charnmbs := [ 1, 2, 5, 7, 8, 9 ], ctbl := [ [ 1, 55, 55, 66, 165, 330 ], [ 1, 15, -25, -6, 45, -30 ], [ 1, 13, 13, -18, -3, -6 ], [ 1, -5, 7, 6, 9, -18 ], [ 1, -7, -3, -6, 1, 14 ], [ 1, 5, -3, 6, -11, 2 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 55, 0, 0, 0, 0 ], [ 1, 8, 4, 0, 18, 24 ], [ 0, 4, 12, 0, 3, 36 ], [ 0, 0, 0, 10, 10, 35 ], [ 0, 6, 1, 4, 20, 24 ], [ 0, 4, 6, 7, 12, 26 ] ], [ [ 0, 0, 55, 0, 0, 0 ], [ 0, 4, 12, 0, 3, 36 ], [ 1, 12, 0, 0, 30, 12 ], [ 0, 0, 0, 10, 20, 25 ], [ 0, 1, 10, 8, 4, 32 ], [ 0, 6, 2, 5, 16, 26 ] ], [ [ 0, 0, 0, 66, 0, 0 ], [ 0, 0, 0, 12, 12, 42 ], [ 0, 0, 0, 12, 24, 30 ], [ 1, 10, 10, 0, 15, 30 ], [ 0, 4, 8, 6, 16, 32 ], [ 0, 7, 5, 6, 16, 32 ] ], [ [ 0, 0, 0, 0, 165, 0 ], [ 0, 18, 3, 12, 60, 72 ], [ 0, 3, 30, 24, 12, 96 ], [ 0, 10, 20, 15, 40, 80 ], [ 1, 20, 4, 16, 56, 68 ], [ 0, 12, 16, 16, 34, 87 ] ], [ [ 0, 0, 0, 0, 0, 330 ], [ 0, 24, 36, 42, 72, 156 ], [ 0, 36, 12, 30, 96, 156 ], [ 0, 35, 25, 30, 80, 160 ], [ 0, 24, 32, 32, 68, 174 ], [ 1, 26, 26, 32, 87, 158 ] ] ] ), rec( name := "M22.2", sbgname := "L3(4).2_2", filename := "L34.2_2", degree := 22, rank := 2, permchar := "1a^+ + 21a^+", charnmbs := [ 1, 3 ], ctbl := [ [ 1, 21 ], [ 1, -1 ] ], mats := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 21 ], [ 1, 20 ] ] ] ), rec( name := "M22.2", sbgname := "2^3:L3(2)x2", filename := "2^3:L32x2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 330, rank := 5, permchar := "1a^+ + 21a^+ + 55a^+ + 99a^+ + 154a^+", charnmbs := [ 1, 3, 9, 11, 13 ], ctbl := [ [ 1, 7, 42, 112, 168 ], [ 1, -4, 9, 24, -30 ], [ 1, 4, 9, -8, -6 ], [ 1, -3, 2, -8, 8 ], [ 1, 1, -6, 4, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 7, 0, 0, 0 ], [ 1, 0, 6, 0, 0 ], [ 0, 1, 2, 0, 4 ], [ 0, 0, 0, 1, 6 ], [ 0, 0, 1, 4, 2 ] ], [ [ 0, 0, 42, 0, 0 ], [ 0, 6, 12, 0, 24 ], [ 1, 2, 7, 16, 16 ], [ 0, 0, 6, 18, 18 ], [ 0, 1, 4, 12, 25 ] ], [ [ 0, 0, 0, 112, 0 ], [ 0, 0, 0, 16, 96 ], [ 0, 0, 16, 48, 48 ], [ 1, 1, 18, 44, 48 ], [ 0, 4, 12, 32, 64 ] ], [ [ 0, 0, 0, 0, 168 ], [ 0, 0, 24, 96, 48 ], [ 0, 4, 16, 48, 100 ], [ 0, 6, 18, 48, 96 ], [ 1, 2, 25, 64, 76 ] ] ] ), rec( name := "M22.2", sbgname := "2^4:A5 leq 2^4:S6", filename := "2^4:A5", degree := 924, rank := 10, permchar := "1a^{+-} + 21a^{+-} + 55a^{+-} + 154a^{+-} + 231a^{+-}", charnmbs := [ 1, 2, 3, 4, 9, 10, 13, 14, 17, 18 ], ctbl := [ [ 1, 1, 5, 5, 96, 96, 120, 120, 240, 240 ], [ 1, -1, -5, 5, -96, 96, -120, 120, -240, 240 ], [ 1, 1, 5, 5, -36, -36, 10, 10, 20, 20 ], [ 1, -1, -5, 5, 36, -36, -10, 10, -20, 20 ], [ 1, 1, 5, 5, 12, 12, -6, -6, -12, -12 ], [ 1, -1, -5, 5, -12, 12, 6, -6, 12, -12 ], [ 1, 1, -1, -1, 0, 0, 12, 12, -12, -12 ], [ 1, -1, 1, -1, 0, 0, -12, 12, 12, -12 ], [ 1, -1, 1, -1, 0, 0, 8, -8, -8, 8 ], [ 1, 1, -1, -1, 0, 0, -8, -8, 8, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 5, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 5, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 4, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 4, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 5, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 5, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 4 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 4, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0, 3 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 3, 0 ] ], [ [ 0, 0, 0, 5, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 5, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 4, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 4, 0, 0, 0, 0, 0, 0 ] , [ 0, 0, 0, 0, 5, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 5, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 4, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 4 ], [ 0, 0, 0, 0, 0, 0, 2, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 0, 3 ] ], [ [ 0, 0, 0, 0, 96, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 96, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 96, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 96, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 5, 0, 0, 0, 30, 0, 60 ], [ 0, 1, 5, 0, 0, 0, 30, 0, 60, 0 ], [ 0, 0, 0, 0, 0, 24, 0, 24, 0, 48 ], [ 0, 0, 0, 0, 24, 0, 24, 0, 48, 0 ], [ 0, 0, 0, 0, 0, 24, 0, 24, 0, 48 ], [ 0, 0, 0, 0, 24, 0, 24, 0, 48, 0 ] ], [ [ 0, 0, 0, 0, 0, 96, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 96, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 96, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 96, 0, 0, 0, 0 ], [ 0, 1, 5, 0, 0, 0, 30, 0, 60, 0 ], [ 1, 0, 0, 5, 0, 0, 0, 30, 0, 60 ], [ 0, 0, 0, 0, 24, 0, 24, 0, 48, 0 ], [ 0, 0, 0, 0, 0, 24, 0, 24, 0, 48 ], [ 0, 0, 0, 0, 24, 0, 24, 0, 48, 0 ], [ 0, 0, 0, 0, 0, 24, 0, 24, 0, 48 ] ], [ [ 0, 0, 0, 0, 0, 0, 120, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 120, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 24, 0, 96 ], [ 0, 0, 0, 0, 0, 0, 24, 0, 96, 0 ], [ 0, 0, 0, 0, 0, 30, 0, 30, 0, 60 ], [ 0, 0, 0, 0, 30, 0, 30, 0, 60, 0 ], [ 1, 0, 0, 1, 0, 24, 0, 34, 0, 60 ], [ 0, 1, 1, 0, 24, 0, 34, 0, 60, 0 ], [ 0, 0, 0, 2, 0, 24, 0, 30, 0, 64 ], [ 0, 0, 2, 0, 24, 0, 30, 0, 64, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 120, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 120, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 24, 0, 96, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 24, 0, 96 ], [ 0, 0, 0, 0, 30, 0, 30, 0, 60, 0 ], [ 0, 0, 0, 0, 0, 30, 0, 30, 0, 60 ], [ 0, 1, 1, 0, 24, 0, 34, 0, 60, 0 ], [ 1, 0, 0, 1, 0, 24, 0, 34, 0, 60 ], [ 0, 0, 2, 0, 24, 0, 30, 0, 64, 0 ], [ 0, 0, 0, 2, 0, 24, 0, 30, 0, 64 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 240, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 240 ], [ 0, 0, 0, 0, 0, 0, 0, 96, 0, 144 ], [ 0, 0, 0, 0, 0, 0, 96, 0, 144, 0 ], [ 0, 0, 0, 0, 0, 60, 0, 60, 0, 120 ], [ 0, 0, 0, 0, 60, 0, 60, 0, 120, 0 ], [ 0, 0, 0, 4, 0, 48, 0, 60, 0, 128 ], [ 0, 0, 4, 0, 48, 0, 60, 0, 128, 0 ], [ 1, 0, 0, 3, 0, 48, 0, 64, 0, 124 ], [ 0, 1, 3, 0, 48, 0, 64, 0, 124, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 240 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 240, 0 ], [ 0, 0, 0, 0, 0, 0, 96, 0, 144, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 96, 0, 144 ], [ 0, 0, 0, 0, 60, 0, 60, 0, 120, 0 ], [ 0, 0, 0, 0, 0, 60, 0, 60, 0, 120 ], [ 0, 0, 4, 0, 48, 0, 60, 0, 128, 0 ], [ 0, 0, 0, 4, 0, 48, 0, 60, 0, 128 ], [ 0, 1, 3, 0, 48, 0, 64, 0, 124, 0 ], [ 1, 0, 0, 3, 0, 48, 0, 64, 0, 124 ] ] ] ), rec( name := "M22.2", sbgname := "2^4:A6 leq 2^4:S6", filename := "2^4:A6", degree := 154, rank := 6, permchar := "1a^{+-} + 21a^{+-} + 55a^{+-}", charnmbs := [ 1, 2, 3, 4, 9, 10 ], ctbl := [ [ 1, 1, 16, 16, 60, 60 ], [ 1, -1, -16, 16, -60, 60 ], [ 1, 1, -6, -6, 5, 5 ], [ 1, -1, 6, -6, -5, 5 ], [ 1, 1, 2, 2, -3, -3 ], [ 1, -1, -2, 2, 3, -3 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 16, 0, 0, 0 ], [ 0, 0, 0, 16, 0, 0 ], [ 1, 0, 0, 0, 0, 15 ], [ 0, 1, 0, 0, 15, 0 ], [ 0, 0, 0, 4, 0, 12 ], [ 0, 0, 4, 0, 12, 0 ] ], [ [ 0, 0, 0, 16, 0, 0 ], [ 0, 0, 16, 0, 0, 0 ], [ 0, 1, 0, 0, 15, 0 ], [ 1, 0, 0, 0, 0, 15 ], [ 0, 0, 4, 0, 12, 0 ], [ 0, 0, 0, 4, 0, 12 ] ], [ [ 0, 0, 0, 0, 60, 0 ], [ 0, 0, 0, 0, 0, 60 ], [ 0, 0, 0, 15, 0, 45 ], [ 0, 0, 15, 0, 45, 0 ], [ 1, 0, 0, 12, 0, 47 ], [ 0, 1, 12, 0, 47, 0 ] ], [ [ 0, 0, 0, 0, 0, 60 ], [ 0, 0, 0, 0, 60, 0 ], [ 0, 0, 15, 0, 45, 0 ], [ 0, 0, 0, 15, 0, 45 ], [ 0, 1, 12, 0, 47, 0 ], [ 1, 0, 0, 12, 0, 47 ] ] ] ), rec( name := "M22.2", sbgname := "2^4:S5 leq 2^4:S6", filename := "2^4:S5", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 462, rank := 5, permchar := "1a^+ + 21a^+ + 55a^+ + 154a^+ + 231a^-", charnmbs := [ 1, 3, 9, 13, 18 ], ctbl := [ [ 1, 5, 96, 120, 240 ], [ 1, 5, -36, 10, 20 ], [ 1, 5, 12, -6, -12 ], [ 1, -1, 0, 12, -12 ], [ 1, -1, 0, -8, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 5, 0, 0, 0 ], [ 1, 4, 0, 0, 0 ], [ 0, 0, 5, 0, 0 ], [ 0, 0, 0, 1, 4 ], [ 0, 0, 0, 2, 3 ] ], [ [ 0, 0, 96, 0, 0 ], [ 0, 0, 96, 0, 0 ], [ 1, 5, 0, 30, 60 ], [ 0, 0, 24, 24, 48 ], [ 0, 0, 24, 24, 48 ] ], [ [ 0, 0, 0, 120, 0 ], [ 0, 0, 0, 24, 96 ], [ 0, 0, 30, 30, 60 ], [ 1, 1, 24, 34, 60 ], [ 0, 2, 24, 30, 64 ] ], [ [ 0, 0, 0, 0, 240 ], [ 0, 0, 0, 96, 144 ], [ 0, 0, 60, 60, 120 ], [ 0, 4, 48, 60, 128 ], [ 1, 3, 48, 64, 124 ] ] ] ), rec( name := "M22.2", sbgname := "2^4:S5 leq 2^5:S5", filename := "2^4:S5", degree := 462, rank := 8, permchar := "1a^{+-} + 21a^{+-} + 55a^{+-} + 154a^{+-}", charnmbs := [ 1, 2, 3, 4, 9, 10, 13, 14 ], ctbl := [ [ 1, 1, 30, 30, 40, 40, 160, 160 ], [ 1, -1, -30, 30, -40, 40, -160, 160 ], [ 1, 1, -3, -3, 18, 18, -16, -16 ], [ 1, -1, 3, -3, -18, 18, 16, -16 ], [ 1, 1, 9, 9, -2, -2, -8, -8 ], [ 1, -1, -9, 9, 2, -2, 8, -8 ], [ 1, 1, -3, -3, -2, -2, 4, 4 ], [ 1, -1, 3, -3, 2, -2, -4, 4 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 30, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 30, 0, 0, 0, 0 ], [ 1, 0, 0, 9, 0, 4, 0, 16 ], [ 0, 1, 9, 0, 4, 0, 16, 0 ], [ 0, 0, 0, 3, 0, 3, 0, 24 ], [ 0, 0, 3, 0, 3, 0, 24, 0 ], [ 0, 0, 0, 3, 0, 6, 0, 21 ], [ 0, 0, 3, 0, 6, 0, 21, 0 ] ], [ [ 0, 0, 0, 30, 0, 0, 0, 0 ], [ 0, 0, 30, 0, 0, 0, 0, 0 ], [ 0, 1, 9, 0, 4, 0, 16, 0 ], [ 1, 0, 0, 9, 0, 4, 0, 16 ], [ 0, 0, 3, 0, 3, 0, 24, 0 ], [ 0, 0, 0, 3, 0, 3, 0, 24 ], [ 0, 0, 3, 0, 6, 0, 21, 0 ], [ 0, 0, 0, 3, 0, 6, 0, 21 ] ], [ [ 0, 0, 0, 0, 40, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 40, 0, 0 ], [ 0, 0, 0, 4, 0, 4, 0, 32 ], [ 0, 0, 4, 0, 4, 0, 32, 0 ], [ 1, 0, 0, 3, 0, 20, 0, 16 ], [ 0, 1, 3, 0, 20, 0, 16, 0 ], [ 0, 0, 0, 6, 0, 4, 0, 30 ], [ 0, 0, 6, 0, 4, 0, 30, 0 ] ], [ [ 0, 0, 0, 0, 0, 40, 0, 0 ], [ 0, 0, 0, 0, 40, 0, 0, 0 ], [ 0, 0, 4, 0, 4, 0, 32, 0 ], [ 0, 0, 0, 4, 0, 4, 0, 32 ], [ 0, 1, 3, 0, 20, 0, 16, 0 ], [ 1, 0, 0, 3, 0, 20, 0, 16 ], [ 0, 0, 6, 0, 4, 0, 30, 0 ], [ 0, 0, 0, 6, 0, 4, 0, 30 ] ], [ [ 0, 0, 0, 0, 0, 0, 160, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 160 ], [ 0, 0, 0, 16, 0, 32, 0, 112 ], [ 0, 0, 16, 0, 32, 0, 112, 0 ], [ 0, 0, 0, 24, 0, 16, 0, 120 ], [ 0, 0, 24, 0, 16, 0, 120, 0 ], [ 1, 0, 0, 21, 0, 30, 0, 108 ], [ 0, 1, 21, 0, 30, 0, 108, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 160 ], [ 0, 0, 0, 0, 0, 0, 160, 0 ], [ 0, 0, 16, 0, 32, 0, 112, 0 ], [ 0, 0, 0, 16, 0, 32, 0, 112 ], [ 0, 0, 24, 0, 16, 0, 120, 0 ], [ 0, 0, 0, 24, 0, 16, 0, 120 ], [ 0, 1, 21, 0, 30, 0, 108, 0 ], [ 1, 0, 0, 21, 0, 30, 0, 108 ] ] ] ), rec( name := "M22.2", sbgname := "2^4:(A5x2) leq 2^5:S5", filename := "2^4:A5x2", degree := 462, rank := 6, permchar := "1a^+ + 21a^{+-} + 55a^+ + 154a^+ + 210a^-", charnmbs := [ 1, 3, 4, 9, 13, 16 ], ctbl := [ [ 1, 1, 40, 40, 60, 320 ], [ 1, 1, 18, 18, -6, -32 ], [ 1, -1, -20, 20, 0, 0 ], [ 1, 1, -2, -2, 18, -16 ], [ 1, 1, -2, -2, -6, 8 ], [ 1, -1, 2, -2, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 40, 0, 0, 0 ], [ 0, 0, 0, 40, 0, 0 ], [ 1, 0, 1, 19, 3, 16 ], [ 0, 1, 19, 1, 3, 16 ], [ 0, 0, 2, 2, 4, 32 ], [ 0, 0, 2, 2, 6, 30 ] ], [ [ 0, 0, 0, 40, 0, 0 ], [ 0, 0, 40, 0, 0, 0 ], [ 0, 1, 19, 1, 3, 16 ], [ 1, 0, 1, 19, 3, 16 ], [ 0, 0, 2, 2, 4, 32 ], [ 0, 0, 2, 2, 6, 30 ] ], [ [ 0, 0, 0, 0, 60, 0 ], [ 0, 0, 0, 0, 60, 0 ], [ 0, 0, 3, 3, 6, 48 ], [ 0, 0, 3, 3, 6, 48 ], [ 1, 1, 4, 4, 18, 32 ], [ 0, 0, 6, 6, 6, 42 ] ], [ [ 0, 0, 0, 0, 0, 320 ], [ 0, 0, 0, 0, 0, 320 ], [ 0, 0, 16, 16, 48, 240 ], [ 0, 0, 16, 16, 48, 240 ], [ 0, 0, 32, 32, 32, 224 ], [ 1, 1, 30, 30, 42, 216 ] ] ] ), rec( name := "M22.2", sbgname := "2^4:S6", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 77, rank := 3, permchar := "1a^+ + 21a^+ + 55a^+", charnmbs := [ 1, 3, 9 ], ctbl := [ [ 1, 16, 60 ], [ 1, -6, 5 ], [ 1, 2, -3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 16, 0 ], [ 1, 0, 15 ], [ 0, 4, 12 ] ], [ [ 0, 0, 60 ], [ 0, 15, 45 ], [ 1, 12, 47 ] ] ] ), rec( name := "M22.2", sbgname := "2^5:S5", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 231, rank := 4, permchar := "1a^+ + 21a^+ + 55a^+ + 154a^+", charnmbs := [ 1, 3, 9, 13 ], ctbl := [ [ 1, 30, 40, 160 ], [ 1, -3, 18, -16 ], [ 1, 9, -2, -8 ], [ 1, -3, -2, 4 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 30, 0, 0 ], [ 1, 9, 4, 16 ], [ 0, 3, 3, 24 ], [ 0, 3, 6, 21 ] ], [ [ 0, 0, 40, 0 ], [ 0, 4, 4, 32 ], [ 1, 3, 20, 16 ], [ 0, 6, 4, 30 ] ], [ [ 0, 0, 0, 160 ], [ 0, 16, 32, 112 ], [ 0, 24, 16, 120 ], [ 1, 21, 30, 108 ] ] ] ), rec( name := "M22.2", sbgname := "2^3:L3(2) leq 2^3:L3(2)x2", filename := "2^3:L32", degree := 660, rank := 10, permchar := "1a^{+-} + 21a^{+-} + 55a^{+-} + 99a^{+-} + 154a^{+-}", charnmbs := [ 1, 2, 3, 4, 9, 10, 11, 12, 13, 14 ], ctbl := [ [ 1, 1, 7, 7, 42, 42, 112, 112, 168, 168 ], [ 1, -1, -7, 7, -42, 42, -112, 112, -168, 168 ], [ 1, 1, -4, -4, 9, 9, 24, 24, -30, -30 ], [ 1, -1, 4, -4, -9, 9, -24, 24, 30, -30 ], [ 1, 1, 4, 4, 9, 9, -8, -8, -6, -6 ], [ 1, -1, -4, 4, -9, 9, 8, -8, 6, -6 ], [ 1, 1, -3, -3, 2, 2, -8, -8, 8, 8 ], [ 1, -1, 3, -3, -2, 2, 8, -8, -8, 8 ], [ 1, 1, 1, 1, -6, -6, 4, 4, 0, 0 ], [ 1, -1, -1, 1, 6, -6, -4, 4, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 7, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 7, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 6, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 6, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 2, 0, 0, 0, 4 ], [ 0, 0, 1, 0, 2, 0, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 6 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 6, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 4, 0, 2 ], [ 0, 0, 0, 0, 1, 0, 4, 0, 2, 0 ] ], [ [ 0, 0, 0, 7, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 7, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 6, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 6, 0, 0, 0, 0 ] , [ 0, 0, 1, 0, 2, 0, 0, 0, 4, 0 ], [ 0, 0, 0, 1, 0, 2, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 6, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 6 ], [ 0, 0, 0, 0, 1, 0, 4, 0, 2, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 4, 0, 2 ] ], [ [ 0, 0, 0, 0, 42, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 42, 0, 0, 0, 0 ], [ 0, 0, 0, 6, 0, 12, 0, 0, 0, 24 ], [ 0, 0, 6, 0, 12, 0, 0, 0, 24, 0 ], [ 1, 0, 0, 2, 0, 7, 0, 16, 0, 16 ], [ 0, 1, 2, 0, 7, 0, 16, 0, 16, 0 ], [ 0, 0, 0, 0, 0, 6, 0, 18, 0, 18 ], [ 0, 0, 0, 0, 6, 0, 18, 0, 18, 0 ], [ 0, 0, 0, 1, 0, 4, 0, 12, 0, 25 ], [ 0, 0, 1, 0, 4, 0, 12, 0, 25, 0 ] ], [ [ 0, 0, 0, 0, 0, 42, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 42, 0, 0, 0, 0, 0 ], [ 0, 0, 6, 0, 12, 0, 0, 0, 24, 0 ], [ 0, 0, 0, 6, 0, 12, 0, 0, 0, 24 ], [ 0, 1, 2, 0, 7, 0, 16, 0, 16, 0 ], [ 1, 0, 0, 2, 0, 7, 0, 16, 0, 16 ], [ 0, 0, 0, 0, 6, 0, 18, 0, 18, 0 ], [ 0, 0, 0, 0, 0, 6, 0, 18, 0, 18 ], [ 0, 0, 1, 0, 4, 0, 12, 0, 25, 0 ], [ 0, 0, 0, 1, 0, 4, 0, 12, 0, 25 ] ], [ [ 0, 0, 0, 0, 0, 0, 112, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 112, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 16, 0, 96 ], [ 0, 0, 0, 0, 0, 0, 16, 0, 96, 0 ], [ 0, 0, 0, 0, 0, 16, 0, 48, 0, 48 ], [ 0, 0, 0, 0, 16, 0, 48, 0, 48, 0 ], [ 1, 0, 0, 1, 0, 18, 0, 44, 0, 48 ], [ 0, 1, 1, 0, 18, 0, 44, 0, 48, 0 ], [ 0, 0, 0, 4, 0, 12, 0, 32, 0, 64 ], [ 0, 0, 4, 0, 12, 0, 32, 0, 64, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 112, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 112, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 16, 0, 96, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 16, 0, 96 ], [ 0, 0, 0, 0, 16, 0, 48, 0, 48, 0 ], [ 0, 0, 0, 0, 0, 16, 0, 48, 0, 48 ], [ 0, 1, 1, 0, 18, 0, 44, 0, 48, 0 ], [ 1, 0, 0, 1, 0, 18, 0, 44, 0, 48 ], [ 0, 0, 4, 0, 12, 0, 32, 0, 64, 0 ], [ 0, 0, 0, 4, 0, 12, 0, 32, 0, 64 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 168, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 168 ], [ 0, 0, 0, 0, 0, 24, 0, 96, 0, 48 ], [ 0, 0, 0, 0, 24, 0, 96, 0, 48, 0 ], [ 0, 0, 0, 4, 0, 16, 0, 48, 0, 100 ], [ 0, 0, 4, 0, 16, 0, 48, 0, 100, 0 ], [ 0, 0, 0, 6, 0, 18, 0, 48, 0, 96 ], [ 0, 0, 6, 0, 18, 0, 48, 0, 96, 0 ], [ 1, 0, 0, 2, 0, 25, 0, 64, 0, 76 ], [ 0, 1, 2, 0, 25, 0, 64, 0, 76, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 168 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 168, 0 ], [ 0, 0, 0, 0, 24, 0, 96, 0, 48, 0 ], [ 0, 0, 0, 0, 0, 24, 0, 96, 0, 48 ], [ 0, 0, 4, 0, 16, 0, 48, 0, 100, 0 ], [ 0, 0, 0, 4, 0, 16, 0, 48, 0, 100 ], [ 0, 0, 6, 0, 18, 0, 48, 0, 96, 0 ], [ 0, 0, 0, 6, 0, 18, 0, 48, 0, 96 ], [ 0, 1, 2, 0, 25, 0, 64, 0, 76, 0 ], [ 1, 0, 0, 2, 0, 25, 0, 64, 0, 76 ] ] ] ), rec( name := "M22.2", sbgname := "A6.2^2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 616, rank := 5, permchar := "1a^+ + 21a^+ + 55a^+ + 154a^+ + 385a^+", charnmbs := [ 1, 3, 9, 13, 20 ], ctbl := [ [ 1, 30, 45, 180, 360 ], [ 1, 8, -21, 48, -36 ], [ 1, 16, 3, -16, -4 ], [ 1, -2, 9, 8, -16 ], [ 1, -2, -3, -4, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 30, 0, 0, 0 ], [ 1, 14, 3, 0, 12 ], [ 0, 2, 4, 0, 24 ], [ 0, 0, 0, 14, 16 ], [ 0, 1, 3, 8, 18 ] ], [ [ 0, 0, 45, 0, 0 ], [ 0, 3, 6, 0, 36 ], [ 1, 4, 0, 32, 8 ], [ 0, 0, 8, 5, 32 ], [ 0, 3, 1, 16, 25 ] ], [ [ 0, 0, 0, 180, 0 ], [ 0, 0, 0, 84, 96 ], [ 0, 0, 32, 20, 128 ], [ 1, 14, 5, 72, 88 ], [ 0, 8, 16, 44, 112 ] ], [ [ 0, 0, 0, 0, 360 ], [ 0, 12, 36, 96, 216 ], [ 0, 24, 8, 128, 200 ], [ 0, 16, 32, 88, 224 ], [ 1, 18, 25, 112, 204 ] ] ] ), rec( name := "M22.2", sbgname := "L3(4) leq L3(4).2_2", filename := "L34", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 44, rank := 4, permchar := "1a^{+-} + 21a^{+-}", charnmbs := [ 1, 2, 3, 4 ], ctbl := [ [ 1, 1, 21, 21 ], [ 1, -1, 21, -21 ], [ 1, 1, -1, -1 ], [ 1, -1, -1, 1 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 0, 0, 21, 0 ], [ 0, 0, 0, 21 ], [ 1, 0, 20, 0 ], [ 0, 1, 0, 20 ] ], [ [ 0, 0, 0, 21 ], [ 0, 0, 21, 0 ], [ 0, 1, 0, 20 ], [ 1, 0, 20, 0 ] ] ] ), rec( name := "M22.2", sbgname := "L2(11).2", filename := "L211.2", degree := 672, rank := 6, permchar := "1a^+ + 21a^- + 55a^+ + 154a^+ + 210a^- + 231a^-", charnmbs := [ 1, 4, 9, 13, 16, 18 ], ctbl := [ [ 1, 55, 55, 66, 165, 330 ], [ 1, -25, 15, -6, 45, -30 ], [ 1, 13, 13, -18, -3, -6 ], [ 1, 7, -5, 6, 9, -18 ], [ 1, -3, -7, -6, 1, 14 ], [ 1, -3, 5, 6, -11, 2 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 55, 0, 0, 0, 0 ], [ 1, 0, 12, 0, 30, 12 ], [ 0, 12, 4, 0, 3, 36 ], [ 0, 0, 0, 10, 20, 25 ], [ 0, 10, 1, 8, 4, 32 ], [ 0, 2, 6, 5, 16, 26 ] ], [ [ 0, 0, 55, 0, 0, 0 ], [ 0, 12, 4, 0, 3, 36 ], [ 1, 4, 8, 0, 18, 24 ], [ 0, 0, 0, 10, 10, 35 ], [ 0, 1, 6, 4, 20, 24 ], [ 0, 6, 4, 7, 12, 26 ] ], [ [ 0, 0, 0, 66, 0, 0 ], [ 0, 0, 0, 12, 24, 30 ], [ 0, 0, 0, 12, 12, 42 ], [ 1, 10, 10, 0, 15, 30 ], [ 0, 8, 4, 6, 16, 32 ], [ 0, 5, 7, 6, 16, 32 ] ], [ [ 0, 0, 0, 0, 165, 0 ], [ 0, 30, 3, 24, 12, 96 ], [ 0, 3, 18, 12, 60, 72 ], [ 0, 20, 10, 15, 40, 80 ], [ 1, 4, 20, 16, 56, 68 ], [ 0, 16, 12, 16, 34, 87 ] ], [ [ 0, 0, 0, 0, 0, 330 ], [ 0, 12, 36, 30, 96, 156 ], [ 0, 36, 24, 42, 72, 156 ], [ 0, 25, 35, 30, 80, 160 ], [ 0, 32, 24, 32, 68, 174 ], [ 1, 26, 26, 32, 87, 158 ] ] ] ), rec( name := "M22.2", sbgname := "L2(11) leq L2(11).2", filename := "L211", degree := 1344, rank := 12, permchar := "1a^{+-} + 21a^{+-} + 55a^{+-} + 154a^{+-} + 210a^{+-} + 231a^{+-}", charnmbs := [ 1, 2, 3, 4, 9, 10, 13, 14, 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ctbl := [ [ 1, 15, 35, 70, 105, 126 ], [ 1, -15, -35, 70, 105, -126 ], [ 1, -7, 13, -18, 17, -6 ], [ 1, 7, -13, -18, 17, 6 ], [ 1, 3, 3, 2, -3, -6 ], [ 1, -3, -3, 2, -3, 6 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 15, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 14, 0 ], [ 0, 0, 0, 12, 3, 0 ], [ 0, 0, 6, 0, 0, 9 ], [ 0, 2, 1, 0, 0, 12 ], [ 0, 0, 0, 5, 10, 0 ] ], [ [ 0, 0, 35, 0, 0, 0 ], [ 0, 0, 0, 28, 7, 0 ], [ 1, 0, 0, 4, 30, 0 ], [ 0, 6, 2, 0, 0, 27 ], [ 0, 1, 10, 0, 0, 24 ], [ 0, 0, 0, 15, 20, 0 ] ], [ [ 0, 0, 0, 70, 0, 0 ], [ 0, 0, 28, 0, 0, 42 ], [ 0, 12, 4, 0, 0, 54 ], [ 1, 0, 0, 18, 51, 0 ], [ 0, 0, 0, 34, 36, 0 ], [ 0, 5, 15, 0, 0, 50 ] ], [ [ 0, 0, 0, 0, 105, 0 ], [ 0, 14, 7, 0, 0, 84 ], [ 0, 3, 30, 0, 0, 72 ], [ 0, 0, 0, 51, 54, 0 ], [ 1, 0, 0, 36, 68, 0 ], [ 0, 10, 20, 0, 0, 75 ] ], [ [ 0, 0, 0, 0, 0, 126 ], [ 0, 0, 0, 42, 84, 0 ], [ 0, 0, 0, 54, 72, 0 ], [ 0, 9, 27, 0, 0, 90 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-12, 12, 8, -8 ], [ 1, 1, -2, -2, -3, -3, -4, -4, 8, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 30, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 30, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 14, 0, 3, 0, 0, 0, 0, 12 ], [ 0, 1, 0, 14, 0, 3, 0, 0, 12, 0 ], [ 0, 0, 2, 0, 4, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 2, 0, 4, 0, 0, 24, 0 ], [ 0, 0, 0, 0, 0, 0, 6, 8, 8, 8 ], [ 0, 0, 0, 0, 0, 0, 8, 6, 8, 8 ], [ 0, 0, 0, 1, 0, 3, 4, 4, 14, 4 ], [ 0, 0, 1, 0, 3, 0, 4, 4, 4, 14 ] ], [ [ 0, 0, 0, 30, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 30, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 14, 0, 3, 0, 0, 12, 0 ], [ 1, 0, 14, 0, 3, 0, 0, 0, 0, 12 ], [ 0, 0, 0, 2, 0, 4, 0, 0, 24, 0 ], [ 0, 0, 2, 0, 4, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 0, 0, 0, 8, 6, 8, 8 ], [ 0, 0, 0, 0, 0, 0, 6, 8, 8, 8 ], [ 0, 0, 1, 0, 3, 0, 4, 4, 4, 14 ], [ 0, 0, 0, 1, 0, 3, 4, 4, 14, 4 ] ], [ [ 0, 0, 0, 0, 45, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 45, 0, 0, 0, 0 ], [ 0, 0, 3, 0, 6, 0, 0, 0, 0, 36 ], [ 0, 0, 0, 3, 0, 6, 0, 0, 36, 0 ], [ 1, 0, 4, 0, 0, 0, 16, 16, 0, 8 ], [ 0, 1, 0, 4, 0, 0, 16, 16, 8, 0 ], [ 0, 0, 0, 0, 4, 4, 5, 0, 16, 16 ], [ 0, 0, 0, 0, 4, 4, 0, 5, 16, 16 ], [ 0, 0, 0, 3, 0, 1, 8, 8, 13, 12 ], [ 0, 0, 3, 0, 1, 0, 8, 8, 12, 13 ] ], [ [ 0, 0, 0, 0, 0, 45, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 45, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3, 0, 6, 0, 0, 36, 0 ], [ 0, 0, 3, 0, 6, 0, 0, 0, 0, 36 ], [ 0, 1, 0, 4, 0, 0, 16, 16, 8, 0 ], [ 1, 0, 4, 0, 0, 0, 16, 16, 0, 8 ], [ 0, 0, 0, 0, 4, 4, 0, 5, 16, 16 ], [ 0, 0, 0, 0, 4, 4, 5, 0, 16, 16 ], [ 0, 0, 3, 0, 1, 0, 8, 8, 12, 13 ], [ 0, 0, 0, 3, 0, 1, 8, 8, 13, 12 ] ], [ [ 0, 0, 0, 0, 0, 0, 180, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 180, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 36, 48, 48, 48 ], [ 0, 0, 0, 0, 0, 0, 48, 36, 48, 48 ], [ 0, 0, 0, 0, 16, 16, 20, 0, 64, 64 ], [ 0, 0, 0, 0, 16, 16, 0, 20, 64, 64 ], [ 1, 0, 6, 8, 5, 0, 44, 28, 48, 40 ], [ 0, 1, 8, 6, 0, 5, 28, 44, 40, 48 ], [ 0, 0, 4, 4, 8, 8, 24, 20, 56, 56 ], [ 0, 0, 4, 4, 8, 8, 20, 24, 56, 56 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 180, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 180, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 48, 36, 48, 48 ], [ 0, 0, 0, 0, 0, 0, 36, 48, 48, 48 ], [ 0, 0, 0, 0, 16, 16, 0, 20, 64, 64 ], [ 0, 0, 0, 0, 16, 16, 20, 0, 64, 64 ], [ 0, 1, 8, 6, 0, 5, 28, 44, 40, 48 ], [ 1, 0, 6, 8, 5, 0, 44, 28, 48, 40 ], [ 0, 0, 4, 4, 8, 8, 20, 24, 56, 56 ], [ 0, 0, 4, 4, 8, 8, 24, 20, 56, 56 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 360, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 360 ], [ 0, 0, 0, 12, 0, 36, 48, 48, 168, 48 ], [ 0, 0, 12, 0, 36, 0, 48, 48, 48, 168 ], [ 0, 0, 0, 24, 0, 8, 64, 64, 104, 96 ], [ 0, 0, 24, 0, 8, 0, 64, 64, 96, 104 ], [ 0, 0, 8, 8, 16, 16, 48, 40, 112, 112 ], [ 0, 0, 8, 8, 16, 16, 40, 48, 112, 112 ], [ 1, 0, 14, 4, 13, 12, 56, 56, 96, 108 ], [ 0, 1, 4, 14, 12, 13, 56, 56, 108, 96 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 360 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 360, 0 ], [ 0, 0, 12, 0, 36, 0, 48, 48, 48, 168 ], [ 0, 0, 0, 12, 0, 36, 48, 48, 168, 48 ], [ 0, 0, 24, 0, 8, 0, 64, 64, 96, 104 ], [ 0, 0, 0, 24, 0, 8, 64, 64, 104, 96 ], [ 0, 0, 8, 8, 16, 16, 40, 48, 112, 112 ], [ 0, 0, 8, 8, 16, 16, 48, 40, 112, 112 ], [ 0, 1, 4, 14, 12, 13, 56, 56, 108, 96 ], [ 1, 0, 14, 4, 13, 12, 56, 56, 96, 108 ] ] ] ), rec( name := "J2", sbgname := "2^{2+4}.(3xS3)", filename := "2^2+4.3xS3", degree := 525, rank := 6, permchar := "1a + 36a + 63a + 90a + 160a + 175a", charnmbs := [ 1, 6, 7, 10, 12, 13 ], ctbl := [ [ 1, 12, 32, 96, 192, 192 ], [ 1, 7, -8, 16, -28, 12 ], [ 1, -3, 12, 6, -18, 2 ], [ 1, 5, 4, -2, 10, -18 ], [ 1, 0, -1, -12, 0, 12 ], [ 1, -3, -4, 6, 6, -6 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 12, 0, 0, 0, 0 ], [ 1, 3, 0, 8, 0, 0 ], [ 0, 0, 0, 0, 12, 0 ], [ 0, 1, 0, 3, 2, 6 ], [ 0, 0, 2, 1, 6, 3 ], [ 0, 0, 0, 3, 3, 6 ] ], [ [ 0, 0, 32, 0, 0, 0 ], [ 0, 0, 0, 0, 32, 0 ], [ 1, 0, 7, 12, 0, 12 ], [ 0, 0, 4, 4, 12, 12 ], [ 0, 2, 0, 6, 12, 12 ], [ 0, 0, 2, 6, 12, 12 ] ], [ [ 0, 0, 0, 96, 0, 0 ], [ 0, 8, 0, 24, 16, 48 ], [ 0, 0, 12, 12, 36, 36 ], [ 1, 3, 4, 16, 30, 42 ], [ 0, 1, 6, 15, 41, 33 ], [ 0, 3, 6, 21, 33, 33 ] ], [ [ 0, 0, 0, 0, 192, 0 ], [ 0, 0, 32, 16, 96, 48 ], [ 0, 12, 0, 36, 72, 72 ], [ 0, 2, 12, 30, 82, 66 ], [ 1, 6, 12, 41, 60, 72 ], [ 0, 3, 12, 33, 72, 72 ] ], [ [ 0, 0, 0, 0, 0, 192 ], [ 0, 0, 0, 48, 48, 96 ], [ 0, 0, 12, 36, 72, 72 ], [ 0, 6, 12, 42, 66, 66 ], [ 0, 3, 12, 33, 72, 72 ], [ 1, 6, 12, 33, 72, 68 ] ] ] ), rec( name := "J2", sbgname := "2_^{1+4}:A5", filename := "2_^1+4:A5", degree := 315, rank := 6, permchar := "1a + 14ab + 36a + 90a + 160a + 175a", charnmbs := [ 1, 2, 3, 6, 10, 12 ], ctbl := [ [ 1, 10, 32, 32, 80, 160 ], [ 1, -5, -8*E(5)+4*E(5)^2+4*E(5)^3-8*E(5)^4, 4*E(5)-8*E(5)^2-8*E(5)^3+4*E(5)^4, 20, -20 ], [ 1, -5, 4*E(5)-8*E(5)^2-8*E(5)^3+4*E(5)^4, -8*E(5)+4*E(5)^2+4*E(5)^3-8*E(5)^4, 20, -20 ], [ 1, 5, -8, -8, 10, 0 ], [ 1, 3, 4, 4, -4, -8 ], [ 1, -2, -1, -1, -4, 7 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 10, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 8, 0 ], [ 0, 0, 0, 5, 0, 5 ], [ 0, 0, 5, 0, 0, 5 ], [ 0, 1, 0, 0, 1, 8 ], [ 0, 0, 1, 1, 4, 4 ] ], [ [ 0, 0, 32, 0, 0, 0 ], [ 0, 0, 0, 16, 0, 16 ], [ 1, 0, 5, 1, 20, 5 ], [ 0, 5, 1, 1, 0, 25 ], [ 0, 0, 8, 0, 8, 16 ], [ 0, 1, 1, 5, 8, 17 ] ], [ [ 0, 0, 0, 32, 0, 0 ], [ 0, 0, 16, 0, 0, 16 ], [ 0, 5, 1, 1, 0, 25 ], [ 1, 0, 1, 5, 20, 5 ], [ 0, 0, 0, 8, 8, 16 ], [ 0, 1, 5, 1, 8, 17 ] ], [ [ 0, 0, 0, 0, 80, 0 ], [ 0, 8, 0, 0, 8, 64 ], [ 0, 0, 20, 0, 20, 40 ], [ 0, 0, 0, 20, 20, 40 ], [ 1, 1, 8, 8, 30, 32 ], [ 0, 4, 8, 8, 16, 44 ] ], [ [ 0, 0, 0, 0, 0, 160 ], [ 0, 0, 16, 16, 64, 64 ], [ 0, 5, 5, 25, 40, 85 ], [ 0, 5, 25, 5, 40, 85 ], [ 0, 8, 16, 16, 32, 88 ], [ 1, 4, 17, 17, 44, 77 ] ] ] ), rec( name := "J2", sbgname := "3.A6.2_2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 280, rank := 4, permchar := "1a + 63a + 90a + 126a", charnmbs := [ 1, 7, 10, 11 ], ctbl := [ [ 1, 36, 108, 135 ], [ 1, -4, -12, 15 ], [ 1, 8, -4, -5 ], [ 1, -4, 8, -5 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 36, 0, 0 ], [ 1, 8, 12, 15 ], [ 0, 4, 12, 20 ], [ 0, 4, 16, 16 ] ], [ [ 0, 0, 108, 0 ], [ 0, 12, 36, 60 ], [ 1, 12, 40, 55 ], [ 0, 16, 44, 48 ] ], [ [ 0, 0, 0, 135 ], [ 0, 15, 60, 60 ], [ 0, 20, 55, 60 ], [ 1, 16, 48, 70 ] ] ] ), rec( name := "J2", sbgname := "A4xA5", degree := 840, rank := 7, permchar := "1a + 63a + 90a + 126a + 160a + 175a + 225a", charnmbs := [ 1, 7, 10, 11, 12, 13, 18 ], ctbl := [ [ 1, 15, 20, 24, 180, 240, 360 ], [ 1, 5, 10, -6, 0, 20, -30 ], [ 1, 1, 6, 10, -16, -12, 10 ], [ 1, -5, 0, 4, 20, 0, -20 ], [ 1, 6, -4, 0, 9, -12, 0 ], [ 1, -3, 2, -6, 0, -12, 18 ], [ 1, -1, -4, 0, -12, 16, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 15, 0, 0, 0, 0, 0 ], [ 1, 2, 0, 0, 12, 0, 0 ], [ 0, 0, 3, 0, 0, 12, 0 ], [ 0, 0, 0, 0, 0, 0, 15 ], [ 0, 1, 0, 0, 2, 4, 8 ], [ 0, 0, 1, 0, 3, 5, 6 ], [ 0, 0, 0, 1, 4, 4, 6 ] ], [ [ 0, 0, 20, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 16, 0 ], [ 1, 3, 4, 0, 0, 12, 0 ], [ 0, 0, 0, 5, 0, 0, 15 ], [ 0, 0, 0, 0, 4, 8, 8 ], [ 0, 1, 1, 0, 6, 6, 6 ], [ 0, 0, 0, 1, 4, 4, 11 ] ], [ [ 0, 0, 0, 24, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 6, 0, 0, 18 ], [ 1, 0, 5, 3, 0, 0, 15 ], [ 0, 0, 0, 0, 8, 8, 8 ], [ 0, 0, 0, 0, 6, 6, 12 ], [ 0, 1, 1, 1, 4, 8, 9 ] ], [ [ 0, 0, 0, 0, 180, 0, 0 ], [ 0, 12, 0, 0, 24, 48, 96 ], [ 0, 0, 0, 0, 36, 72, 72 ], [ 0, 0, 0, 0, 60, 60, 60 ], [ 1, 2, 4, 8, 41, 52, 72 ], [ 0, 3, 6, 6, 39, 48, 78 ], [ 0, 4, 4, 4, 36, 52, 80 ] ], [ [ 0, 0, 0, 0, 0, 240, 0 ], [ 0, 0, 16, 0, 48, 80, 96 ], [ 0, 12, 12, 0, 72, 72, 72 ], [ 0, 0, 0, 0, 60, 60, 120 ], [ 0, 4, 8, 8, 52, 64, 104 ], [ 1, 5, 6, 6, 48, 72, 102 ], [ 0, 4, 4, 8, 52, 68, 104 ] ], [ [ 0, 0, 0, 0, 0, 0, 360 ], [ 0, 0, 0, 24, 96, 96, 144 ], [ 0, 0, 0, 18, 72, 72, 198 ], [ 0, 15, 15, 15, 60, 120, 135 ], [ 0, 8, 8, 8, 72, 104, 160 ], [ 0, 6, 6, 12, 78, 102, 156 ], [ 1, 6, 11, 9, 80, 104, 149 ] ] ] ), rec( name := "J2", sbgname := "U3(3)", filename := "U33", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 100, rank := 3, permchar := "1a + 36a + 63a", charnmbs := [ 1, 6, 7 ], ctbl := [ [ 1, 36, 63 ], [ 1, 6, -7 ], [ 1, -4, 3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 36, 0 ], [ 1, 14, 21 ], [ 0, 12, 24 ] ], [ [ 0, 0, 63 ], [ 0, 21, 42 ], [ 1, 24, 38 ] ] ] ), rec( name := "J2.2", sbgname := "2^{1+4}_-:S5", filename := "2_^1+4:S5", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 315, rank := 5, permchar := "1a^+ + 14ab + 36a^+ + 90a^+ + 160a^+", charnmbs := [ 1, 3, 5, 10, 14 ], ctbl := [ [ 1, 10, 64, 80, 160 ], [ 1, -5, 4, 20, -20 ], [ 1, 5, -16, 10, 0 ], [ 1, 3, 8, -4, -8 ], [ 1, -2, -2, -4, 7 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 10, 0, 0, 0 ], [ 1, 1, 0, 8, 0 ], [ 0, 0, 5, 0, 5 ], [ 0, 1, 0, 1, 8 ], [ 0, 0, 2, 4, 4 ] ], [ [ 0, 0, 64, 0, 0 ], [ 0, 0, 32, 0, 32 ], [ 1, 5, 8, 20, 30 ], [ 0, 0, 16, 16, 32 ], [ 0, 2, 12, 16, 34 ] ], [ [ 0, 0, 0, 80, 0 ], [ 0, 8, 0, 8, 64 ], [ 0, 0, 20, 20, 40 ], [ 1, 1, 16, 30, 32 ], [ 0, 4, 16, 16, 44 ] ], [ [ 0, 0, 0, 0, 160 ], [ 0, 0, 32, 64, 64 ], [ 0, 5, 30, 40, 85 ], [ 0, 8, 32, 32, 88 ], [ 1, 4, 34, 44, 77 ] ] ] ), rec( name := "J2.2", sbgname := "3.A6.2^2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 280, rank := 4, permchar := "1a^+ + 63a^+ + 90a^+ + 126a^+", charnmbs := [ 1, 7, 10, 12 ], ctbl := [ [ 1, 36, 108, 135 ], [ 1, -4, -12, 15 ], [ 1, 8, -4, -5 ], [ 1, -4, 8, -5 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 36, 0, 0 ], [ 1, 8, 12, 15 ], [ 0, 4, 12, 20 ], [ 0, 4, 16, 16 ] ], [ [ 0, 0, 108, 0 ], [ 0, 12, 36, 60 ], [ 1, 12, 40, 55 ], [ 0, 16, 44, 48 ] ], [ [ 0, 0, 0, 135 ], [ 0, 15, 60, 60 ], [ 0, 20, 55, 60 ], [ 1, 16, 48, 70 ] ] ] ), rec( name := "J2.2", sbgname := "(A5xD10).2", filename := "A5xD10.2", degree := 1008, rank := 8, permchar := "1a^+ + 14ab + 90a^{+-} + 126a^+ + 160a^+ + 225a^- + 288a^-", charnmbs := [ 1, 3, 10, 11, 12, 14, 21, 23 ], ctbl := [ [ 1, 12, 25, 50, 120, 200, 300, 300 ], [ 1, -6, -5, 20, 30, -10, -60, 30 ], [ 1, -2, 11, 8, -6, 18, -8, -22 ], [ 1, 6, -5, 0, 18, 10, 0, -30 ], [ 1, 4, 5, -10, 0, 0, -20, 20 ], [ 1, 3, 1, 8, -6, -22, 12, 3 ], [ 1, -4, 1, -6, 8, -8, 12, -4 ], [ 1, -1, -5, 0, -10, 10, 0, 5 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 12, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 10, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 12 ], [ 0, 0, 0, 0, 0, 0, 12, 0 ], [ 0, 1, 0, 0, 1, 5, 5, 0 ], [ 0, 0, 0, 0, 3, 3, 3, 3 ], [ 0, 0, 0, 2, 2, 2, 2, 4 ], [ 0, 0, 1, 0, 0, 2, 4, 5 ] ], [ [ 0, 0, 25, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 25 ], [ 1, 0, 4, 4, 0, 16, 0, 0 ], [ 0, 0, 2, 3, 0, 8, 12, 0 ], [ 0, 0, 0, 0, 0, 5, 10, 10 ], [ 0, 0, 2, 2, 3, 6, 6, 6 ], [ 0, 0, 0, 2, 4, 4, 7, 8 ], [ 0, 1, 0, 0, 4, 4, 8, 8 ] ], [ [ 0, 0, 0, 50, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 50, 0 ], [ 0, 0, 4, 6, 0, 16, 24, 0 ], [ 1, 0, 3, 6, 12, 4, 0, 24 ], [ 0, 0, 0, 5, 10, 10, 5, 20 ], [ 0, 0, 2, 1, 6, 14, 15, 12 ], [ 0, 2, 2, 0, 2, 10, 20, 14 ], [ 0, 0, 0, 4, 8, 8, 14, 16 ] ], [ [ 0, 0, 0, 0, 120, 0, 0, 0 ], [ 0, 10, 0, 0, 10, 50, 50, 0 ], [ 0, 0, 0, 0, 0, 24, 48, 48 ], [ 0, 0, 0, 12, 24, 24, 12, 48 ], [ 1, 1, 0, 10, 23, 25, 25, 35 ], [ 0, 3, 3, 6, 15, 21, 39, 33 ], [ 0, 2, 4, 2, 10, 26, 46, 30 ], [ 0, 0, 4, 8, 14, 22, 30, 42 ] ], [ [ 0, 0, 0, 0, 0, 200, 0, 0 ], [ 0, 0, 0, 0, 50, 50, 50, 50 ], [ 0, 0, 16, 16, 24, 48, 48, 48 ], [ 0, 0, 8, 4, 24, 56, 60, 48 ], [ 0, 5, 5, 10, 25, 35, 65, 55 ], [ 1, 3, 6, 14, 21, 35, 63, 57 ], [ 0, 2, 4, 10, 26, 42, 54, 62 ], [ 0, 2, 4, 8, 22, 38, 62, 64 ] ], [ [ 0, 0, 0, 0, 0, 0, 300, 0 ], [ 0, 0, 0, 50, 50, 50, 50, 100 ], [ 0, 0, 0, 24, 48, 48, 84, 96 ], [ 0, 12, 12, 0, 12, 60, 120, 84 ], [ 0, 5, 10, 5, 25, 65, 115, 75 ], [ 0, 3, 6, 15, 39, 63, 81, 93 ], [ 1, 2, 7, 20, 46, 54, 68, 102 ], [ 0, 4, 8, 14, 30, 62, 102, 80 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 300 ], [ 0, 0, 25, 0, 0, 50, 100, 125 ], [ 0, 12, 0, 0, 48, 48, 96, 96 ], [ 0, 0, 0, 24, 48, 48, 84, 96 ], [ 0, 0, 10, 20, 35, 55, 75, 105 ], [ 0, 3, 6, 12, 33, 57, 93, 96 ], [ 0, 4, 8, 14, 30, 62, 102, 80 ], [ 1, 5, 8, 16, 42, 64, 80, 84 ] ] ] ), rec( name := "J2.2", sbgname := "U3(3).2", filename := "U33.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 100, rank := 3, permchar := "1a^+ + 36a^+ + 63a^+", charnmbs := [ 1, 5, 7 ], ctbl := [ [ 1, 36, 63 ], [ 1, 6, -7 ], [ 1, -4, 3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 36, 0 ], [ 1, 14, 21 ], [ 0, 12, 24 ] ], [ [ 0, 0, 63 ], [ 0, 21, 42 ], [ 1, 24, 38 ] ] ] ), rec( name := "J2.2", sbgname := "U3(3) leq U3(3).2", filename := "U33", degree := 200, rank := 6, permchar := "1a^{+-} + 36a^{+-} + 63a^{+-}", charnmbs := [ 1, 2, 5, 6, 7, 8 ], ctbl := [ [ 1, 1, 36, 36, 63, 63 ], [ 1, -1, -36, 36, -63, 63 ], [ 1, 1, 6, 6, -7, -7 ], [ 1, -1, -6, 6, 7, -7 ], [ 1, 1, -4, -4, 3, 3 ], [ 1, -1, 4, -4, -3, 3 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 36, 0, 0, 0 ], [ 0, 0, 0, 36, 0, 0 ], [ 1, 0, 0, 14, 0, 21 ], [ 0, 1, 14, 0, 21, 0 ], [ 0, 0, 0, 12, 0, 24 ], [ 0, 0, 12, 0, 24, 0 ] ], [ [ 0, 0, 0, 36, 0, 0 ], [ 0, 0, 36, 0, 0, 0 ], [ 0, 1, 14, 0, 21, 0 ], [ 1, 0, 0, 14, 0, 21 ], [ 0, 0, 12, 0, 24, 0 ], [ 0, 0, 0, 12, 0, 24 ] ], [ [ 0, 0, 0, 0, 63, 0 ], [ 0, 0, 0, 0, 0, 63 ], [ 0, 0, 0, 21, 0, 42 ], [ 0, 0, 21, 0, 42, 0 ], [ 1, 0, 0, 24, 0, 38 ], [ 0, 1, 24, 0, 38, 0 ] ], [ [ 0, 0, 0, 0, 0, 63 ], [ 0, 0, 0, 0, 63, 0 ], [ 0, 0, 21, 0, 42, 0 ], [ 0, 0, 0, 21, 0, 42 ], [ 0, 1, 24, 0, 38, 0 ], [ 1, 0, 0, 24, 0, 38 ] ] ] ), rec( name := "J2.2", sbgname := "3.A6.2_3 leq 3.A6.2^2", filename := "3.A6.2_3", degree := 560, rank := 7, permchar := "1a^+ + 21ab + 63a^{+-} + 90a^+ + 126a^+ + 175a^-", charnmbs := [ 1, 4, 7, 8, 10, 12, 17 ], ctbl := [ [ 1, 1, 36, 36, 135, 135, 216 ], [ 1, -1, -12, 12, 15, -15, 0 ], [ 1, 1, -4, -4, 15, 15, -24 ], [ 1, -1, 8, -8, 15, -15, 0 ], [ 1, 1, 8, 8, -5, -5, -8 ], [ 1, 1, -4, -4, -5, -5, 16 ], [ 1, -1, 0, 0, -9, 9, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 36, 0, 0, 0, 0 ], [ 0, 0, 0, 36, 0, 0, 0 ], [ 1, 0, 2, 6, 15, 0, 12 ], [ 0, 1, 6, 2, 0, 15, 12 ], [ 0, 0, 4, 0, 8, 8, 16 ], [ 0, 0, 0, 4, 8, 8, 16 ], [ 0, 0, 2, 2, 10, 10, 12 ] ], [ [ 0, 0, 0, 36, 0, 0, 0 ], [ 0, 0, 36, 0, 0, 0, 0 ], [ 0, 1, 6, 2, 0, 15, 12 ], [ 1, 0, 2, 6, 15, 0, 12 ], [ 0, 0, 0, 4, 8, 8, 16 ], [ 0, 0, 4, 0, 8, 8, 16 ], [ 0, 0, 2, 2, 10, 10, 12 ] ], [ [ 0, 0, 0, 0, 135, 0, 0 ], [ 0, 0, 0, 0, 0, 135, 0 ], [ 0, 0, 15, 0, 30, 30, 60 ], [ 0, 0, 0, 15, 30, 30, 60 ], [ 1, 0, 8, 8, 38, 32, 48 ], [ 0, 1, 8, 8, 32, 38, 48 ], [ 0, 0, 10, 10, 30, 30, 55 ] ], [ [ 0, 0, 0, 0, 0, 135, 0 ], [ 0, 0, 0, 0, 135, 0, 0 ], [ 0, 0, 0, 15, 30, 30, 60 ], [ 0, 0, 15, 0, 30, 30, 60 ], [ 0, 1, 8, 8, 32, 38, 48 ], [ 1, 0, 8, 8, 38, 32, 48 ], [ 0, 0, 10, 10, 30, 30, 55 ] ], [ [ 0, 0, 0, 0, 0, 0, 216 ], [ 0, 0, 0, 0, 0, 0, 216 ], [ 0, 0, 12, 12, 60, 60, 72 ], [ 0, 0, 12, 12, 60, 60, 72 ], [ 0, 0, 16, 16, 48, 48, 88 ], [ 0, 0, 16, 16, 48, 48, 88 ], [ 1, 1, 12, 12, 55, 55, 80 ] ] ] ), rec( name := "J2.2", sbgname := "3.A6.2_2 leq 3.A6.2^2", filename := "3.A6.2_2", degree := 560, rank := 8, permchar := "1a^{+-} + 63a^{+-} + 90a^{+-} + 126a^{+-}", charnmbs := [ 1, 2, 7, 8, 10, 11, 12, 13 ], ctbl := [ [ 1, 1, 36, 36, 108, 108, 135, 135 ], [ 1, -1, -36, 36, 108, -108, -135, 135 ], [ 1, 1, -4, -4, -12, -12, 15, 15 ], [ 1, -1, 4, -4, -12, 12, -15, 15 ], [ 1, 1, 8, 8, -4, -4, -5, -5 ], [ 1, -1, -8, 8, -4, 4, 5, -5 ], [ 1, 1, -4, -4, 8, 8, -5, -5 ], [ 1, -1, 4, -4, 8, -8, 5, -5 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 36, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 36, 0, 0, 0, 0 ], [ 1, 0, 0, 8, 12, 0, 0, 15 ], [ 0, 1, 8, 0, 0, 12, 15, 0 ], [ 0, 0, 4, 0, 0, 12, 20, 0 ], [ 0, 0, 0, 4, 12, 0, 0, 20 ], [ 0, 0, 0, 4, 16, 0, 0, 16 ], [ 0, 0, 4, 0, 0, 16, 16, 0 ] ], [ [ 0, 0, 0, 36, 0, 0, 0, 0 ], [ 0, 0, 36, 0, 0, 0, 0, 0 ], [ 0, 1, 8, 0, 0, 12, 15, 0 ], [ 1, 0, 0, 8, 12, 0, 0, 15 ], [ 0, 0, 0, 4, 12, 0, 0, 20 ], [ 0, 0, 4, 0, 0, 12, 20, 0 ], [ 0, 0, 4, 0, 0, 16, 16, 0 ], [ 0, 0, 0, 4, 16, 0, 0, 16 ] ], [ [ 0, 0, 0, 0, 108, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 108, 0, 0 ], [ 0, 0, 12, 0, 0, 36, 60, 0 ], [ 0, 0, 0, 12, 36, 0, 0, 60 ], [ 1, 0, 0, 12, 40, 0, 0, 55 ], [ 0, 1, 12, 0, 0, 40, 55, 0 ], [ 0, 0, 16, 0, 0, 44, 48, 0 ], [ 0, 0, 0, 16, 44, 0, 0, 48 ] ], [ [ 0, 0, 0, 0, 0, 108, 0, 0 ], [ 0, 0, 0, 0, 108, 0, 0, 0 ], [ 0, 0, 0, 12, 36, 0, 0, 60 ], [ 0, 0, 12, 0, 0, 36, 60, 0 ], [ 0, 1, 12, 0, 0, 40, 55, 0 ], [ 1, 0, 0, 12, 40, 0, 0, 55 ], [ 0, 0, 0, 16, 44, 0, 0, 48 ], [ 0, 0, 16, 0, 0, 44, 48, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 135, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 135 ], [ 0, 0, 0, 15, 60, 0, 0, 60 ], [ 0, 0, 15, 0, 0, 60, 60, 0 ], [ 0, 0, 20, 0, 0, 55, 60, 0 ], [ 0, 0, 0, 20, 55, 0, 0, 60 ], [ 1, 0, 0, 16, 48, 0, 0, 70 ], [ 0, 1, 16, 0, 0, 48, 70, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 135 ], [ 0, 0, 0, 0, 0, 0, 135, 0 ], [ 0, 0, 15, 0, 0, 60, 60, 0 ], [ 0, 0, 0, 15, 60, 0, 0, 60 ], [ 0, 0, 0, 20, 55, 0, 0, 60 ], [ 0, 0, 20, 0, 0, 55, 60, 0 ], [ 0, 1, 16, 0, 0, 48, 70, 0 ], [ 1, 0, 0, 16, 48, 0, 0, 70 ] ] ] ), rec( name := "J2.2", sbgname := "2^{1+4}_-:5:4 leq 2^{1+4}_-:S5", filename := "2_^1+4:5:4", degree := 1890, rank := 12, permchar := "1a^+ + 14ab + 36a^+ + 63a^- + 90a^+ + 126a^{+-} + 160a^+ + 288a^- +300a^- + 336a^{+-}", charnmbs := [ 1, 3, 5, 8, 10, 12, 13, 14, 23, 25, 26, 27 ], ctbl := [ [ 1, 5, 20, 40, 64, 80, 80, 160, 160, 320, 320, 640 ], [ 1, 5, -10, -20, 4, 20, 20, -20, -20, 20, 80, -80 ], [ 1, 5, 10, 20, -16, 10, 10, 0, 0, -80, 40, 0 ], [ 1, -1, 8, -8, 0, -24, -8, -32, 32, 0, 32, 0 ], [ 1, 5, 6, 12, 8, -4, -4, -8, -8, 40, -16, -32 ], [ 1, -1, 6, -6, -4, 8, -16, 28, 4, 4, 8, -32 ], [ 1, -1, -2, 2, 20, 16, -8, -12, 12, -20, -8, 0 ], [ 1, 5, -4, -8, -2, -4, -4, 7, 7, -10, -16, 28 ], [ 1, -1, -4, 4, 6, -12, 4, 13, -1, -6, 8, -12 ], [ 1, -1, -4, 4, -8, 2, -10, -8, -8, 8, 8, 16 ], [ 1, -1, E(24)-2*E(24)^8-E(24)^11-2*E(24)^16-E(24)^17+E(24)^19, -E(24)+2*E(24)^8+E(24)^11+2*E(24)^16+E(24)^17-E(24)^19, 2*E(24)+2*E(24)^8-2*E(24)^11+2*E(24)^16-2*E(24)^17+2*E(24)^19, -E(24)-2*E(24)^8+E(24)^11-2*E(24)^16+E(24)^17-E(24)^19, -E(24)-8*E(24)^8+E(24)^11-8*E(24)^16+E(24)^17-E(24)^19, -2, -6*E(24)+2*E(24)^8+6*E(24)^11+2*E(24)^16+6*E(24)^17 -6*E(24)^19, -2*E(24)-2*E(24)^8+2*E(24)^11-2*E(24)^16+2*E(24)^17-2*E(24)^19, 2*E(24)+10*E(24)^8-2*E(24)^11+10*E(24)^16-2*E(24)^17+2*E(24)^19, 6*E(24)-4*E(24)^8-6*E(24)^11-4*E(24)^16-6*E(24)^17+6*E(24)^19 ], [ 1, -1, -E(24)-2*E(24)^8+E(24)^11-2*E(24)^16+E(24)^17-E(24)^19, E(24)+2*E(24)^8-E(24)^11+2*E(24)^16-E(24)^17+E(24)^19, -2*E(24)+2*E(24)^8+2*E(24)^11+2*E(24)^16+2*E(24)^17-2*E(24)^19, E(24)-2*E(24)^8-E(24)^11-2*E(24)^16-E(24)^17+E(24)^19, E(24)-8*E(24)^8-E(24)^11-8*E(24)^16-E(24)^17+E(24)^19, -2, 6*E(24)+2*E(24)^8-6*E(24)^11+2*E(24)^16-6*E(24)^17+6*E(24)^19, 2*E(24)-2*E(24)^8-2*E(24)^11-2*E(24)^16-2*E(24)^17+2*E(24)^19, -2*E(24)+10*E(24)^8+2*E(24)^11+10*E(24)^16+2*E(24)^17 -2*E(24)^19, -6*E(24)-4*E(24)^8+6*E(24)^11-4*E(24)^16+6*E(24)^17-6*E(24)^19 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 4, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 4 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 4, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 3, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 3 ] ], [ [ 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 4, 16, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 16, 0 ], [ 0, 2, 0, 2, 0, 4, 4, 0, 0, 0, 8, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 10 ], [ 0, 0, 0, 2, 0, 1, 1, 8, 0, 0, 0, 8 ], [ 0, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 16 ], [ 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 4, 4 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 8, 4 ], [ 0, 0, 0, 0, 2, 0, 0, 2, 2, 8, 0, 6 ], [ 0, 0, 1, 1, 0, 0, 0, 2, 4, 0, 2, 10 ], [ 0, 0, 0, 0, 1, 1, 2, 1, 1, 3, 5, 6 ] ], [ [ 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 16, 24, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 4, 0, 4, 0, 8, 8, 0, 0, 0, 16, 0 ], [ 1, 3, 2, 2, 0, 4, 4, 0, 0, 0, 24, 0 ], [ 0, 0, 0, 0, 5, 0, 0, 5, 5, 15, 0, 10 ], [ 0, 0, 2, 2, 0, 0, 0, 0, 8, 0, 4, 24 ], [ 0, 0, 2, 2, 0, 0, 0, 8, 8, 0, 4, 16 ], [ 0, 0, 0, 0, 2, 0, 4, 0, 4, 6, 12, 12 ], [ 0, 0, 0, 0, 2, 4, 4, 4, 0, 6, 8, 12 ], [ 0, 0, 0, 0, 3, 0, 0, 3, 3, 17, 0, 14 ], [ 0, 0, 1, 3, 0, 1, 1, 6, 4, 0, 2, 22 ], [ 0, 0, 0, 0, 1, 3, 2, 3, 3, 7, 11, 10 ] ], [ [ 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 32 ], [ 0, 0, 0, 0, 8, 0, 0, 8, 8, 24, 0, 16 ], [ 1, 0, 0, 5, 8, 10, 0, 0, 10, 0, 10, 20 ], [ 0, 0, 0, 0, 8, 8, 0, 0, 8, 8, 8, 24 ], [ 0, 0, 0, 0, 0, 0, 0, 8, 0, 16, 16, 24 ], [ 0, 0, 0, 2, 0, 0, 4, 6, 4, 12, 12, 24 ], [ 0, 0, 0, 2, 4, 4, 0, 4, 6, 8, 12, 24 ], [ 0, 1, 2, 3, 0, 2, 4, 6, 4, 8, 14, 20 ], [ 0, 0, 0, 0, 2, 2, 4, 6, 6, 14, 10, 20 ], [ 0, 0, 1, 1, 2, 3, 3, 6, 6, 10, 10, 22 ] ], [ [ 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 64, 0 ], [ 0, 0, 0, 8, 0, 4, 4, 32, 0, 0, 0, 32 ], [ 0, 0, 4, 4, 0, 0, 0, 0, 16, 0, 8, 48 ], [ 0, 0, 0, 0, 10, 10, 0, 0, 10, 10, 10, 30 ], [ 1, 0, 1, 0, 8, 0, 2, 0, 16, 8, 28, 16 ], [ 0, 1, 1, 0, 0, 2, 8, 0, 8, 16, 20, 24 ], [ 0, 0, 4, 0, 0, 0, 0, 4, 12, 16, 16, 28 ], [ 0, 0, 0, 4, 4, 8, 4, 12, 4, 12, 4, 28 ], [ 0, 0, 0, 0, 2, 2, 4, 8, 6, 18, 14, 26 ], [ 0, 1, 0, 1, 2, 7, 5, 8, 2, 14, 18, 22 ], [ 0, 0, 1, 3, 3, 2, 3, 7, 7, 13, 11, 30 ] ], [ [ 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 64, 0 ], [ 0, 0, 0, 8, 0, 4, 4, 0, 0, 0, 0, 64 ], [ 0, 0, 4, 4, 0, 0, 0, 16, 16, 0, 8, 32 ], [ 0, 0, 0, 0, 0, 0, 0, 10, 0, 20, 20, 30 ], [ 0, 1, 1, 0, 0, 2, 8, 0, 8, 16, 20, 24 ], [ 1, 0, 1, 0, 0, 8, 2, 8, 8, 16, 20, 16 ], [ 0, 0, 0, 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30, 28, 54, 50, 114, 118, 204 ] ] ] ), rec( name := "J2.2", sbgname := "2^{2+4}.(S3xS3)", filename := "2^2+4.S3xS3", degree := 525, rank := 6, permchar := "1a^+ + 36a^+ + 63a^+ + 90a^+ + 160a^+ + 175a^+", charnmbs := [ 1, 5, 7, 10, 14, 16 ], ctbl := [ [ 1, 12, 32, 96, 192, 192 ], [ 1, 7, -8, 16, 12, -28 ], [ 1, -3, 12, 6, 2, -18 ], [ 1, 5, 4, -2, -18, 10 ], [ 1, 0, -1, -12, 12, 0 ], [ 1, -3, -4, 6, -6, 6 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 12, 0, 0, 0, 0 ], [ 1, 3, 0, 8, 0, 0 ], [ 0, 0, 0, 0, 0, 12 ], [ 0, 1, 0, 3, 6, 2 ], [ 0, 0, 0, 3, 6, 3 ], [ 0, 0, 2, 1, 3, 6 ] ], [ [ 0, 0, 32, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 32 ], [ 1, 0, 7, 12, 12, 0 ], [ 0, 0, 4, 4, 12, 12 ], [ 0, 0, 2, 6, 12, 12 ], [ 0, 2, 0, 6, 12, 12 ] ], [ [ 0, 0, 0, 96, 0, 0 ], [ 0, 8, 0, 24, 48, 16 ], [ 0, 0, 12, 12, 36, 36 ], [ 1, 3, 4, 16, 42, 30 ], [ 0, 3, 6, 21, 33, 33 ], [ 0, 1, 6, 15, 33, 41 ] ], [ [ 0, 0, 0, 0, 192, 0 ], [ 0, 0, 0, 48, 96, 48 ], [ 0, 0, 12, 36, 72, 72 ], [ 0, 6, 12, 42, 66, 66 ], [ 1, 6, 12, 33, 68, 72 ], [ 0, 3, 12, 33, 72, 72 ] ], [ [ 0, 0, 0, 0, 0, 192 ], [ 0, 0, 32, 16, 48, 96 ], [ 0, 12, 0, 36, 72, 72 ], [ 0, 2, 12, 30, 66, 82 ], [ 0, 3, 12, 33, 72, 72 ], [ 1, 6, 12, 41, 72, 60 ] ] ] ) , rec( name := "J2.2", sbgname := "2^{2+4}.(S3x3) leq 2^{2+4}.(S3xS3)", filename := "2^2+4.S3x3", degree := 1050, rank := 9, permchar := "1a^+ + 36a^+ + 63a^+ + 70ab + 90a^+ + 160a^{+-} + 175a^+ + 225a^+", charnmbs := [ 1, 5, 7, 9, 10, 14, 15, 16, 20 ], ctbl := [ [ 1, 1, 24, 32, 32, 192, 192, 192, 384 ], [ 1, 1, 14, -8, -8, 32, 12, 12, -56 ], [ 1, 1, -6, 12, 12, 12, 2, 2, -36 ], [ 1, -1, 0, -8, 8, 0, -12, 12, 0 ], [ 1, 1, 10, 4, 4, -4, -18, -18, 20 ], [ 1, 1, 0, -1, -1, -24, 12, 12, 0 ], [ 1, -1, 0, 7, -7, 0, -12, 12, 0 ], [ 1, 1, -6, -4, -4, 12, -6, -6, 12 ], [ 1, -1, 0, 0, 0, 0, 16, -16, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 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72 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 192, 0 ], [ 0, 0, 0, 0, 0, 0, 192, 0, 0 ], [ 0, 0, 0, 0, 0, 48, 48, 48, 48 ], [ 0, 0, 0, 12, 0, 36, 36, 36, 72 ], [ 0, 0, 0, 0, 12, 36, 36, 36, 72 ], [ 0, 0, 6, 6, 6, 42, 33, 33, 66 ], [ 0, 1, 6, 6, 6, 33, 32, 36, 72 ], [ 1, 0, 6, 6, 6, 33, 36, 32, 72 ], [ 0, 0, 3, 6, 6, 33, 36, 36, 72 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 384 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 384 ], [ 0, 0, 0, 32, 32, 32, 48, 48, 192 ], [ 0, 0, 24, 0, 0, 72, 72, 72, 144 ], [ 0, 0, 24, 0, 0, 72, 72, 72, 144 ], [ 0, 0, 4, 12, 12, 60, 66, 66, 164 ], [ 0, 0, 6, 12, 12, 66, 72, 72, 144 ], [ 0, 0, 6, 12, 12, 66, 72, 72, 144 ], [ 1, 1, 12, 12, 12, 82, 72, 72, 120 ] ] ] ), rec( name := "J2.2", sbgname := "2^{2+4}.(3xS3) leq 2^{2+4}.(S3xS3)", filename := "2^2+4.3xS3", degree := 1050, rank := 12, permchar := "1a^{+-} + 36a^{+-} + 63a^{+-} + 90a^{+-} + 160a^{+-} + 175a^{+-}", charnmbs := [ 1, 2, 5, 6, 7, 8, 10, 11, 14, 15, 16, 17 ], ctbl := [ [ 1, 1, 12, 12, 32, 32, 96, 96, 192, 192, 192, 192 ], [ 1, -1, 12, -12, 32, -32, -96, 96, -192, -192, 192, 192 ], [ 1, 1, 7, 7, -8, -8, 16, 16, -28, 12, -28, 12 ], [ 1, -1, 7, -7, -8, 8, -16, 16, 28, -12, -28, 12 ], [ 1, 1, -3, -3, 12, 12, 6, 6, -18, 2, -18, 2 ], [ 1, -1, -3, 3, 12, -12, -6, 6, 18, -2, -18, 2 ], [ 1, 1, 5, 5, 4, 4, -2, -2, 10, -18, 10, -18 ], [ 1, -1, 5, -5, 4, -4, 2, -2, -10, 18, 10, -18 ], [ 1, 1, 0, 0, -1, -1, -12, -12, 0, 12, 0, 12 ], [ 1, -1, 0, 0, -1, 1, 12, -12, 0, -12, 0, 12 ], [ 1, 1, -3, -3, -4, -4, 6, 6, 6, -6, 6, -6 ], [ 1, -1, -3, 3, -4, 4, -6, 6, -6, 6, 6, -6 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 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41, 0, 60, 72, 0, 0 ], [ 0, 0, 0, 3, 0, 12, 33, 0, 72, 72, 0, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192 ], [ 0, 0, 0, 0, 0, 0, 48, 0, 48, 96, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 48, 96 ], [ 0, 0, 0, 0, 0, 12, 36, 0, 72, 72, 0, 0 ], [ 0, 0, 0, 0, 12, 0, 0, 36, 0, 0, 72, 72 ], [ 0, 0, 6, 0, 12, 0, 0, 42, 0, 0, 66, 66 ], [ 0, 0, 0, 6, 0, 12, 42, 0, 66, 66, 0, 0 ], [ 0, 0, 3, 0, 12, 0, 0, 33, 0, 0, 72, 72 ], [ 1, 0, 6, 0, 12, 0, 0, 33, 0, 0, 72, 68 ], [ 0, 0, 0, 3, 0, 12, 33, 0, 72, 72, 0, 0 ], [ 0, 1, 0, 6, 0, 12, 33, 0, 72, 68, 0, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0 ], [ 0, 0, 0, 0, 32, 0, 0, 16, 0, 0, 96, 48 ], [ 0, 0, 0, 0, 0, 32, 16, 0, 96, 48, 0, 0 ], [ 0, 0, 12, 0, 0, 0, 0, 36, 0, 0, 72, 72 ], [ 0, 0, 0, 12, 0, 0, 36, 0, 72, 72, 0, 0 ], [ 0, 0, 0, 2, 0, 12, 30, 0, 82, 66, 0, 0 ], [ 0, 0, 2, 0, 12, 0, 0, 30, 0, 0, 82, 66 ], [ 0, 1, 0, 6, 0, 12, 41, 0, 60, 72, 0, 0 ], [ 0, 0, 0, 3, 0, 12, 33, 0, 72, 72, 0, 0 ], [ 1, 0, 6, 0, 12, 0, 0, 41, 0, 0, 60, 72 ], [ 0, 0, 3, 0, 12, 0, 0, 33, 0, 0, 72, 72 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 48, 96 ], [ 0, 0, 0, 0, 0, 0, 48, 0, 48, 96, 0, 0 ], [ 0, 0, 0, 0, 12, 0, 0, 36, 0, 0, 72, 72 ], [ 0, 0, 0, 0, 0, 12, 36, 0, 72, 72, 0, 0 ], [ 0, 0, 0, 6, 0, 12, 42, 0, 66, 66, 0, 0 ], [ 0, 0, 6, 0, 12, 0, 0, 42, 0, 0, 66, 66 ], [ 0, 0, 0, 3, 0, 12, 33, 0, 72, 72, 0, 0 ], [ 0, 1, 0, 6, 0, 12, 33, 0, 72, 68, 0, 0 ], [ 0, 0, 3, 0, 12, 0, 0, 33, 0, 0, 72, 72 ], [ 1, 0, 6, 0, 12, 0, 0, 33, 0, 0, 72, 68 ] ] ] ), rec( name := "J2.2", sbgname := "(A4xA5).2", filename := "A4xA5.2", degree := 840, rank := 7, permchar := "1a^+ + 63a^+ + 90a^+ + 126a^+ + 160a^+ + 175a^+ + 225a^-", charnmbs := [ 1, 7, 10, 12, 14, 16, 21 ], ctbl := [ [ 1, 15, 20, 24, 180, 240, 360 ], [ 1, 5, 10, -6, 0, 20, -30 ], [ 1, 1, 6, 10, -16, -12, 10 ], [ 1, -5, 0, 4, 20, 0, -20 ], [ 1, 6, -4, 0, 9, -12, 0 ], [ 1, -3, 2, -6, 0, -12, 18 ], [ 1, -1, -4, 0, -12, 16, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 15, 0, 0, 0, 0, 0 ], [ 1, 2, 0, 0, 12, 0, 0 ], [ 0, 0, 3, 0, 0, 12, 0 ], [ 0, 0, 0, 0, 0, 0, 15 ], [ 0, 1, 0, 0, 2, 4, 8 ], [ 0, 0, 1, 0, 3, 5, 6 ], [ 0, 0, 0, 1, 4, 4, 6 ] ], [ [ 0, 0, 20, 0, 0, 0, 0 ], [ 0, 0, 4, 0, 0, 16, 0 ], [ 1, 3, 4, 0, 0, 12, 0 ], [ 0, 0, 0, 5, 0, 0, 15 ], [ 0, 0, 0, 0, 4, 8, 8 ], [ 0, 1, 1, 0, 6, 6, 6 ], [ 0, 0, 0, 1, 4, 4, 11 ] ], [ [ 0, 0, 0, 24, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 6, 0, 0, 18 ], [ 1, 0, 5, 3, 0, 0, 15 ], [ 0, 0, 0, 0, 8, 8, 8 ], [ 0, 0, 0, 0, 6, 6, 12 ], [ 0, 1, 1, 1, 4, 8, 9 ] ], [ [ 0, 0, 0, 0, 180, 0, 0 ], [ 0, 12, 0, 0, 24, 48, 96 ], [ 0, 0, 0, 0, 36, 72, 72 ], [ 0, 0, 0, 0, 60, 60, 60 ], [ 1, 2, 4, 8, 41, 52, 72 ], [ 0, 3, 6, 6, 39, 48, 78 ], [ 0, 4, 4, 4, 36, 52, 80 ] ], [ [ 0, 0, 0, 0, 0, 240, 0 ], [ 0, 0, 16, 0, 48, 80, 96 ], [ 0, 12, 12, 0, 72, 72, 72 ], [ 0, 0, 0, 0, 60, 60, 120 ], [ 0, 4, 8, 8, 52, 64, 104 ], [ 1, 5, 6, 6, 48, 72, 102 ], [ 0, 4, 4, 8, 52, 68, 104 ] ], [ [ 0, 0, 0, 0, 0, 0, 360 ], [ 0, 0, 0, 24, 96, 96, 144 ], [ 0, 0, 0, 18, 72, 72, 198 ], [ 0, 15, 15, 15, 60, 120, 135 ], [ 0, 8, 8, 8, 72, 104, 160 ], [ 0, 6, 6, 12, 78, 102, 156 ], [ 1, 6, 11, 9, 80, 104, 149 ] ] ] ), rec( name := "J2.2", sbgname := "A4xA5 leq (A4xA5).2", filename := "A4xA5", degree := 1680, rank := 14, permchar := "1a^{+-} + 63a^{+-} + 90a^{+-} + 126a^{+-} + 160a^{+-} + 175a^{+-} + 225a^{+-}", charnmbs := [ 1, 2, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21 ], ctbl := [ [ 1, 1, 15, 15, 20, 20, 24, 24, 180, 180, 240, 240, 360, 360 ], [ 1, -1, -15, 15, 20, -20, 24, -24, 180, -180, -240, 240, -360, 360 ], [ 1, 1, 5, 5, 10, 10, -6, -6, 0, 0, 20, 20, -30, -30 ], [ 1, -1, -5, 5, 10, -10, -6, 6, 0, 0, -20, 20, 30, -30 ], [ 1, 1, 1, 1, 6, 6, 10, 10, -16, -16, -12, -12, 10, 10 ], [ 1, -1, -1, 1, 6, -6, 10, -10, -16, 16, 12, -12, -10, 10 ], [ 1, 1, -5, -5, 0, 0, 4, 4, 20, 20, 0, 0, -20, -20 ], [ 1, -1, 5, -5, 0, 0, 4, -4, 20, -20, 0, 0, 20, -20 ], [ 1, 1, 6, 6, -4, -4, 0, 0, 9, 9, -12, -12, 0, 0 ], [ 1, -1, -6, 6, -4, 4, 0, 0, 9, -9, 12, -12, 0, 0 ], [ 1, 1, -3, -3, 2, 2, -6, -6, 0, 0, -12, -12, 18, 18 ], [ 1, -1, 3, -3, 2, -2, -6, 6, 0, 0, 12, -12, -18, 18 ], [ 1, -1, 1, -1, -4, 4, 0, 0, -12, 12, -16, 16, 0, 0 ], [ 1, 1, -1, -1, -4, -4, 0, 0, -12, -12, 16, 16, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 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8, 0, 72, 104, 0, 160, 0 ], [ 0, 0, 0, 8, 8, 0, 8, 0, 72, 0, 0, 104, 0, 160 ], [ 0, 0, 0, 6, 6, 0, 12, 0, 78, 0, 0, 102, 0, 156 ], [ 0, 0, 6, 0, 0, 6, 0, 12, 0, 78, 102, 0, 156, 0 ], [ 1, 0, 0, 6, 11, 0, 9, 0, 80, 0, 0, 104, 0, 149 ], [ 0, 1, 6, 0, 0, 11, 0, 9, 0, 80, 104, 0, 149, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 24, 0, 96, 96, 0, 144, 0 ], [ 0, 0, 0, 0, 0, 0, 24, 0, 96, 0, 0, 96, 0, 144 ], [ 0, 0, 0, 0, 0, 0, 18, 0, 72, 0, 0, 72, 0, 198 ], [ 0, 0, 0, 0, 0, 0, 0, 18, 0, 72, 72, 0, 198, 0 ], [ 0, 0, 0, 15, 15, 0, 15, 0, 60, 0, 0, 120, 0, 135 ], [ 0, 0, 15, 0, 0, 15, 0, 15, 0, 60, 120, 0, 135, 0 ], [ 0, 0, 0, 8, 8, 0, 8, 0, 72, 0, 0, 104, 0, 160 ], [ 0, 0, 8, 0, 0, 8, 0, 8, 0, 72, 104, 0, 160, 0 ], [ 0, 0, 6, 0, 0, 6, 0, 12, 0, 78, 102, 0, 156, 0 ], [ 0, 0, 0, 6, 6, 0, 12, 0, 78, 0, 0, 102, 0, 156 ], [ 0, 1, 6, 0, 0, 11, 0, 9, 0, 80, 104, 0, 149, 0 ], [ 1, 0, 0, 6, 11, 0, 9, 0, 80, 0, 0, 104, 0, 149 ] ] ] ), rec( name := "J2.2", sbgname := "5^2:(4xS3)", filename := "5^2:4xS3", degree := 2016, rank := 12, permchar := "1a^+ + 63a^- + 90a^{+-} + 126a^{+-} + 160a^+ + 175a^+ + 225a^- + 288a^- + 336a^{+-}", charnmbs := [ 1, 8, 10, 11, 12, 13, 14, 16, 21, 23, 26, 27 ], ctbl := [ [ 1, 15, 25, 75, 100, 150, 150, 150, 150, 300, 300, 600 ], [ 1, -3, -13, 27, -12, -30, 6, -6, 6, 36, 12, -24 ], [ 1, 1, 11, 19, 16, 10, -18, -18, -18, 20, -8, -16 ], [ 1, 9, -5, -5, 0, 10, 30, -10, -10, 20, -40, 0 ], [ 1, 7, 5, 7, -20, -2, 6, -6, -6, -28, 28, 8 ], [ 1, -3, 7, 7, -12, 10, 6, 14, 26, -4, -28, -24 ], [ 1, 6, 1, -6, 16, -15, -3, 12, 12, 0, 12, -36 ], [ 1, -3, -5, 3, 4, 18, 6, 18, -18, -12, 12, -24 ], [ 1, -1, 1, -13, -12, 6, -10, -2, -2, 28, 12, -8 ], [ 1, 2, -5, 2, 0, 3, -19, 4, 4, -8, -12, 28 ], [ 1, -3, E(24)-E(24)^8-E(24)^11-E(24)^16-E(24)^17+E(24)^19, -3, -E(24)-4*E(24)^8+E(24)^11-4*E(24)^16+E(24)^17-E(24)^19, -4*E(24)+6*E(24)^8+4*E(24)^11+6*E(24)^16+4*E(24)^17-4*E(24)^19, 6, 5*E(24)+6*E(24)^8-5*E(24)^11+6*E(24)^16-5*E(24)^17+5*E(24)^19, -4*E(24)+4*E(24)^11+4*E(24)^17-4*E(24)^19, 2*E(24)+6*E(24)^8-2*E(24)^11+6*E(24)^16-2*E(24)^17+2*E(24)^19, -3*E(24)+3*E(24)^11+3*E(24)^17-3*E(24)^19, 4*E(24)-12*E(24)^8-4*E(24)^11-12*E(24)^16-4*E(24)^17+4*E(24)^19 ], [ 1, -3, -E(24)-E(24)^8+E(24)^11-E(24)^16+E(24)^17-E(24)^19, -3, E(24)-4*E(24)^8-E(24)^11-4*E(24)^16-E(24)^17+E(24)^19, 4*E(24)+6*E(24)^8-4*E(24)^11+6*E(24)^16-4*E(24)^17+4*E(24)^19, 6, -5*E(24)+6*E(24)^8+5*E(24)^11+6*E(24)^16+5*E(24)^17-5*E(24)^19, 4*E(24)-4*E(24)^11-4*E(24)^17+4*E(24)^19, -2*E(24)+6*E(24)^8+2*E(24)^11+6*E(24)^16+2*E(24)^17-2*E(24)^19, 3*E(24)-3*E(24)^11-3*E(24)^17+3*E(24)^19, -4*E(24)-12*E(24)^8+4*E(24)^11-12*E(24)^16+4*E(24)^17-4*E(24)^19 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 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10, 16, 24, 24, 24, 22, 42, 44, 88 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 300, 0 ], [ 0, 0, 20, 20, 0, 0, 0, 40, 40, 0, 100, 80 ], [ 0, 12, 0, 0, 12, 24, 24, 12, 12, 36, 48, 120 ], [ 0, 4, 0, 16, 12, 16, 32, 20, 16, 40, 48, 96 ], [ 0, 0, 3, 9, 24, 24, 24, 30, 33, 45, 30, 78 ], [ 0, 0, 4, 8, 16, 24, 20, 24, 16, 40, 52, 96 ], [ 0, 0, 4, 16, 16, 20, 8, 24, 24, 32, 60, 96 ], [ 0, 4, 2, 10, 20, 24, 24, 24, 14, 50, 44, 84 ], [ 0, 4, 2, 8, 22, 16, 24, 14, 16, 52, 46, 96 ], [ 0, 0, 3, 10, 15, 20, 16, 25, 26, 52, 45, 88 ] , [ 1, 5, 4, 12, 10, 26, 30, 22, 23, 45, 36, 86 ], [ 0, 2, 5, 12, 13, 24, 24, 21, 24, 44, 43, 88 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600 ], [ 0, 0, 0, 40, 0, 80, 40, 40, 40, 80, 80, 200 ], [ 0, 0, 0, 24, 24, 24, 72, 48, 24, 96, 120, 168 ], [ 0, 8, 8, 8, 32, 48, 40, 48, 48, 80, 96, 184 ], [ 0, 0, 6, 24, 18, 48, 48, 42, 48, 96, 78, 192 ], [ 0, 8, 4, 24, 32, 36, 40, 40, 56, 96, 96, 168 ], [ 0, 4, 12, 20, 32, 40, 52, 40, 40, 96, 96, 168 ], [ 0, 4, 8, 24, 28, 40, 40, 36, 40, 96, 84, 200 ], [ 0, 4, 4, 24, 32, 56, 40, 40, 32, 88, 96, 184 ], [ 0, 4, 8, 20, 32, 48, 48, 48, 44, 84, 88, 176 ], [ 0, 4, 10, 24, 26, 48, 48, 42, 48, 88, 86, 176 ], [ 1, 5, 7, 23, 32, 42, 42, 50, 46, 88, 88, 176 ] ] ] ), rec( name := "M23", sbgname := "M22", degree := 23, rank := 2, permchar := "1a + 22a", charnmbs := [ 1, 2 ], ctbl := [ [ 1, 22 ], [ 1, -1 ] ], mats := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 22 ], [ 1, 21 ] ] ] ), rec( name := "M23", sbgname := "2^4:A7", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 253, rank := 3, permchar := "1a + 22a + 230a", charnmbs := [ 1, 2, 5 ], ctbl := [ [ 1, 112, 140 ], [ 1, -26, 25 ], [ 1, 2, -3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 112, 0 ], [ 1, 36, 75 ], [ 0, 60, 52 ] ], [ [ 0, 0, 140 ], [ 0, 75, 65 ], [ 1, 52, 87 ] ] ] ), rec( name := "M23", sbgname := "A8", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 506, rank := 4, permchar := "1a + 22a + 230a + 253a", charnmbs := [ 1, 2, 5, 9 ], ctbl := [ [ 1, 15, 210, 280 ], [ 1, -8, 49, -42 ], [ 1, 4, 1, -6 ], [ 1, -3, -6, 8 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 15, 0, 0 ], [ 1, 0, 14, 0 ], [ 0, 1, 2, 12 ], [ 0, 0, 9, 6 ] ], [ [ 0, 0, 210, 0 ], [ 0, 14, 28, 168 ], [ 1, 2, 111, 96 ], [ 0, 9, 72, 129 ] ], [ [ 0, 0, 0, 280 ], [ 0, 0, 168, 112 ], [ 0, 12, 96, 172 ], [ 1, 6, 129, 144 ] ] ] ), rec( name := "M23", sbgname := "L3(4).2_2", filename := "L34.2_2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 253, rank := 3, permchar := "1a + 22a + 230a", charnmbs := [ 1, 2, 5 ], ctbl := [ [ 1, 42, 210 ], [ 1, 19, -20 ], [ 1, -2, 1 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 42, 0 ], [ 1, 21, 20 ], [ 0, 4, 38 ] ], [ [ 0, 0, 210 ], [ 0, 20, 190 ], [ 1, 38, 171 ] ] ] ), rec( name := "M23", sbgname := "M11", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 1288, rank := 4, permchar := "1a + 22a + 230a + 1035a", charnmbs := [ 1, 2, 5, 16 ], ctbl := [ [ 1, 165, 330, 792 ], [ 1, -65, 100, -36 ], [ 1, 19, 16, -36 ], [ 1, -3, -6, 8 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 165, 0, 0 ], [ 1, 0, 92, 72 ], [ 0, 46, 11, 108 ], [ 0, 15, 45, 105 ] ], [ [ 0, 0, 330, 0 ], [ 0, 92, 22, 216 ], [ 1, 11, 138, 180 ], [ 0, 45, 75, 210 ] ], [ [ 0, 0, 0, 792 ], [ 0, 72, 216, 504 ], [ 0, 108, 180, 504 ], [ 1, 105, 210, 476 ] ] ] ), rec( name := "HS", sbgname := "U3(5).2", filename := "U35.2", degree := 176, rank := 2, permchar := "1a + 175a", permchar2 := "1a + 175a", charnmbs := [ 1, 7 ], charnmbs2 := [ 1, 7 ], ctbl := [ [ 1, 175 ], [ 1, -1 ] ], mats := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 175 ], [ 1, 174 ] ] ] ), rec( name := "HS", sbgname := "4.2^4:S5", degree := 5775, rank := 9, permchar := "1a + 77a + 154a + 175a + 693a + 825a + 1056a + 1386a + 1408a", charnmbs := [ 1, 3, 4, 7, 9, 13, 16, 17, 18 ], ctbl := [ [ 1, 30, 80, 128, 480, 640, 960, 1536, 1920 ], [ 1, 15, 20, -32, 60, 80, 0, 96, -240 ], [ 1, 15, 20, 8, 60, -20, 0, -144, 60 ], [ 1, -3, 14, 40, -48, 68, 36, -48, -60 ], [ 1, 5, -10, 8, 0, 20, -60, 16, 20 ], [ 1, 7, 4, 0, -28, -32, 16, 32, 0 ], [ 1, -5, 10, -12, -10, 10, -20, -4, 30 ], [ 1, -5, 0, 8, 20, -20, 0, 16, -20 ], [ 1, 0, -10, -7, 0, 10, 30, -24, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 30, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 5, 8, 0, 16, 0, 0, 0, 0 ], [ 0, 3, 3, 0, 12, 0, 12, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 30 ], [ 0, 1, 2, 0, 7, 8, 4, 0, 8 ], [ 0, 0, 0, 0, 6, 6, 3, 12, 3 ], [ 0, 0, 1, 0, 2, 2, 7, 8, 10 ], [ 0, 0, 0, 0, 0, 5, 5, 15, 5 ], [ 0, 0, 0, 2, 2, 1, 5, 4, 16 ] ], [ [ 0, 0, 80, 0, 0, 0, 0, 0, 0 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128, 64, 256, 64 ], [ 0, 0, 24, 16, 48, 120, 120, 192, 120 ], [ 0, 0, 10, 50, 0, 100, 120, 120, 240 ], [ 0, 8, 8, 0, 56, 64, 104, 208, 192 ], [ 1, 6, 15, 20, 48, 88, 114, 180, 168 ], [ 0, 2, 10, 16, 52, 76, 120, 160, 204 ], [ 0, 5, 10, 10, 65, 75, 100, 170, 205 ], [ 0, 1, 5, 16, 48, 56, 102, 164, 248 ] ], [ [ 0, 0, 0, 0, 0, 0, 960, 0, 0 ], [ 0, 0, 32, 0, 64, 64, 224, 256, 320 ], [ 0, 12, 12, 48, 72, 120, 96, 288, 312 ], [ 0, 0, 30, 30, 60, 120, 180, 240, 300 ], [ 0, 4, 12, 16, 88, 104, 152, 256, 328 ], [ 0, 3, 15, 24, 78, 114, 180, 240, 306 ], [ 1, 7, 8, 24, 76, 120, 140, 256, 328 ], [ 0, 5, 15, 20, 80, 100, 160, 260, 320 ], [ 0, 5, 13, 20, 82, 102, 164, 256, 318 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 1536, 0 ], [ 0, 0, 0, 0, 0, 256, 256, 768, 256 ], [ 0, 0, 0, 0, 96, 192, 288, 576, 384 ], [ 0, 0, 0, 24, 120, 120, 240, 432, 600 ], [ 0, 0, 16, 32, 112, 208, 256, 480, 432 ], [ 0, 12, 24, 24, 156, 180, 240, 408, 492 ], [ 0, 8, 24, 32, 128, 160, 256, 416, 512 ], [ 1, 15, 30, 36, 150, 170, 260, 364, 510 ], [ 0, 4, 16, 40, 108, 164, 256, 408, 540 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1920 ], [ 0, 0, 0, 128, 128, 64, 320, 256, 1024 ], [ 0, 0, 24, 48, 144, 120, 312, 384, 888 ], [ 0, 30, 30, 0, 240, 240, 300, 600, 480 ], [ 0, 8, 24, 64, 136, 192, 328, 432, 736 ], [ 0, 3, 15, 48, 144, 168, 306, 492, 744 ], [ 0, 10, 26, 40, 164, 204, 328, 512, 636 ], [ 0, 5, 20, 50, 135, 205, 320, 510, 675 ], [ 1, 16, 37, 32, 184, 248, 318, 540, 544 ] ] ] ), rec( name := "HS", sbgname := "A8 leq A8.2", filename := "A8", degree := 2200, rank := 9, permchar := "1a + 22a + 77a + 154abc + 175a + 693a + 770a", charnmbs := [ 1, 2, 3, 4, 5, 6, 7, 9, 10 ], ctbl := [ [ 1, 1, 28, 28, 105, 105, 336, 336, 1260 ], [ 1, -1, 0, 0, -35, 35, -112, 112, 0 ], [ 1, 1, -12, -12, 25, 25, 16, 16, -60 ], [ 1, 1, 8, 8, 15, 15, -24, -24, 0 ], [ 1, -1, -10, 10, 15, -15, -12, 12, 0 ], [ 1, -1, 10, -10, 15, -15, -12, 12, 0 ], [ 1, 1, 6, 6, -5, -5, 28, 28, -60 ], [ 1, 1, -2, -2, -5, -5, -4, -4, 20 ], [ 1, -1, 0, 0, -5, 5, 8, -8, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 28, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 28, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 15, 0, 0, 12, 0 ], [ 0, 1, 0, 0, 0, 15, 12, 0, 0 ], [ 0, 0, 4, 0, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 4, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 1, 0, 0, 6, 6, 15 ], [ 0, 0, 1, 0, 0, 0, 6, 6, 15 ], [ 0, 0, 0, 0, 2, 2, 4, 4, 16 ] ], [ [ 0, 0, 0, 28, 0, 0, 0, 0, 0 ], [ 0, 0, 28, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 15, 12, 0, 0 ], [ 1, 0, 0, 0, 15, 0, 0, 12, 0 ], [ 0, 0, 0, 4, 0, 0, 0, 0, 24 ], [ 0, 0, 4, 0, 0, 0, 0, 0, 24 ], [ 0, 0, 1, 0, 0, 0, 6, 6, 15 ], [ 0, 0, 0, 1, 0, 0, 6, 6, 15 ], [ 0, 0, 0, 0, 2, 2, 4, 4, 16 ] ], [ [ 0, 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 0, 90 ], [ 0, 0, 0, 15, 0, 0, 0, 0, 90 ], [ 1, 0, 0, 0, 12, 12, 0, 32, 48 ], [ 0, 1, 0, 0, 12, 12, 32, 0, 48 ], [ 0, 0, 0, 0, 0, 10, 5, 30, 60 ], [ 0, 0, 0, 0, 10, 0, 30, 5, 60 ], [ 0, 0, 2, 2, 4, 4, 16, 16, 61 ] ], [ [ 0, 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 0, 15, 0, 0, 0, 0, 90 ], [ 0, 0, 15, 0, 0, 0, 0, 0, 90 ], [ 0, 1, 0, 0, 12, 12, 32, 0, 48 ], [ 1, 0, 0, 0, 12, 12, 0, 32, 48 ], [ 0, 0, 0, 0, 10, 0, 30, 5, 60 ], [ 0, 0, 0, 0, 0, 10, 5, 30, 60 ], [ 0, 0, 2, 2, 4, 4, 16, 16, 61 ] ], [ [ 0, 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 336, 0 ], [ 0, 0, 0, 12, 0, 0, 72, 72, 180 ], [ 0, 0, 12, 0, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 0, 0, 32, 16, 96, 192 ], [ 0, 0, 0, 0, 32, 0, 96, 16, 192 ], [ 1, 0, 6, 6, 5, 30, 12, 96, 180 ], [ 0, 1, 6, 6, 30, 5, 96, 12, 180 ], [ 0, 0, 4, 4, 16, 16, 48, 48, 200 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 336, 0 ], [ 0, 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 12, 0, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 12, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 0, 32, 0, 96, 16, 192 ], [ 0, 0, 0, 0, 0, 32, 16, 96, 192 ], [ 0, 1, 6, 6, 30, 5, 96, 12, 180 ], [ 1, 0, 6, 6, 5, 30, 12, 96, 180 ], [ 0, 0, 4, 4, 16, 16, 48, 48, 200 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1260 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1260 ], [ 0, 0, 0, 0, 90, 90, 180, 180, 720 ], [ 0, 0, 0, 0, 90, 90, 180, 180, 720 ], [ 0, 0, 24, 24, 48, 48, 192, 192, 732 ], [ 0, 0, 24, 24, 48, 48, 192, 192, 732 ], [ 0, 0, 15, 15, 60, 60, 180, 180, 750 ], [ 0, 0, 15, 15, 60, 60, 180, 180, 750 ], [ 1, 1, 16, 16, 61, 61, 200, 200, 704 ] ] ] ), rec( name := "HS", sbgname := "4^3:L3(2)", filename := "4^3:L32", degree := 4125, rank := 9, permchar := "1a + 22a + 77a + 154a + 175a + 693a + 770a + 825a + 1408a", charnmbs := [ 1, 2, 3, 4, 7, 9, 10, 13, 18 ], ctbl := [ [ 1, 28, 64, 112, 336, 448, 896, 896, 1344 ], [ 1, -7, -36, 42, -84, 168, -224, 56, 84 ], [ 1, 13, 14, 32, 6, 28, 16, -164, 54 ], [ 1, 13, 4, 22, 36, -32, -64, 56, -36 ], [ 1, -5, 20, 2, 6, 52, 16, 16, -108 ], [ 1, 3, 4, 2, -34, -12, 16, 16, 4 ], [ 1, -7, -6, 12, 6, -12, 16, -4, -6 ], [ 1, 5, -10, -8, 6, 12, 16, -4, -18 ], [ 1, -2, 4, -8, 6, -2, -19, -4, 24 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 28, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 3, 0, 12, 12, 0, 0, 0, 0 ], [ 0, 0, 0, 7, 0, 0, 0, 0, 21 ], [ 0, 3, 4, 3, 6, 0, 0, 0, 12 ], [ 0, 1, 0, 2, 5, 4, 0, 8, 8 ], [ 0, 0, 0, 0, 3, 1, 12, 0, 12 ], [ 0, 0, 0, 0, 0, 6, 6, 4, 12 ], [ 0, 0, 0, 0, 3, 0, 4, 15, 6 ], [ 0, 0, 1, 1, 2, 4, 8, 4, 8 ] ], [ [ 0, 0, 64, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 16, 0, 0, 0, 0, 48 ], [ 1, 0, 0, 7, 0, 42, 0, 14, 0 ], [ 0, 4, 4, 0, 12, 0, 32, 0, 12 ], [ 0, 0, 0, 4, 4, 16, 0, 16, 24 ], [ 0, 0, 6, 0, 12, 0, 32, 8, 6 ], [ 0, 0, 0, 4, 0, 16, 4, 16, 24 ], [ 0, 0, 1, 0, 6, 4, 16, 22, 15 ], [ 0, 1, 0, 1, 6, 2, 16, 10, 28 ] ], [ [ 0, 0, 0, 112, 0, 0, 0, 0, 0 ], [ 0, 12, 16, 12, 24, 0, 0, 0, 48 ], [ 0, 7, 7, 0, 21, 0, 56, 0, 21 ], [ 1, 3, 0, 16, 12, 24, 0, 8, 48 ], [ 0, 2, 4, 4, 18, 0, 32, 24, 28 ], [ 0, 0, 0, 6, 0, 30, 8, 20, 48 ], [ 0, 0, 4, 0, 12, 4, 40, 16, 36 ], [ 0, 0, 0, 1, 9, 10, 16, 46, 30 ], [ 0, 1, 1, 4, 7, 16, 24, 20, 39 ] ], [ [ 0, 0, 0, 0, 336, 0, 0, 0, 0 ], [ 0, 12, 0, 24, 60, 48, 0, 96, 96 ], [ 0, 0, 0, 21, 21, 84, 0, 84, 126 ], [ 0, 6, 12, 12, 54, 0, 96, 72, 84 ], [ 1, 5, 4, 18, 4, 44, 48, 96, 116 ], [ 0, 3, 12, 0, 33, 12, 120, 60, 96 ], [ 0, 0, 0, 12, 18, 60, 54, 72, 120 ], [ 0, 3, 6, 9, 36, 30, 72, 78, 102 ], [ 0, 2, 6, 7, 29, 32, 80, 68, 112 ] ], [ [ 0, 0, 0, 0, 0, 448, 0, 0, 0 ], [ 0, 0, 0, 0, 48, 16, 192, 0, 192 ], [ 0, 0, 42, 0, 84, 0, 224, 56, 42 ], [ 0, 0, 0, 24, 0, 120, 32, 80, 192 ], [ 0, 4, 16, 0, 44, 16, 160, 80, 128 ], [ 1, 1, 0, 30, 12, 116, 24, 120, 144 ], [ 0, 6, 16, 4, 60, 12, 142, 88, 120 ], [ 0, 0, 4, 10, 30, 60, 88, 112, 144 ], [ 0, 4, 2, 16, 32, 48, 80, 96, 170 ] ], [ [ 0, 0, 0, 0, 0, 0, 896, 0, 0 ], [ 0, 0, 0, 0, 0, 192, 192, 128, 384 ], [ 0, 0, 0, 56, 0, 224, 56, 224, 336 ], [ 0, 0, 32, 0, 96, 32, 320, 128, 288 ], [ 0, 0, 0, 32, 48, 160, 144, 192, 320 ], [ 0, 12, 32, 8, 120, 24, 284, 176, 240 ], [ 1, 6, 4, 40, 54, 142, 117, 220, 312 ], [ 0, 4, 16, 16, 72, 88, 220, 192, 288 ], [ 0, 8, 16, 24, 80, 80, 208, 192, 288 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 896, 0 ], [ 0, 0, 0, 0, 96, 0, 128, 480, 192 ], [ 0, 0, 14, 0, 84, 56, 224, 308, 210 ], [ 0, 0, 0, 8, 72, 80, 128, 368, 240 ], [ 0, 8, 16, 24, 96, 80, 192, 208, 272 ], [ 0, 0, 8, 20, 60, 120, 176, 224, 288 ], [ 0, 4, 16, 16, 72, 88, 220, 192, 288 ], [ 1, 15, 22, 46, 78, 112, 192, 112, 318 ], [ 0, 4, 10, 20, 68, 96, 192, 212, 294 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1344 ], [ 0, 0, 48, 48, 96, 192, 384, 192, 384 ], [ 0, 21, 0, 21, 126, 42, 336, 210, 588 ], [ 0, 12, 12, 48, 84, 192, 288, 240, 468 ], [ 0, 8, 24, 28, 116, 128, 320, 272, 448 ], [ 0, 12, 6, 48, 96, 144, 240, 288, 510 ], [ 0, 12, 24, 36, 120, 120, 312, 288, 432 ], [ 0, 6, 15, 30, 102, 144, 288, 318, 441 ], [ 1, 8, 28, 39, 112, 170, 288, 294, 404 ] ] ] ), rec( name := "HS", sbgname := "A8.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 1100, rank := 5, permchar := "1a + 77a + 154a + 175a + 693a", charnmbs := [ 1, 3, 4, 7, 9 ], ctbl := [ [ 1, 28, 105, 336, 630 ], [ 1, -12, 25, 16, -30 ], [ 1, 8, 15, -24, 0 ], [ 1, 6, -5, 28, -30 ], [ 1, -2, -5, -4, 10 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 28, 0, 0, 0 ], [ 1, 0, 15, 12, 0 ], [ 0, 4, 0, 0, 24 ], [ 0, 1, 0, 12, 15 ], [ 0, 0, 4, 8, 16 ] ], [ [ 0, 0, 105, 0, 0 ], [ 0, 15, 0, 0, 90 ], [ 1, 0, 24, 32, 48 ], [ 0, 0, 10, 35, 60 ], [ 0, 4, 8, 32, 61 ] ], [ [ 0, 0, 0, 336, 0 ], [ 0, 12, 0, 144, 180 ], [ 0, 0, 32, 112, 192 ], [ 1, 12, 35, 108, 180 ], [ 0, 8, 32, 96, 200 ] ], [ [ 0, 0, 0, 0, 630 ], [ 0, 0, 90, 180, 360 ], [ 0, 24, 48, 192, 366 ], [ 0, 15, 60, 180, 375 ], [ 1, 16, 61, 200, 352 ] ] ] ), rec( name := "HS", sbgname := "L3(4).2_1", filename := "L34.2_1", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 1100, rank := 5, permchar := "1a + 22a + 77a + 175a + 825a", charnmbs := [ 1, 2, 3, 7, 13 ], ctbl := [ [ 1, 42, 105, 280, 672 ], [ 1, 12, -45, 80, -48 ], [ 1, 22, 5, -20, -8 ], [ 1, -2, 17, 16, -32 ], [ 1, -2, -3, -4, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 42, 0, 0, 0 ], [ 1, 20, 5, 0, 16 ], [ 0, 2, 8, 0, 32 ], [ 0, 0, 0, 18, 24 ], [ 0, 1, 5, 10, 26 ] ], [ [ 0, 0, 105, 0, 0 ], [ 0, 5, 20, 0, 80 ], [ 1, 8, 0, 64, 32 ], [ 0, 0, 24, 9, 72 ], [ 0, 5, 5, 30, 65 ] ], [ [ 0, 0, 0, 280, 0 ], [ 0, 0, 0, 120, 160 ], [ 0, 0, 64, 24, 192 ], [ 1, 18, 9, 108, 144 ], [ 0, 10, 30, 60, 180 ] ], [ [ 0, 0, 0, 0, 672 ], [ 0, 16, 80, 160, 416 ], [ 0, 32, 32, 192, 416 ], [ 0, 24, 72, 144, 432 ], [ 1, 26, 65, 180, 400 ] ] ] ), rec( name := "HS", sbgname := "M11", degree := 5600, rank := 9, permchar := "1a + 22a + 77a + 154b + 175a + 770a + 825a + 1056a + 2520a", permchar2 := "1a + 22a + 77a + 154c + 175a + 770a + 825a + 1056a + 2520a", charnmbs := [ 1, 2, 3, 5, 7, 10, 13, 16, 22 ], charnmbs2 := [ 1, 2, 3, 6, 7, 10, 13, 16, 22 ], ctbl := [ [ 1, 55, 132, 165, 495, 660, 792, 1320, 1980 ], [ 1, 5, 52, -85, 195, -140, 72, -280, 180 ], [ 1, -20, 37, 40, 45, 85, -138, -80, 30 ], [ 1, -19, -12, -21, 27, 84, 72, -24, -108 ], [ 1, 7, 4, 37, 63, -44, 24, 40, -132 ], [ 1, -4, 13, -16, -3, -11, -18, 56, -18 ], [ 1, 12, -11, -8, 13, 21, -26, 0, -2 ], [ 1, 6, 13, 4, -23, 9, 22, -24, -8 ], [ 1, -4, -7, 4, -3, -11, 2, -4, 22 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 55, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 18, 36, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 30, 10, 15 ], [ 0, 0, 0, 0, 3, 4, 24, 24, 0 ], [ 0, 2, 0, 1, 8, 0, 8, 16, 20 ], [ 0, 3, 0, 1, 0, 0, 6, 18, 27 ], [ 0, 0, 5, 5, 5, 5, 0, 10, 25 ], [ 0, 0, 1, 3, 6, 9, 6, 12, 18 ], [ 0, 0, 1, 0, 5, 9, 10, 12, 18 ] ], [ [ 0, 0, 132, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 72, 24, 36 ], [ 1, 0, 15, 0, 30, 20, 6, 0, 60 ], [ 0, 0, 0, 20, 0, 48, 0, 40, 24 ], [ 0, 0, 8, 0, 32, 4, 16, 8, 64 ], [ 0, 0, 4, 12, 3, 23, 6, 36, 48 ], [ 0, 5, 1, 0, 10, 5, 31, 30, 50 ], [ 0, 1, 0, 5, 3, 18, 18, 51, 36 ], [ 0, 1, 4, 2, 16, 16, 20, 24, 49 ] ], [ [ 0, 0, 0, 165, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 9, 12, 72, 72, 0 ], [ 0, 0, 0, 25, 0, 60, 0, 50, 30 ], [ 1, 0, 20, 0, 72, 0, 24, 0, 48 ], [ 0, 1, 0, 24, 0, 32, 8, 80, 20 ], [ 0, 1, 12, 0, 24, 12, 12, 14, 90 ], [ 0, 5, 0, 5, 5, 10, 30, 60, 50 ] , [ 0, 3, 5, 0, 30, 7, 36, 18, 66 ], [ 0, 0, 2, 4, 5, 30, 20, 44, 60 ] ], [ [ 0, 0, 0, 0, 495, 0, 0, 0, 0 ], [ 0, 18, 0, 9, 72, 0, 72, 144, 180 ], [ 0, 0, 30, 0, 120, 15, 60, 30, 240 ], [ 0, 3, 0, 72, 0, 96, 24, 240, 60 ], [ 1, 8, 32, 0, 118, 16, 96, 32, 192 ], [ 0, 0, 3, 24, 12, 102, 48, 150, 156 ], [ 0, 5, 10, 5, 60, 40, 95, 110, 170 ], [ 0, 6, 3, 30, 12, 75, 66, 165, 138 ], [ 0, 5, 16, 5, 48, 52, 68, 92, 209 ] ], [ [ 0, 0, 0, 0, 0, 660, 0, 0, 0 ], [ 0, 36, 0, 12, 0, 0, 72, 216, 324 ], [ 0, 0, 20, 60, 15, 115, 30, 180, 240 ], [ 0, 4, 48, 0, 96, 48, 48, 56, 360 ], [ 0, 0, 4, 32, 16, 136, 64, 200, 208 ], [ 1, 0, 23, 12, 102, 96, 102, 108, 216 ], [ 0, 5, 5, 10, 40, 85, 135, 180, 200 ], [ 0, 9, 18, 7, 75, 54, 108, 125, 264 ], [ 0, 9, 16, 30, 52, 72, 80, 176, 225 ] ], [ [ 0, 0, 0, 0, 0, 0, 792, 0, 0 ], [ 0, 0, 72, 72, 72, 72, 0, 144, 360 ], [ 0, 30, 6, 0, 60, 30, 186, 180, 300 ], [ 0, 24, 0, 24, 24, 48, 144, 288, 240 ], [ 0, 8, 16, 8, 96, 64, 152, 176, 272 ], [ 0, 6, 6, 12, 48, 102, 162, 216, 240 ], [ 1, 0, 31, 30, 95, 135, 80, 150, 270 ], [ 0, 6, 18, 36, 66, 108, 90, 192, 276 ], [ 0, 10, 20, 20, 68, 80, 108, 184, 302 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 1320, 0 ], [ 0, 0, 24, 72, 144, 216, 144, 288, 432 ], [ 0, 10, 0, 50, 30, 180, 180, 510, 360 ], [ 0, 24, 40, 0, 240, 56, 288, 144, 528 ], [ 0, 16, 8, 80, 32, 200, 176, 440, 368 ], [ 0, 18, 36, 14, 150, 108, 216, 250, 528 ], [ 0, 10, 30, 60, 110, 180, 150, 320, 460 ], [ 1, 12, 51, 18, 165, 125, 192, 258, 498 ], [ 0, 12, 24, 44, 92, 176, 184, 332, 456 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1980 ], [ 0, 0, 36, 0, 180, 324, 360, 432, 648 ], [ 0, 15, 60, 30, 240, 240, 300, 360, 735 ], [ 0, 0, 24, 48, 60, 360, 240, 528, 720 ], [ 0, 20, 64, 20, 192, 208, 272, 368, 836 ], [ 0, 27, 48, 90, 156, 216, 240, 528, 675 ], [ 0, 25, 50, 50, 170, 200, 270, 460, 755 ], [ 0, 18, 36, 66, 138, 264, 276, 498, 684 ], [ 1, 18, 49, 60, 209, 225, 302, 456, 660 ] ] ] ), rec( name := "HS", sbgname := "M22", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 100, rank := 3, permchar := "1a + 22a + 77a", charnmbs := [ 1, 2, 3 ], ctbl := [ [ 1, 22, 77 ], [ 1, -8, 7 ], [ 1, 2, -3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 22, 0 ], [ 1, 0, 21 ], [ 0, 6, 16 ] ], [ [ 0, 0, 77 ], [ 0, 21, 56 ], [ 1, 16, 60 ] ] ] ), rec( name := "HS", sbgname := "U3(5) leq U3(5).2", filename := "U35", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 352, rank := 4, permchar := "1a + 22a + 154b + 175a", permchar2 := "1a + 22a + 154b + 175a", charnmbs := [ 1, 2, 5, 7 ], charnmbs2 := [ 1, 2, 5, 7 ], ctbl := [ [ 1, 1, 175, 175 ], [ 1, -1, 35, -35 ], [ 1, -1, -5, 5 ], [ 1, 1, -1, -1 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 0, 0, 175, 0 ], [ 0, 0, 0, 175 ], [ 1, 0, 102, 72 ], [ 0, 1, 72, 102 ] ], [ [ 0, 0, 0, 175 ], [ 0, 0, 175, 0 ], [ 0, 1, 72, 102 ], [ 1, 0, 102, 72 ] ] ] ), rec( name := "HS.2", sbgname := "A8.2x2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 1100, rank := 5, permchar := "1a^+ + 77a^+ + 154a^+ + 175a^+ + 693a^+", charnmbs := [ 1, 5, 7, 10, 14 ], ctbl := [ [ 1, 28, 105, 336, 630 ], [ 1, -12, 25, 16, -30 ], [ 1, 8, 15, -24, 0 ], [ 1, 6, -5, 28, -30 ], [ 1, -2, -5, -4, 10 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 28, 0, 0, 0 ], [ 1, 0, 15, 12, 0 ], [ 0, 4, 0, 0, 24 ], [ 0, 1, 0, 12, 15 ], [ 0, 0, 4, 8, 16 ] ], [ [ 0, 0, 105, 0, 0 ], [ 0, 15, 0, 0, 90 ], [ 1, 0, 24, 32, 48 ], [ 0, 0, 10, 35, 60 ], [ 0, 4, 8, 32, 61 ] ], [ [ 0, 0, 0, 336, 0 ], [ 0, 12, 0, 144, 180 ], [ 0, 0, 32, 112, 192 ], [ 1, 12, 35, 108, 180 ], [ 0, 8, 32, 96, 200 ] ], [ [ 0, 0, 0, 0, 630 ], [ 0, 0, 90, 180, 360 ], [ 0, 24, 48, 192, 366 ], [ 0, 15, 60, 180, 375 ], [ 1, 16, 61, 200, 352 ] ] ] ), rec( name := "HS.2", sbgname := "L3(4).2^2", filename := "L34.2^2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 1100, rank := 5, permchar := "1a^+ + 22a^+ + 77a^+ + 175a^+ + 825a^+", charnmbs := [ 1, 3, 5, 10, 19 ], ctbl := [ [ 1, 42, 105, 280, 672 ], [ 1, 12, -45, 80, -48 ], [ 1, 22, 5, -20, -8 ], [ 1, -2, 17, 16, -32 ], [ 1, -2, -3, -4, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 42, 0, 0, 0 ], [ 1, 20, 5, 0, 16 ], [ 0, 2, 8, 0, 32 ], [ 0, 0, 0, 18, 24 ], [ 0, 1, 5, 10, 26 ] ], [ [ 0, 0, 105, 0, 0 ], [ 0, 5, 20, 0, 80 ], [ 1, 8, 0, 64, 32 ], [ 0, 0, 24, 9, 72 ], [ 0, 5, 5, 30, 65 ] ], [ [ 0, 0, 0, 280, 0 ], [ 0, 0, 0, 120, 160 ], [ 0, 0, 64, 24, 192 ], [ 1, 18, 9, 108, 144 ], [ 0, 10, 30, 60, 180 ] ], [ [ 0, 0, 0, 0, 672 ], [ 0, 16, 80, 160, 416 ], [ 0, 32, 32, 192, 416 ], [ 0, 24, 72, 144, 432 ], [ 1, 26, 65, 180, 400 ] ] ] ), rec( name := "HS.2", sbgname := "M22.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 100, rank := 3, permchar := "1a^+ + 22a^+ + 77a^+", charnmbs := [ 1, 3, 5 ], ctbl := [ [ 1, 22, 77 ], [ 1, -8, 7 ], [ 1, 2, -3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 22, 0 ], [ 1, 0, 21 ], [ 0, 6, 16 ] ], [ [ 0, 0, 77 ], [ 0, 21, 56 ], [ 1, 16, 60 ] ] ] ), rec( name := "HS.2", sbgname := "U3(5).2", filename := "U35.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 352, rank := 4, permchar := "1a^{+-} + 175a^{+-}", charnmbs := [ 1, 2, 10, 11 ], ctbl := [ [ 1, 50, 126, 175 ], [ 1, -50, -126, 175 ], [ 1, 6, -6, -1 ], [ 1, -6, 6, -1 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 50, 0, 0 ], [ 1, 0, 0, 49 ], [ 0, 0, 0, 50 ], [ 0, 14, 36, 0 ] ], [ [ 0, 0, 126, 0 ], [ 0, 0, 0, 126 ], [ 1, 0, 0, 125 ], [ 0, 36, 90, 0 ] ], [ [ 0, 0, 0, 175 ], [ 0, 49, 126, 0 ], [ 0, 50, 125, 0 ], [ 1, 0, 0, 174 ] ] ] ), rec( name := "HS.2", sbgname := "M22 leq M22.2", filename := "M22", degree := 200, rank := 6, permchar := "1a^{+-} + 22a^{+-} + 77a^{+-}", charnmbs := [ 1, 2, 3, 4, 5, 6 ], ctbl := [ [ 1, 1, 22, 22, 77, 77 ], [ 1, -1, -22, 22, -77, 77 ], [ 1, 1, -8, -8, 7, 7 ], [ 1, -1, 8, -8, -7, 7 ], [ 1, 1, 2, 2, -3, -3 ], [ 1, -1, -2, 2, 3, -3 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 22, 0, 0, 0 ], [ 0, 0, 0, 22, 0, 0 ], [ 1, 0, 0, 0, 0, 21 ], [ 0, 1, 0, 0, 21, 0 ], [ 0, 0, 0, 6, 0, 16 ], [ 0, 0, 6, 0, 16, 0 ] ], [ [ 0, 0, 0, 22, 0, 0 ], [ 0, 0, 22, 0, 0, 0 ], [ 0, 1, 0, 0, 21, 0 ], [ 1, 0, 0, 0, 0, 21 ], [ 0, 0, 6, 0, 16, 0 ], [ 0, 0, 0, 6, 0, 16 ] ], [ [ 0, 0, 0, 0, 77, 0 ], [ 0, 0, 0, 0, 0, 77 ], [ 0, 0, 0, 21, 0, 56 ], [ 0, 0, 21, 0, 56, 0 ], [ 1, 0, 0, 16, 0, 60 ], [ 0, 1, 16, 0, 60, 0 ] ], [ [ 0, 0, 0, 0, 0, 77 ], [ 0, 0, 0, 0, 77, 0 ], [ 0, 0, 21, 0, 56, 0 ], [ 0, 0, 0, 21, 0, 56 ], [ 0, 1, 16, 0, 60, 0 ], [ 1, 0, 0, 16, 0, 60 ] ] ] ), rec( name := "HS.2", sbgname := "L3(4).2_1 leq L3(4).2^2", filename := "L34.2_1", degree := 2200, rank := 10, permchar := "1a^{+-} + 22a^{+-} + 77a^{+-} + 175a^{+-} + 825a^{+-}", charnmbs := [ 1, 2, 3, 4, 5, 6, 10, 11, 19, 20 ], ctbl := [ [ 1, 1, 42, 42, 105, 105, 280, 280, 672, 672 ], [ 1, -1, -42, 42, 105, -105, 280, -280, 672, -672 ], [ 1, 1, 12, 12, -45, -45, 80, 80, -48, -48 ], [ 1, -1, -12, 12, -45, 45, 80, -80, -48, 48 ], [ 1, 1, 22, 22, 5, 5, -20, -20, -8, -8 ], [ 1, -1, -22, 22, 5, -5, -20, 20, -8, 8 ], [ 1, 1, -2, -2, 17, 17, 16, 16, -32, -32 ], [ 1, -1, 2, -2, 17, -17, 16, -16, -32, 32 ], [ 1, 1, -2, -2, -3, -3, -4, -4, 8, 8 ], [ 1, -1, 2, -2, -3, 3, -4, 4, 8, -8 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 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144, 0, 432, 0 ], [ 0, 1, 26, 0, 0, 65, 0, 180, 0, 400 ], [ 1, 0, 0, 26, 65, 0, 180, 0, 400, 0 ] ] ] ), rec( name := "HS.2", sbgname := "A8.2 leq A8.2x2", filename := "A8.2", degree := 2200, rank := 10, permchar := "1a^{+-} + 77a^{+-} + 154a^{+-} + 175a^{+-} + 693a^{+-}", charnmbs := [ 1, 2, 5, 6, 7, 8, 10, 11, 14, 15 ], ctbl := [ [ 1, 1, 28, 28, 105, 105, 336, 336, 630, 630 ], [ 1, -1, -28, 28, -105, 105, -336, 336, 630, -630 ], [ 1, 1, -12, -12, 25, 25, 16, 16, -30, -30 ], [ 1, -1, 12, -12, -25, 25, -16, 16, -30, 30 ], [ 1, 1, 8, 8, 15, 15, -24, -24, 0, 0 ], [ 1, -1, -8, 8, -15, 15, 24, -24, 0, 0 ], [ 1, 1, 6, 6, -5, -5, 28, 28, -30, -30 ], [ 1, -1, -6, 6, 5, -5, -28, 28, -30, 30 ], [ 1, 1, -2, -2, -5, -5, -4, -4, 10, 10 ], [ 1, -1, 2, -2, 5, -5, 4, -4, 10, -10 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 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0, 180, 375, 0 ], [ 1, 0, 0, 16, 0, 61, 0, 200, 352, 0 ], [ 0, 1, 16, 0, 61, 0, 200, 0, 0, 352 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 630 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 630, 0 ], [ 0, 0, 0, 0, 0, 90, 0, 180, 360, 0 ], [ 0, 0, 0, 0, 90, 0, 180, 0, 0, 360 ], [ 0, 0, 0, 24, 0, 48, 0, 192, 366, 0 ], [ 0, 0, 24, 0, 48, 0, 192, 0, 0, 366 ], [ 0, 0, 0, 15, 0, 60, 0, 180, 375, 0 ], [ 0, 0, 15, 0, 60, 0, 180, 0, 0, 375 ], [ 0, 1, 16, 0, 61, 0, 200, 0, 0, 352 ], [ 1, 0, 0, 16, 0, 61, 0, 200, 352, 0 ] ] ] ), rec( name := "HS.2", sbgname := "U3(5) leq U3(5).2", filename := "U35", degree := 704, rank := 7, permchar := "1a^{+-} + 22a^{+-} + 154bc + 175a^{+-}", charnmbs := [ 1, 2, 3, 4, 9, 10, 11 ], ctbl := [ [ 1, 1, 50, 50, 175, 175, 252 ], [ 1, 1, -50, -50, 175, 175, -252 ], [ 1, -1, -20, 20, 35, -35, 0 ], [ 1, -1, 20, -20, 35, -35, 0 ], [ 1, -1, 0, 0, -5, 5, 0 ], [ 1, 1, 6, 6, -1, -1, -12 ], [ 1, 1, -6, -6, -1, -1, 12 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 50, 0, 0, 0, 0 ], [ 0, 0, 0, 50, 0, 0, 0 ], [ 1, 0, 0, 0, 42, 7, 0 ], [ 0, 1, 0, 0, 7, 42, 0 ], [ 0, 0, 12, 2, 0, 0, 36 ], [ 0, 0, 2, 12, 0, 0, 36 ], [ 0, 0, 0, 0, 25, 25, 0 ] ], [ [ 0, 0, 0, 50, 0, 0, 0 ], [ 0, 0, 50, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 7, 42, 0 ], [ 1, 0, 0, 0, 42, 7, 0 ], [ 0, 0, 2, 12, 0, 0, 36 ], [ 0, 0, 12, 2, 0, 0, 36 ], [ 0, 0, 0, 0, 25, 25, 0 ] ], [ [ 0, 0, 0, 0, 175, 0, 0 ], [ 0, 0, 0, 0, 0, 175, 0 ], [ 0, 0, 42, 7, 0, 0, 126 ], [ 0, 0, 7, 42, 0, 0, 126 ], [ 1, 0, 0, 0, 102, 72, 0 ], [ 0, 1, 0, 0, 72, 102, 0 ], [ 0, 0, 25, 25, 0, 0, 125 ] ], [ [ 0, 0, 0, 0, 0, 175, 0 ], [ 0, 0, 0, 0, 175, 0, 0 ], [ 0, 0, 7, 42, 0, 0, 126 ], [ 0, 0, 42, 7, 0, 0, 126 ], [ 0, 1, 0, 0, 72, 102, 0 ], [ 1, 0, 0, 0, 102, 72, 0 ], [ 0, 0, 25, 25, 0, 0, 125 ] ], [ [ 0, 0, 0, 0, 0, 0, 252 ], [ 0, 0, 0, 0, 0, 0, 252 ], [ 0, 0, 0, 0, 126, 126, 0 ], [ 0, 0, 0, 0, 126, 126, 0 ], [ 0, 0, 36, 36, 0, 0, 180 ], [ 0, 0, 36, 36, 0, 0, 180 ], [ 1, 1, 0, 0, 125, 125, 0 ] ] ] ), rec( name := "HS.2", sbgname := "A8.2 leq A8.2x2", filename := "A8.2", degree := 2200, rank := 8, permchar := "1a^+ + 22a^- + 77a^+ + 154a^+bc + 175a^+ + 693a^+ + 770a^-", charnmbs := [ 1, 4, 5, 7, 9, 10, 14, 17 ], ctbl := [ [ 1, 1, 56, 105, 105, 336, 336, 1260 ], [ 1, -1, 0, 35, -35, -112, 112, 0 ], [ 1, 1, -24, 25, 25, 16, 16, -60 ], [ 1, 1, 16, 15, 15, -24, -24, 0 ], [ 1, -1, 0, -15, 15, -12, 12, 0 ], [ 1, 1, 12, -5, -5, 28, 28, -60 ], [ 1, 1, -4, -5, -5, -4, -4, 20 ], [ 1, -1, 0, 5, -5, 8, -8, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 56, 0, 0, 0, 0, 0 ], [ 0, 0, 56, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 15, 15, 12, 12, 0 ], [ 0, 0, 8, 0, 0, 0, 0, 48 ], [ 0, 0, 8, 0, 0, 0, 0, 48 ], [ 0, 0, 2, 0, 0, 12, 12, 30 ], [ 0, 0, 2, 0, 0, 12, 12, 30 ], [ 0, 0, 0, 4, 4, 8, 8, 32 ] ], [ [ 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 90 ], [ 1, 0, 0, 12, 12, 0, 32, 48 ], [ 0, 1, 0, 12, 12, 32, 0, 48 ], [ 0, 0, 0, 0, 10, 30, 5, 60 ], [ 0, 0, 0, 10, 0, 5, 30, 60 ], [ 0, 0, 4, 4, 4, 16, 16, 61 ] ], [ [ 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 15, 0, 0, 0, 0, 90 ], [ 0, 1, 0, 12, 12, 32, 0, 48 ], [ 1, 0, 0, 12, 12, 0, 32, 48 ], [ 0, 0, 0, 10, 0, 5, 30, 60 ], [ 0, 0, 0, 0, 10, 30, 5, 60 ], [ 0, 0, 4, 4, 4, 16, 16, 61 ] ], [ [ 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 336, 0 ], [ 0, 0, 12, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 0, 32, 96, 16, 192 ], [ 0, 0, 0, 32, 0, 16, 96, 192 ], [ 1, 0, 12, 30, 5, 12, 96, 180 ], [ 0, 1, 12, 5, 30, 96, 12, 180 ], [ 0, 0, 8, 16, 16, 48, 48, 200 ] ], [ [ 0, 0, 0, 0, 0, 0, 336, 0 ], [ 0, 0, 0, 0, 0, 336, 0, 0 ], [ 0, 0, 12, 0, 0, 72, 72, 180 ], [ 0, 0, 0, 32, 0, 16, 96, 192 ], [ 0, 0, 0, 0, 32, 96, 16, 192 ], [ 0, 1, 12, 5, 30, 96, 12, 180 ], [ 1, 0, 12, 30, 5, 12, 96, 180 ], [ 0, 0, 8, 16, 16, 48, 48, 200 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 1260 ], [ 0, 0, 0, 0, 0, 0, 0, 1260 ], [ 0, 0, 0, 90, 90, 180, 180, 720 ], [ 0, 0, 48, 48, 48, 192, 192, 732 ], [ 0, 0, 48, 48, 48, 192, 192, 732 ], [ 0, 0, 30, 60, 60, 180, 180, 750 ], [ 0, 0, 30, 60, 60, 180, 180, 750 ], [ 1, 1, 32, 61, 61, 200, 200, 704 ] ] ] ), rec( name := "HS.2", sbgname := "A8x2 leq A8.2x2", filename := "A8x2", degree := 2200, rank := 8, permchar := "1a^+ + 22a^+ + 77a^+ + 154a^+bc + 175a^+ + 693a^+ + 770a^+", charnmbs := [ 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24, 0, 28, 0, 116, 0, 128, 0, 320, 0, 272, 448, 0 ], [ 0, 0, 0, 8, 24, 0, 28, 0, 116, 0, 128, 0, 272, 0, 320, 0, 0, 448 ], [ 0, 0, 12, 0, 0, 6, 0, 48, 0, 96, 0, 144, 0, 240, 0, 288, 510, 0 ], [ 0, 0, 0, 12, 6, 0, 48, 0, 96, 0, 144, 0, 288, 0, 240, 0, 0, 510 ], [ 0, 0, 6, 0, 0, 15, 0, 30, 0, 102, 0, 144, 0, 288, 0, 318, 441, 0 ], [ 0, 0, 0, 12, 24, 0, 36, 0, 120, 0, 120, 0, 288, 0, 312, 0, 0, 432 ], [ 0, 0, 12, 0, 0, 24, 0, 36, 0, 120, 0, 120, 0, 312, 0, 288, 432, 0 ], [ 0, 0, 0, 6, 15, 0, 30, 0, 102, 0, 144, 0, 318, 0, 288, 0, 0, 441 ], [ 0, 1, 0, 8, 28, 0, 39, 0, 112, 0, 170, 0, 294, 0, 288, 0, 0, 404 ], [ 1, 0, 8, 0, 0, 28, 0, 39, 0, 112, 0, 170, 0, 288, 0, 294, 404, 0 ] ] ] ), rec( name := "HS.2", sbgname := "M11", degree := 11200, rank := 17, permchar := "1a^{+-} + 22a^{+-} + 77a^{+-} + 154bc + 175a^{+-} + 770a^{+-} + 825a^{+-} + 1056a^{+-} + 2520a^{+-}", charnmbs := [ 1, 2, 3, 4, 5, 6, 9, 10, 11, 16, 17, 19, 20, 22, 23, 34, 35 ], ctbl := [ [ 1, 12, 55, 110, 132, 165, 330, 396, 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128, 0, 64, 0, 320, 256, 0, 0, 1024 ], [ 0, 0, 0, 0, 24, 0, 0, 48, 144, 0, 120, 0, 312, 0, 0, 384, 888, 0 ], [ 0, 0, 0, 0, 0, 24, 48, 0, 0, 144, 0, 120, 0, 312, 384, 0, 0, 888 ], [ 0, 0, 0, 30, 0, 30, 0, 0, 0, 240, 0, 240, 0, 300, 600, 0, 0, 480 ], [ 0, 0, 30, 0, 30, 0, 0, 0, 240, 0, 240, 0, 300, 0, 0, 600, 480, 0 ], [ 0, 0, 8, 0, 24, 0, 0, 64, 136, 0, 192, 0, 328, 0, 0, 432, 736, 0 ], [ 0, 0, 0, 8, 0, 24, 64, 0, 0, 136, 0, 192, 0, 328, 432, 0, 0, 736 ], [ 0, 0, 3, 0, 15, 0, 0, 48, 144, 0, 168, 0, 306, 0, 0, 492, 744, 0 ], [ 0, 0, 0, 3, 0, 15, 48, 0, 0, 144, 0, 168, 0, 306, 492, 0, 0, 744 ], [ 0, 0, 10, 0, 26, 0, 0, 40, 164, 0, 204, 0, 328, 0, 0, 512, 636, 0 ], [ 0, 0, 0, 10, 0, 26, 40, 0, 0, 164, 0, 204, 0, 328, 512, 0, 0, 636 ], [ 0, 0, 0, 5, 0, 20, 50, 0, 0, 135, 0, 205, 0, 320, 510, 0, 0, 675 ], [ 0, 0, 5, 0, 20, 0, 0, 50, 135, 0, 205, 0, 320, 0, 0, 510, 675, 0 ], [ 1, 0, 16, 0, 37, 0, 0, 32, 184, 0, 248, 0, 318, 0, 0, 540, 544, 0 ], [ 0, 1, 0, 16, 0, 37, 32, 0, 0, 184, 0, 248, 0, 318, 540, 0, 0, 544 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1920 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1920, 0 ], [ 0, 0, 0, 0, 0, 0, 128, 0, 0, 128, 0, 64, 0, 320, 256, 0, 0, 1024 ], [ 0, 0, 0, 0, 0, 0, 0, 128, 128, 0, 64, 0, 320, 0, 0, 256, 1024, 0 ], [ 0, 0, 0, 0, 0, 24, 48, 0, 0, 144, 0, 120, 0, 312, 384, 0, 0, 888 ], [ 0, 0, 0, 0, 24, 0, 0, 48, 144, 0, 120, 0, 312, 0, 0, 384, 888, 0 ], [ 0, 0, 30, 0, 30, 0, 0, 0, 240, 0, 240, 0, 300, 0, 0, 600, 480, 0 ], [ 0, 0, 0, 30, 0, 30, 0, 0, 0, 240, 0, 240, 0, 300, 600, 0, 0, 480 ], [ 0, 0, 0, 8, 0, 24, 64, 0, 0, 136, 0, 192, 0, 328, 432, 0, 0, 736 ], [ 0, 0, 8, 0, 24, 0, 0, 64, 136, 0, 192, 0, 328, 0, 0, 432, 736, 0 ], [ 0, 0, 0, 3, 0, 15, 48, 0, 0, 144, 0, 168, 0, 306, 492, 0, 0, 744 ], [ 0, 0, 3, 0, 15, 0, 0, 48, 144, 0, 168, 0, 306, 0, 0, 492, 744, 0 ], [ 0, 0, 0, 10, 0, 26, 40, 0, 0, 164, 0, 204, 0, 328, 512, 0, 0, 636 ], [ 0, 0, 10, 0, 26, 0, 0, 40, 164, 0, 204, 0, 328, 0, 0, 512, 636, 0 ], [ 0, 0, 5, 0, 20, 0, 0, 50, 135, 0, 205, 0, 320, 0, 0, 510, 675, 0 ], [ 0, 0, 0, 5, 0, 20, 50, 0, 0, 135, 0, 205, 0, 320, 510, 0, 0, 675 ], [ 0, 1, 0, 16, 0, 37, 32, 0, 0, 184, 0, 248, 0, 318, 540, 0, 0, 544 ], [ 1, 0, 16, 0, 37, 0, 0, 32, 184, 0, 248, 0, 318, 0, 0, 540, 544, 0 ] ] ] ), rec( name := "HS.2", sbgname := "2^{1+6}_+:S5", filename := "2_+^1+6:S5", degree := 5775, rank := 9, permchar := "1a^+ + 77a^+ + 154a^+ + 175a^+ + 693a^+ + 825a^+ + 1056a^+ + 1386a^- + 1408a^+", charnmbs := [ 1, 5, 7, 10, 14, 19, 22, 25, 26 ], ctbl := [ [ 1, 30, 80, 128, 480, 640, 960, 1536, 1920 ], [ 1, 15, 20, -32, 60, 80, 0, 96, -240 ], [ 1, 15, 20, 8, 60, -20, 0, -144, 60 ], [ 1, -3, 14, 40, -48, 68, 36, -48, -60 ], [ 1, 5, -10, 8, 0, 20, -60, 16, 20 ], [ 1, 7, 4, 0, -28, -32, 16, 32, 0 ], [ 1, -5, 10, -12, -10, 10, -20, -4, 30 ], [ 1, -5, 0, 8, 20, -20, 0, 16, -20 ], [ 1, 0, -10, -7, 0, 10, 30, -24, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 30, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 5, 8, 0, 16, 0, 0, 0, 0 ], [ 0, 3, 3, 0, 12, 0, 12, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 30 ], [ 0, 1, 2, 0, 7, 8, 4, 0, 8 ], [ 0, 0, 0, 0, 6, 6, 3, 12, 3 ], [ 0, 0, 1, 0, 2, 2, 7, 8, 10 ], [ 0, 0, 0, 0, 0, 5, 5, 15, 5 ], [ 0, 0, 0, 2, 2, 1, 5, 4, 16 ] ], [ [ 0, 0, 80, 0, 0, 0, 0, 0, 0 ], [ 0, 8, 8, 0, 32, 0, 32, 0, 0 ], [ 1, 3, 4, 0, 12, 24, 12, 0, 24 ], [ 0, 0, 0, 10, 0, 10, 30, 0, 30 ], [ 0, 2, 2, 0, 16, 8, 12, 16, 24 ], [ 0, 0, 3, 2, 6, 15, 15, 24, 15 ], [ 0, 1, 1, 4, 6, 10, 8, 24, 26 ], [ 0, 0, 0, 0, 5, 10, 15, 30, 20 ], [ 0, 0, 1, 2, 6, 5, 13, 16, 37 ] ], [ [ 0, 0, 0, 128, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 128 ], [ 0, 0, 0, 16, 0, 16, 48, 0, 48 ], [ 1, 0, 10, 13, 0, 50, 30, 24, 0 ], [ 0, 0, 0, 0, 16, 0, 16, 32, 64 ], [ 0, 0, 2, 10, 0, 20, 24, 24, 48 ], [ 0, 0, 4, 4, 8, 16, 24, 32, 40 ], [ 0, 0, 0, 2, 10, 10, 20, 36, 50 ], [ 0, 2, 2, 0, 16, 16, 20, 40, 32 ] ], [ [ 0, 0, 0, 0, 480, 0, 0, 0, 0 ], [ 0, 16, 32, 0, 112, 128, 64, 0, 128 ], [ 0, 12, 12, 0, 96, 48, 72, 96, 144 ], [ 0, 0, 0, 0, 60, 0, 60, 120, 240 ], [ 1, 7, 16, 16, 48, 56, 88, 112, 136 ], [ 0, 6, 6, 0, 42, 48, 78, 156, 144 ], [ 0, 2, 6, 8, 44, 52, 76, 128, 164 ], [ 0, 0, 5, 10, 35, 65, 80, 150, 135 ], [ 0, 2, 6, 16, 34, 48, 82, 108, 184 ] ], [ [ 0, 0, 0, 0, 0, 640, 0, 0, 0 ], [ 0, 0, 0, 0, 128, 128, 64, 256, 64 ], [ 0, 0, 24, 16, 48, 120, 120, 192, 120 ], [ 0, 0, 10, 50, 0, 100, 120, 120, 240 ], [ 0, 8, 8, 0, 56, 64, 104, 208, 192 ], [ 1, 6, 15, 20, 48, 88, 114, 180, 168 ], [ 0, 2, 10, 16, 52, 76, 120, 160, 204 ], [ 0, 5, 10, 10, 65, 75, 100, 170, 205 ], [ 0, 1, 5, 16, 48, 56, 102, 164, 248 ] ], [ [ 0, 0, 0, 0, 0, 0, 960, 0, 0 ], [ 0, 0, 32, 0, 64, 64, 224, 256, 320 ], [ 0, 12, 12, 48, 72, 120, 96, 288, 312 ], [ 0, 0, 30, 30, 60, 120, 180, 240, 300 ], [ 0, 4, 12, 16, 88, 104, 152, 256, 328 ], [ 0, 3, 15, 24, 78, 114, 180, 240, 306 ], [ 1, 7, 8, 24, 76, 120, 140, 256, 328 ], [ 0, 5, 15, 20, 80, 100, 160, 260, 320 ], [ 0, 5, 13, 20, 82, 102, 164, 256, 318 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 1536, 0 ], [ 0, 0, 0, 0, 0, 256, 256, 768, 256 ], [ 0, 0, 0, 0, 96, 192, 288, 576, 384 ], [ 0, 0, 0, 24, 120, 120, 240, 432, 600 ], [ 0, 0, 16, 32, 112, 208, 256, 480, 432 ], [ 0, 12, 24, 24, 156, 180, 240, 408, 492 ], [ 0, 8, 24, 32, 128, 160, 256, 416, 512 ], [ 1, 15, 30, 36, 150, 170, 260, 364, 510 ], [ 0, 4, 16, 40, 108, 164, 256, 408, 540 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1920 ], [ 0, 0, 0, 128, 128, 64, 320, 256, 1024 ], [ 0, 0, 24, 48, 144, 120, 312, 384, 888 ], [ 0, 30, 30, 0, 240, 240, 300, 600, 480 ], [ 0, 8, 24, 64, 136, 192, 328, 432, 736 ], [ 0, 3, 15, 48, 144, 168, 306, 492, 744 ], [ 0, 10, 26, 40, 164, 204, 328, 512, 636 ], [ 0, 5, 20, 50, 135, 205, 320, 510, 675 ], [ 1, 16, 37, 32, 184, 248, 318, 540, 544 ] ] ] ), rec( name := "HS.2", sbgname := "L3(4).2_3 leq L3(4).2^2", filename := "L34.2_3", degree := 2200, rank := 9, permchar := "1a^+ + 22a^{+-} + 77a^{+-} + 175a^+ + 231a^- + 770a^- + 825a^+", charnmbs := [ 1, 3, 4, 5, 6, 10, 13, 17, 19 ], ctbl := [ [ 1, 1, 42, 42, 105, 105, 560, 672, 672 ], [ 1, 1, 12, 12, -45, -45, 160, -48, -48 ], [ 1, -1, -28, 28, -35, 35, 0, -112, 112 ], [ 1, 1, 22, 22, 5, 5, -40, -8, -8 ], [ 1, -1, -18, 18, 15, -15, 0, 48, -48 ], [ 1, 1, -2, -2, 17, 17, 32, -32, -32 ], [ 1, -1, 2, -2, 15, -15, 0, -32, 32 ], [ 1, -1, 2, -2, -5, 5, 0, 8, -8 ], [ 1, 1, -2, -2, -3, -3, -8, 8, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 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30, 35 ], [ 0, 0, 5, 0, 5, 0, 30, 35, 30 ] ], [ [ 0, 0, 0, 0, 0, 105, 0, 0, 0 ], [ 0, 0, 0, 0, 105, 0, 0, 0, 0 ], [ 0, 0, 5, 0, 20, 0, 0, 80, 0 ], [ 0, 0, 0, 5, 0, 20, 0, 0, 80 ], [ 0, 1, 8, 0, 0, 0, 64, 32, 0 ], [ 1, 0, 0, 8, 0, 0, 64, 0, 32 ], [ 0, 0, 0, 0, 12, 12, 9, 36, 36 ], [ 0, 0, 5, 0, 5, 0, 30, 35, 30 ], [ 0, 0, 0, 5, 0, 5, 30, 30, 35 ] ], [ [ 0, 0, 0, 0, 0, 0, 560, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 560, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 240, 160, 160 ], [ 0, 0, 0, 0, 0, 0, 240, 160, 160 ], [ 0, 0, 0, 0, 64, 64, 48, 192, 192 ], [ 0, 0, 0, 0, 64, 64, 48, 192, 192 ], [ 1, 1, 18, 18, 9, 9, 216, 144, 144 ], [ 0, 0, 10, 10, 30, 30, 120, 180, 180 ], [ 0, 0, 10, 10, 30, 30, 120, 180, 180 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 672, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 672 ], [ 0, 0, 0, 16, 0, 80, 160, 96, 320 ], [ 0, 0, 16, 0, 80, 0, 160, 320, 96 ], [ 0, 0, 0, 32, 0, 32, 192, 192, 224 ], [ 0, 0, 32, 0, 32, 0, 192, 224, 192 ], [ 0, 0, 12, 12, 36, 36, 144, 216, 216 ], [ 1, 0, 6, 20, 30, 35, 180, 180, 220 ], [ 0, 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350, 712, 716, 756 ], [ 0, 4, 22, 32, 44, 88, 188, 184, 184, 346, 350, 330, 720, 728, 780 ], [ 0, 10, 24, 56, 38, 86, 170, 178, 176, 362, 356, 360, 732, 724, 728 ], [ 1, 9, 18, 54, 46, 92, 193, 177, 186, 376, 358, 364, 724, 698, 704 ], [ 0, 12, 22, 32, 48, 92, 188, 176, 184, 354, 378, 390, 728, 704, 692 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4000 ], [ 0, 0, 80, 0, 0, 80, 80, 240, 160, 320, 320, 320, 480, 960, 960 ], [ 0, 32, 32, 64, 32, 96, 160, 160, 192, 384, 288, 416, 768, 704, 672 ], [ 0, 0, 32, 32, 0, 0, 256, 0, 128, 512, 512, 512, 512, 512, 992 ], [ 0, 0, 16, 0, 0, 96, 128, 192, 160, 336, 336, 368, 736, 768, 864 ], [ 0, 8, 24, 0, 48, 120, 160, 160, 176, 408, 328, 376, 656, 736, 800 ], [ 0, 4, 20, 64, 32, 80, 164, 228, 160, 352, 376, 312, 704, 752, 752 ], [ 0, 12, 20, 0, 48, 80, 228, 164, 176, 360, 376, 360, 752, 704, 720 ], [ 0, 8, 24, 32, 40, 88, 160, 176, 192, 368, 384, 320, 720, 736, 752 ], [ 0, 8, 24, 64, 42, 102, 176, 180, 184, 348, 334, 350, 748, 708, 732 ], [ 0, 8, 18, 64, 42, 82, 188, 188, 192, 334, 372, 344, 716, 756, 696 ], [ 0, 8, 26, 64, 46, 94, 156, 180, 160, 350, 344, 348, 708, 780, 736 ], [ 0, 6, 24, 32, 46, 82, 176, 188, 180, 374, 358, 354, 720, 728, 732 ], [ 0, 12, 22, 32, 48, 92, 188, 176, 184, 354, 378, 390, 728, 704, 692 ], [ 1, 12, 21, 62, 54, 100, 188, 180, 188, 366, 348, 368, 732, 692, 688 ] ] ] ), rec( name := "HS.2", sbgname := "4^3:(L3(2)x2)", filename := "4^3:L32x2", degree := 4125, rank := 9, permchar := "1a^+ + 22a^+ + 77a^+ + 154a^+ + 175a^+ + 693a^+ + 770a^+ + 825a^+ + 1408a^+", charnmbs := [ 1, 3, 5, 7, 10, 14, 16, 19, 26 ], ctbl := [ [ 1, 28, 64, 112, 336, 448, 896, 896, 1344 ], [ 1, -7, -36, 42, -84, 168, -224, 56, 84 ], [ 1, 13, 14, 32, 6, 28, 16, -164, 54 ], [ 1, 13, 4, 22, 36, -32, -64, 56, -36 ], [ 1, -5, 20, 2, 6, 52, 16, 16, -108 ], [ 1, 3, 4, 2, -34, -12, 16, 16, 4 ], [ 1, -7, -6, 12, 6, -12, 16, -4, -6 ], [ 1, 5, -10, -8, 6, 12, 16, -4, -18 ], [ 1, -2, 4, -8, 6, -2, -19, -4, 24 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 28, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 3, 0, 12, 12, 0, 0, 0, 0 ], [ 0, 0, 0, 7, 0, 0, 0, 0, 21 ], [ 0, 3, 4, 3, 6, 0, 0, 0, 12 ], [ 0, 1, 0, 2, 5, 4, 0, 8, 8 ], [ 0, 0, 0, 0, 3, 1, 12, 0, 12 ], [ 0, 0, 0, 0, 0, 6, 6, 4, 12 ], [ 0, 0, 0, 0, 3, 0, 4, 15, 6 ], [ 0, 0, 1, 1, 2, 4, 8, 4, 8 ] ], [ [ 0, 0, 64, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 16, 0, 0, 0, 0, 48 ], [ 1, 0, 0, 7, 0, 42, 0, 14, 0 ], [ 0, 4, 4, 0, 12, 0, 32, 0, 12 ], [ 0, 0, 0, 4, 4, 16, 0, 16, 24 ], [ 0, 0, 6, 0, 12, 0, 32, 8, 6 ], [ 0, 0, 0, 4, 0, 16, 4, 16, 24 ], [ 0, 0, 1, 0, 6, 4, 16, 22, 15 ], [ 0, 1, 0, 1, 6, 2, 16, 10, 28 ] ], [ [ 0, 0, 0, 112, 0, 0, 0, 0, 0 ], [ 0, 12, 16, 12, 24, 0, 0, 0, 48 ], [ 0, 7, 7, 0, 21, 0, 56, 0, 21 ], [ 1, 3, 0, 16, 12, 24, 0, 8, 48 ], [ 0, 2, 4, 4, 18, 0, 32, 24, 28 ], [ 0, 0, 0, 6, 0, 30, 8, 20, 48 ], [ 0, 0, 4, 0, 12, 4, 40, 16, 36 ], [ 0, 0, 0, 1, 9, 10, 16, 46, 30 ], [ 0, 1, 1, 4, 7, 16, 24, 20, 39 ] ], [ [ 0, 0, 0, 0, 336, 0, 0, 0, 0 ], [ 0, 12, 0, 24, 60, 48, 0, 96, 96 ], [ 0, 0, 0, 21, 21, 84, 0, 84, 126 ], [ 0, 6, 12, 12, 54, 0, 96, 72, 84 ], [ 1, 5, 4, 18, 4, 44, 48, 96, 116 ], [ 0, 3, 12, 0, 33, 12, 120, 60, 96 ], [ 0, 0, 0, 12, 18, 60, 54, 72, 120 ], [ 0, 3, 6, 9, 36, 30, 72, 78, 102 ], [ 0, 2, 6, 7, 29, 32, 80, 68, 112 ] ], [ [ 0, 0, 0, 0, 0, 448, 0, 0, 0 ], [ 0, 0, 0, 0, 48, 16, 192, 0, 192 ], [ 0, 0, 42, 0, 84, 0, 224, 56, 42 ], [ 0, 0, 0, 24, 0, 120, 32, 80, 192 ], [ 0, 4, 16, 0, 44, 16, 160, 80, 128 ], [ 1, 1, 0, 30, 12, 116, 24, 120, 144 ], [ 0, 6, 16, 4, 60, 12, 142, 88, 120 ], [ 0, 0, 4, 10, 30, 60, 88, 112, 144 ], [ 0, 4, 2, 16, 32, 48, 80, 96, 170 ] ], [ [ 0, 0, 0, 0, 0, 0, 896, 0, 0 ], [ 0, 0, 0, 0, 0, 192, 192, 128, 384 ], [ 0, 0, 0, 56, 0, 224, 56, 224, 336 ], [ 0, 0, 32, 0, 96, 32, 320, 128, 288 ], [ 0, 0, 0, 32, 48, 160, 144, 192, 320 ], [ 0, 12, 32, 8, 120, 24, 284, 176, 240 ], [ 1, 6, 4, 40, 54, 142, 117, 220, 312 ], [ 0, 4, 16, 16, 72, 88, 220, 192, 288 ], [ 0, 8, 16, 24, 80, 80, 208, 192, 288 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 896, 0 ], [ 0, 0, 0, 0, 96, 0, 128, 480, 192 ], [ 0, 0, 14, 0, 84, 56, 224, 308, 210 ], [ 0, 0, 0, 8, 72, 80, 128, 368, 240 ], [ 0, 8, 16, 24, 96, 80, 192, 208, 272 ], [ 0, 0, 8, 20, 60, 120, 176, 224, 288 ], [ 0, 4, 16, 16, 72, 88, 220, 192, 288 ], [ 1, 15, 22, 46, 78, 112, 192, 112, 318 ], [ 0, 4, 10, 20, 68, 96, 192, 212, 294 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 1344 ], [ 0, 0, 48, 48, 96, 192, 384, 192, 384 ], [ 0, 21, 0, 21, 126, 42, 336, 210, 588 ], [ 0, 12, 12, 48, 84, 192, 288, 240, 468 ], [ 0, 8, 24, 28, 116, 128, 320, 272, 448 ], [ 0, 12, 6, 48, 96, 144, 240, 288, 510 ], [ 0, 12, 24, 36, 120, 120, 312, 288, 432 ], [ 0, 6, 15, 30, 102, 144, 288, 318, 441 ], [ 1, 8, 28, 39, 112, 170, 288, 294, 404 ] ] ] ), rec( name := "J3", sbgname := "L2(16).2", filename := "L216.2", degree := 6156, rank := 8, permchar := "1a + 323ab + 324a + 1140a + 1215ab + 1615a", charnmbs := [ 1, 4, 5, 6, 10, 11, 12, 13 ], ctbl := [ [ 1, 85, 120, 510, 680, 1360, 1360, 2040 ], [ 1, 13, 12, -30, -40, -64*E(5)+8*E(5)^2+8*E(5)^3-64*E(5)^4, 8*E(5)-64*E(5)^2-64*E(5)^3+8*E(5)^4, -12 ], [ 1, 13, 12, -30, -40, 8*E(5)-64*E(5)^2-64*E(5)^3+8*E(5)^4, -64*E(5)+8*E(5)^2+8*E(5)^3-64*E(5)^4, -12 ], [ 1, -17, -18, 0, 0, 68, 68, -102 ], [ 1, 13, -6, 6, 32, -8, -8, -30 ], [ 1, 3*E(17)+3*E(17)^2+5*E(17)^3+3*E(17)^4+5*E(17)^5+5*E(17)^6+5*E(17)^7+3*E(17)^8+3*E(17)^9+5*E(17)^10+5*E(17)^11+5*E(17)^12+3*E(17)^13+5*E(17)^14+3*E(17)^15+3*E(17)^16, 8*E(17)+8*E(17)^2+4*E(17)^3+8*E(17)^4+4*E(17)^5+4*E(17)^6+4*E(17)^7 +8*E(17)^8+8*E(17)^9+4*E(17)^10+4*E(17)^11+4*E(17)^12+8*E(17)^13+4*E(17)^14+8*E(17)^15+8*E(17)^16, 6*E(17)+6*E(17)^2+16*E(17)^3+6*E(17)^4+16*E(17)^5+16*E(17)^6+16*E(17)^7+6*E(17)^8+6*E(17)^9+16*E(17)^10+16*E(17)^11+16*E(17)^12+6*E(17)^13 +16*E(17)^14+6*E(17)^15+6*E(17)^16, 8*E(17)+8*E(17)^2-4*E(17)^3+8*E(17)^4-4*E(17)^5-4*E(17)^6-4*E(17)^7+8*E(17)^8+8*E(17)^9-4*E(17)^10-4*E(17)^11-4*E(17)^12+8*E(17)^13-4*E(17)^14+8*E(17)^15+8*E(17)^16, -8, -8, -40*E(17)-40*E(17)^2-36*E(17)^3-40*E(17)^4-36*E(17)^5-36*E(17)^6-36*E(17)^7-40*E(17)^8-40*E(17)^9-36*E(17)^10-36*E(17)^11-36*E(17)^12-40*E(17)^13-36*E(17)^14-40*E(17)^15-40*E(17)^16 ], [ 1, 5*E(17)+5*E(17)^2+3*E(17)^3+5*E(17)^4+3*E(17)^5+3*E(17)^6+3*E(17)^7+5*E(17)^8+5*E(17)^9+3*E(17)^10+3*E(17)^11+3*E(17)^12+5*E(17)^13+3*E(17)^14+5*E(17)^15+5*E(17)^16, 4*E(17)+4*E(17)^2+8*E(17)^3+4*E(17)^4+8*E(17)^5+8*E(17)^6+8*E(17)^7 +4*E(17)^8+4*E(17)^9+8*E(17)^10+8*E(17)^11+8*E(17)^12+4*E(17)^13+8*E(17)^14+4*E(17)^15+4*E(17)^16, 16*E(17)+16*E(17)^2+6*E(17)^3+16*E(17)^4+6*E(17)^5+6*E(17)^6+6*E(17)^7+16*E(17)^8+16*E(17)^9+6*E(17)^10+6*E(17)^11+6*E(17)^12+16*E(17)^13 +6*E(17)^14+16*E(17)^15+16*E(17)^16, -4*E(17)-4*E(17)^2+8*E(17)^3-4*E(17)^4+8*E(17)^5+8*E(17)^6+8*E(17)^7-4*E(17)^8-4*E(17)^9+8*E(17)^10+8*E(17)^11+8*E(17)^12-4*E(17)^13+8*E(17)^14-4*E(17)^15-4*E(17)^16, -8, -8, -36*E(17)-36*E(17)^2-40*E(17)^3-36*E(17)^4-40*E(17)^5-40*E(17)^6-40*E(17)^7-36*E(17)^8-36*E(17)^9-40*E(17)^10-40*E(17)^11-40*E(17)^12-36*E(17)^13-40*E(17)^14-36*E(17)^15-36*E(17)^16 ], [ 1, -5, 12, 24, -4, -8, -8, -12 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 85, 0, 0, 0, 0, 0, 0 ], [ 1, 4, 0, 0, 16, 32, 32, 0 ], [ 0, 0, 0, 0, 0, 34, 34, 17 ], [ 0, 0, 0, 5, 16, 16, 16, 32 ], [ 0, 2, 0, 12, 15, 16, 16, 24 ], [ 0, 2, 3, 6, 8, 23, 10, 33 ], [ 0, 2, 3, 6, 8, 10, 23, 33 ], [ 0, 0, 1, 8, 8, 22, 22, 24 ] ], [ [ 0, 0, 120, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 48, 48, 24 ], [ 1, 0, 0, 17, 0, 34, 34, 34 ], [ 0, 0, 4, 16, 16, 24, 24, 36 ], [ 0, 0, 0, 12, 12, 24, 24, 48 ], [ 0, 3, 3, 9, 12, 30, 18, 45 ], [ 0, 3, 3, 9, 12, 18, 30, 45 ], [ 0, 1, 2, 9, 16, 30, 30, 32 ] ], [ [ 0, 0, 0, 510, 0, 0, 0, 0 ], [ 0, 0, 0, 30, 96, 96, 96, 192 ], [ 0, 0, 17, 68, 68, 102, 102, 153 ], [ 1, 5, 16, 32, 56, 112, 112, 176 ], [ 0, 12, 12, 42, 48, 120, 120, 156 ], [ 0, 6, 9, 42, 60, 96, 126, 171 ], [ 0, 6, 9, 42, 60, 126, 96, 171 ], [ 0, 8, 9, 44, 52, 114, 114, 169 ] ], [ [ 0, 0, 0, 0, 680, 0, 0, 0 ], [ 0, 16, 0, 96, 120, 128, 128, 192 ], [ 0, 0, 0, 68, 68, 136, 136, 272 ], [ 0, 16, 16, 56, 64, 160, 160, 208 ], [ 1, 15, 12, 48, 72, 152, 152, 228 ], [ 0, 8, 12, 60, 76, 128, 168, 228 ], [ 0, 8, 12, 60, 76, 168, 128, 228 ], [ 0, 8, 16, 52, 76, 152, 152, 224 ] ], [ [ 0, 0, 0, 0, 0, 1360, 0, 0 ], [ 0, 32, 48, 96, 128, 368, 160, 528 ], [ 0, 34, 34, 102, 136, 340, 204, 510 ], [ 0, 16, 24, 112, 160, 256, 336, 456 ], [ 0, 16, 24, 120, 152, 256, 336, 456 ], [ 1, 23, 30, 96, 128, 356, 300, 426 ], [ 0, 10, 18, 126, 168, 300, 300, 438 ], [ 0, 22, 30, 114, 152, 284, 292, 466 ] ], [ [ 0, 0, 0, 0, 0, 0, 1360, 0 ], [ 0, 32, 48, 96, 128, 160, 368, 528 ], [ 0, 34, 34, 102, 136, 204, 340, 510 ], [ 0, 16, 24, 112, 160, 336, 256, 456 ], [ 0, 16, 24, 120, 152, 336, 256, 456 ], [ 0, 10, 18, 126, 168, 300, 300, 438 ], [ 1, 23, 30, 96, 128, 300, 356, 426 ], [ 0, 22, 30, 114, 152, 292, 284, 466 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 2040 ], [ 0, 0, 24, 192, 192, 528, 528, 576 ], [ 0, 17, 34, 153, 272, 510, 510, 544 ], [ 0, 32, 36, 176, 208, 456, 456, 676 ], [ 0, 24, 48, 156, 228, 456, 456, 672 ], [ 0, 33, 45, 171, 228, 426, 438, 699 ], [ 0, 33, 45, 171, 228, 438, 426, 699 ], [ 1, 24, 32, 169, 224, 466, 466, 658 ] ] ] ), rec( name := "J3.2", sbgname := "L2(16).4", filename := "L216.4", degree := 6156, rank := 7, permchar := "1a^+ + 323ab + 324a^- + 1140a^+ + 1215a^-b^- + 1615a^+", charnmbs := [ 1, 4, 6, 10, 13, 15, 16 ], ctbl := [ [ 1, 85, 120, 510, 680, 2040, 2720 ], [ 1, 13, 12, -30, -40, -12, 56 ], [ 1, -17, -18, 0, 0, -102, 136 ], [ 1, 13, -6, 6, 32, -30, -16 ], [ 1, 5*E(17)+5*E(17)^2+3*E(17)^3+5*E(17)^4+3*E(17)^5+3*E(17)^6+3*E(17)^7+5*E(17)^8+5*E(17)^9+3*E(17)^10+3*E(17)^11+3*E(17)^12+5*E(17)^13+3*E(17)^14+5*E(17)^15+5*E(17)^16, 4*E(17)+4*E(17)^2+8*E(17)^3+4*E(17)^4+8*E(17)^5+8*E(17)^6+8*E(17)^7 +4*E(17)^8+4*E(17)^9+8*E(17)^10+8*E(17)^11+8*E(17)^12+4*E(17)^13+8*E(17)^14+4*E(17)^15+4*E(17)^16, 16*E(17)+16*E(17)^2+6*E(17)^3+16*E(17)^4+6*E(17)^5+6*E(17)^6+6*E(17)^7+16*E(17)^8+16*E(17)^9+6*E(17)^10+6*E(17)^11+6*E(17)^12+16*E(17)^13 +6*E(17)^14+16*E(17)^15+16*E(17)^16, -4*E(17)-4*E(17)^2+8*E(17)^3-4*E(17)^4+8*E(17)^5+8*E(17)^6+8*E(17)^7-4*E(17)^8-4*E(17)^9+8*E(17)^10+8*E(17)^11+8*E(17)^12-4*E(17)^13+8*E(17)^14-4*E(17)^15-4*E(17)^16, -36*E(17)-36*E(17)^2-40*E(17)^3-36*E(17)^4-40*E(17)^5-40*E(17)^6-40*E(17)^7-36*E(17)^8-36*E(17)^9-40*E(17)^10-40*E(17)^11-40*E(17)^12-36*E(17)^13-40*E(17)^14-36*E(17)^15-36*E(17)^16, -16 ], [ 1, 3*E(17)+3*E(17)^2+5*E(17)^3+3*E(17)^4+5*E(17)^5+5*E(17)^6+5*E(17)^7+3*E(17)^8+3*E(17)^9+5*E(17)^10+5*E(17)^11+5*E(17)^12+3*E(17)^13+5*E(17)^14+3*E(17)^15+3*E(17)^16, 8*E(17)+8*E(17)^2+4*E(17)^3+8*E(17)^4+4*E(17)^5+4*E(17)^6+4*E(17)^7 +8*E(17)^8+8*E(17)^9+4*E(17)^10+4*E(17)^11+4*E(17)^12+8*E(17)^13+4*E(17)^14+8*E(17)^15+8*E(17)^16, 6*E(17)+6*E(17)^2+16*E(17)^3+6*E(17)^4+16*E(17)^5+16*E(17)^6+16*E(17)^7+6*E(17)^8+6*E(17)^9+16*E(17)^10+16*E(17)^11+16*E(17)^12+6*E(17)^13 +16*E(17)^14+6*E(17)^15+6*E(17)^16, 8*E(17)+8*E(17)^2-4*E(17)^3+8*E(17)^4-4*E(17)^5-4*E(17)^6-4*E(17)^7+8*E(17)^8+8*E(17)^9-4*E(17)^10-4*E(17)^11-4*E(17)^12+8*E(17)^13-4*E(17)^14+8*E(17)^15+8*E(17)^16, -40*E(17)-40*E(17)^2-36*E(17)^3-40*E(17)^4-36*E(17)^5-36*E(17)^6-36*E(17)^7-40*E(17)^8-40*E(17)^9-36*E(17)^10-36*E(17)^11-36*E(17)^12-40*E(17)^13-36*E(17)^14-40*E(17)^15-40*E(17)^16, -16 ], [ 1, -5, 12, 24, -4, -12, -16 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 85, 0, 0, 0, 0, 0 ], [ 1, 4, 0, 0, 16, 0, 64 ], [ 0, 0, 0, 0, 0, 17, 68 ], [ 0, 0, 0, 5, 16, 32, 32 ], [ 0, 2, 0, 12, 15, 24, 32 ], [ 0, 0, 1, 8, 8, 24, 44 ], [ 0, 2, 3, 6, 8, 33, 33 ] ], [ [ 0, 0, 120, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 24, 96 ], [ 1, 0, 0, 17, 0, 34, 68 ], [ 0, 0, 4, 16, 16, 36, 48 ], [ 0, 0, 0, 12, 12, 48, 48 ], [ 0, 1, 2, 9, 16, 32, 60 ], [ 0, 3, 3, 9, 12, 45, 48 ] ], [ [ 0, 0, 0, 510, 0, 0, 0 ], [ 0, 0, 0, 30, 96, 192, 192 ], [ 0, 0, 17, 68, 68, 153, 204 ], [ 1, 5, 16, 32, 56, 176, 224 ], [ 0, 12, 12, 42, 48, 156, 240 ], [ 0, 8, 9, 44, 52, 169, 228 ], [ 0, 6, 9, 42, 60, 171, 222 ] ], [ [ 0, 0, 0, 0, 680, 0, 0 ], [ 0, 16, 0, 96, 120, 192, 256 ], [ 0, 0, 0, 68, 68, 272, 272 ], [ 0, 16, 16, 56, 64, 208, 320 ], [ 1, 15, 12, 48, 72, 228, 304 ], [ 0, 8, 16, 52, 76, 224, 304 ], [ 0, 8, 12, 60, 76, 228, 296 ] ], [ [ 0, 0, 0, 0, 0, 2040, 0 ], [ 0, 0, 24, 192, 192, 576, 1056 ], [ 0, 17, 34, 153, 272, 544, 1020 ], [ 0, 32, 36, 176, 208, 676, 912 ], [ 0, 24, 48, 156, 228, 672, 912 ], [ 1, 24, 32, 169, 224, 658, 932 ], [ 0, 33, 45, 171, 228, 699, 864 ] ], [ [ 0, 0, 0, 0, 0, 0, 2720 ], [ 0, 64, 96, 192, 256, 1056, 1056 ], [ 0, 68, 68, 204, 272, 1020, 1088 ], [ 0, 32, 48, 224, 320, 912, 1184 ], [ 0, 32, 48, 240, 304, 912, 1184 ], [ 0, 44, 60, 228, 304, 932, 1152 ], [ 1, 33, 48, 222, 296, 864, 1256 ] ] ] ), rec( name := "J3.2", sbgname := "3^2.3^{1+2}:8.2", filename := "3^2.3^1+2:8.2", degree := 25840, rank := 15, permchar := "1a^+ + 324a^+ + 1140a^+ + 1215a^{+-}b^{+-} + 1615a^+ + 1920a^+b^+c^+ + 1938ab + 2432a^+ + 2754a^+ + 3078a^+", charnmbs := [ 1, 5, 10, 12, 13, 14, 15, 16, 18, 20, 22, 24, 25, 27, 29 ], ctbl := [ [ 1, 81, 243, 243, 972, 972, 1944, 1944, 1944, 1944, 1944, 1944, 3888, 3888, 3888 ], [ 1, 21, -17, 63, -78, 22, 164, -16, 44, 24, -16, 164, -232, -152, 8 ], [ 1, 21, 3, -5, 46, 42, -44, -64, -28, 40, 96, 12, -24, 8, -104 ], [ 1, -9*E(17)-9*E(17)^2-7*E(17)^3-9*E(17)^4-7*E(17)^5-7*E(17)^6-7*E(17)^7-9*E(17)^8-9*E(17)^9-7*E(17)^10-7*E(17)^11-7*E(17)^12-9*E(17)^13-7*E(17)^14-9*E(17)^15-9*E(17)^16, -19*E(17)-19*E(17)^2-25*E(17)^3-19*E(17)^4-25*E(17)^5-25*E(17)^6 -25*E(17)^7-19*E(17)^8-19*E(17)^9-25*E(17)^10-25*E(17)^11-25*E(17)^12-19*E(17)^13-25*E(17)^14-19*E(17)^15-19*E(17)^16, -11*E(17)-11*E(17)^2-15*E(17)^3-11*E(17)^4-15*E(17)^5-15*E(17)^6-15*E(17)^7-11*E(17)^8-11*E(17)^9-15*E(17)^10 -15*E(17)^11-15*E(17)^12-11*E(17)^13-15*E(17)^14-11*E(17)^15-11*E(17)^16, 20*E(17)+20*E(17)^2+4*E(17)^3+20*E(17)^4+4*E(17)^5+4*E(17)^6+4*E(17)^7+20*E(17)^8+20*E(17)^9+4*E(17)^10+4*E(17)^11+4*E(17)^12+20*E(17)^13+4*E(17)^14+20*E(17)^15 +20*E(17)^16, -12*E(17)-12*E(17)^2-4*E(17)^3-12*E(17)^4-4*E(17)^5-4*E(17)^6-4*E(17)^7-12*E(17)^8-12*E(17)^9-4*E(17)^10-4*E(17)^11-4*E(17)^12-12*E(17)^13-4*E(17)^14-12*E(17)^15-12*E(17)^16, 72*E(17)+72*E(17)^2+48*E(17)^3+72*E(17)^4+48*E(17)^5+48*E(17)^6+48*E(17)^7+72*E(17)^8+72*E(17)^9+48*E(17)^10+48*E(17)^11+48*E(17)^12+72*E(17)^13+48*E(17)^14+72*E(17)^15+72*E(17)^16, 8*E(17)+8*E(17)^2+32*E(17)^3+8*E(17)^4+32*E(17)^5 +32*E(17)^6+32*E(17)^7+8*E(17)^8+8*E(17)^9+32*E(17)^10+32*E(17)^11+32*E(17)^12+8*E(17)^13+32*E(17)^14+8*E(17)^15+8*E(17)^16, -24*E(17)-24*E(17)^2-8*E(17)^3-24*E(17)^4-8*E(17)^5-8*E(17)^6-8*E(17)^7-24*E(17)^8-24*E(17)^9-8*E(17)^10 -8*E(17)^11-8*E(17)^12-24*E(17)^13-8*E(17)^14-24*E(17)^15-24*E(17)^16, 24, 72*E(17)+72*E(17)^2+56*E(17)^3+72*E(17)^4+56*E(17)^5+56*E(17)^6+56*E(17)^7+72*E(17)^8+72*E(17)^9+56*E(17)^10+56*E(17)^11+56*E(17)^12+72*E(17)^13+56*E(17)^14 +72*E(17)^15+72*E(17)^16, 8*E(17)+8*E(17)^2+24*E(17)^3+8*E(17)^4+24*E(17)^5+24*E(17)^6+24*E(17)^7+8*E(17)^8+8*E(17)^9+24*E(17)^10+24*E(17)^11+24*E(17)^12+8*E(17)^13+24*E(17)^14+8*E(17)^15+8*E(17)^16, -16*E(17)-16*E(17)^2-32*E(17)^3-16*E(17)^4-32*E(17)^5-32*E(17)^6-32*E(17)^7-16*E(17)^8-16*E(17)^9-32*E(17)^10-32*E(17)^11-32*E(17)^12-16*E(17)^13-32*E(17)^14-16*E(17)^15-16*E(17)^16, -16*E(17)-16*E(17)^2+32*E(17)^3-16*E(17)^4+32*E(17)^5 +32*E(17)^6+32*E(17)^7-16*E(17)^8-16*E(17)^9+32*E(17)^10+32*E(17)^11+32*E(17)^12-16*E(17)^13+32*E(17)^14-16*E(17)^15-16*E(17)^16, -48*E(17)-48*E(17)^2-80*E(17)^3-48*E(17)^4-80*E(17)^5-80*E(17)^6-80*E(17)^7-48*E(17)^8-48*E(17)^9 -80*E(17)^10-80*E(17)^11-80*E(17)^12-48*E(17)^13-80*E(17)^14-48*E(17)^15-48*E(17)^16 ], [ 1, -E(17)-E(17)^2-7*E(17)^3-E(17)^4-7*E(17)^5-7*E(17)^6-7*E(17)^7-E(17)^8-E(17)^9-7*E(17)^10-7*E(17)^11-7*E(17)^12-E(17)^13-7*E(17)^14-E(17)^15 -E(17)^16, -5*E(17)-5*E(17)^2-E(17)^3-5*E(17)^4-E(17)^5-E(17)^6-E(17)^7-5*E(17)^8-5*E(17)^9-E(17)^10-E(17)^11-E(17)^12-5*E(17)^13-E(17)^14-5*E(17)^15-5*E(17)^16, 19*E(17)+19*E(17)^2+25*E(17)^3+19*E(17)^4+25*E(17)^5+25*E(17)^6+25*E(17)^7 +19*E(17)^8+19*E(17)^9+25*E(17)^10+25*E(17)^11+25*E(17)^12+19*E(17)^13+25*E(17)^14+19*E(17)^15+19*E(17)^16, -20*E(17)-20*E(17)^2-4*E(17)^3-20*E(17)^4-4*E(17)^5-4*E(17)^6-4*E(17)^7-20*E(17)^8-20*E(17)^9-4*E(17)^10-4*E(17)^11-4*E(17)^12 -20*E(17)^13-4*E(17)^14-20*E(17)^15-20*E(17)^16, -4*E(17)-4*E(17)^2-12*E(17)^3-4*E(17)^4-12*E(17)^5-12*E(17)^6-12*E(17)^7-4*E(17)^8-4*E(17)^9-12*E(17)^10-12*E(17)^11-12*E(17)^12-4*E(17)^13-12*E(17)^14-4*E(17)^15-4*E(17)^16, 20*E(17)+20*E(17)^2+20*E(17)^4+20*E(17)^8+20*E(17)^9+20*E(17)^13+20*E(17)^15+20*E(17)^16, -80*E(17)-80*E(17)^2-64*E(17)^3-80*E(17)^4-64*E(17)^5-64*E(17)^6-64*E(17)^7-80*E(17)^8-80*E(17)^9-64*E(17)^10-64*E(17)^11-64*E(17)^12-80*E(17)^13 -64*E(17)^14-80*E(17)^15-80*E(17)^16, 16*E(17)+16*E(17)^2+40*E(17)^3+16*E(17)^4+40*E(17)^5+40*E(17)^6+40*E(17)^7+16*E(17)^8+16*E(17)^9+40*E(17)^10+40*E(17)^11+40*E(17)^12+16*E(17)^13+40*E(17)^14+16*E(17)^15+16*E(17)^16, 16*E(17)+16*E(17)^2+40*E(17)^3+16*E(17)^4+40*E(17)^5+40*E(17)^6+40*E(17)^7+16*E(17)^8+16*E(17)^9+40*E(17)^10+40*E(17)^11+40*E(17)^12+16*E(17)^13+40*E(17)^14+16*E(17)^15+16*E(17)^16, 4*E(17)+4*E(17)^2+8*E(17)^3+4*E(17)^4+8*E(17)^5+8*E(17)^6 +8*E(17)^7+4*E(17)^8+4*E(17)^9+8*E(17)^10+8*E(17)^11+8*E(17)^12+4*E(17)^13+8*E(17)^14+4*E(17)^15+4*E(17)^16, -52*E(17)-52*E(17)^2-40*E(17)^3-52*E(17)^4-40*E(17)^5-40*E(17)^6-40*E(17)^7-52*E(17)^8-52*E(17)^9-40*E(17)^10-40*E(17)^11 -40*E(17)^12-52*E(17)^13-40*E(17)^14-52*E(17)^15-52*E(17)^16, -4*E(17)-4*E(17)^2-16*E(17)^3-4*E(17)^4-16*E(17)^5-16*E(17)^6-16*E(17)^7-4*E(17)^8-4*E(17)^9-16*E(17)^10-16*E(17)^11-16*E(17)^12-4*E(17)^13-16*E(17)^14-4*E(17)^15-4*E(17)^16, 108*E(17)+108*E(17)^2+80*E(17)^3+108*E(17)^4+80*E(17)^5+80*E(17)^6+80*E(17)^7+108*E(17)^8+108*E(17)^9+80*E(17)^10+80*E(17)^11+80*E(17)^12+108*E(17)^13+80*E(17)^14+108*E(17)^15+108*E(17)^16, -16*E(17)-16*E(17)^2-48*E(17)^3-16*E(17)^4-48*E(17)^5-48*E(17)^6-48*E(17)^7-16*E(17)^8-16*E(17)^9-48*E(17)^10-48*E(17)^11-48*E(17)^12-16*E(17)^13-48*E(17)^14-16*E(17)^15-16*E(17)^16 ], [ 1, -7*E(17)-7*E(17)^2-9*E(17)^3-7*E(17)^4-9*E(17)^5-9*E(17)^6-9*E(17)^7-7*E(17)^8-7*E(17)^9-9*E(17)^10-9*E(17)^11-9*E(17)^12-7*E(17)^13-9*E(17)^14-7*E(17)^15-7*E(17)^16, -25*E(17)-25*E(17)^2-19*E(17)^3-25*E(17)^4-19*E(17)^5-19*E(17)^6 -19*E(17)^7-25*E(17)^8-25*E(17)^9-19*E(17)^10-19*E(17)^11-19*E(17)^12-25*E(17)^13-19*E(17)^14-25*E(17)^15-25*E(17)^16, -15*E(17)-15*E(17)^2-11*E(17)^3-15*E(17)^4-11*E(17)^5-11*E(17)^6-11*E(17)^7-15*E(17)^8-15*E(17)^9-11*E(17)^10 -11*E(17)^11-11*E(17)^12-15*E(17)^13-11*E(17)^14-15*E(17)^15-15*E(17)^16, 4*E(17)+4*E(17)^2+20*E(17)^3+4*E(17)^4+20*E(17)^5+20*E(17)^6+20*E(17)^7+4*E(17)^8+4*E(17)^9+20*E(17)^10+20*E(17)^11+20*E(17)^12+4*E(17)^13+20*E(17)^14+4*E(17)^15 +4*E(17)^16, -4*E(17)-4*E(17)^2-12*E(17)^3-4*E(17)^4-12*E(17)^5-12*E(17)^6-12*E(17)^7-4*E(17)^8-4*E(17)^9-12*E(17)^10-12*E(17)^11-12*E(17)^12-4*E(17)^13-12*E(17)^14-4*E(17)^15-4*E(17)^16, 48*E(17)+48*E(17)^2+72*E(17)^3+48*E(17)^4+72*E(17)^5+72*E(17)^6+72*E(17)^7+48*E(17)^8+48*E(17)^9+72*E(17)^10+72*E(17)^11+72*E(17)^12+48*E(17)^13+72*E(17)^14+48*E(17)^15+48*E(17)^16, 32*E(17)+32*E(17)^2+8*E(17)^3+32*E(17)^4+8*E(17)^5 +8*E(17)^6+8*E(17)^7+32*E(17)^8+32*E(17)^9+8*E(17)^10+8*E(17)^11+8*E(17)^12+32*E(17)^13+8*E(17)^14+32*E(17)^15+32*E(17)^16, -8*E(17)-8*E(17)^2-24*E(17)^3-8*E(17)^4-24*E(17)^5-24*E(17)^6-24*E(17)^7-8*E(17)^8-8*E(17)^9-24*E(17)^10 -24*E(17)^11-24*E(17)^12-8*E(17)^13-24*E(17)^14-8*E(17)^15-8*E(17)^16, 24, 56*E(17)+56*E(17)^2+72*E(17)^3+56*E(17)^4+72*E(17)^5+72*E(17)^6+72*E(17)^7+56*E(17)^8+56*E(17)^9+72*E(17)^10+72*E(17)^11+72*E(17)^12+56*E(17)^13+72*E(17)^14 +56*E(17)^15+56*E(17)^16, 24*E(17)+24*E(17)^2+8*E(17)^3+24*E(17)^4+8*E(17)^5+8*E(17)^6+8*E(17)^7+24*E(17)^8+24*E(17)^9+8*E(17)^10+8*E(17)^11+8*E(17)^12+24*E(17)^13+8*E(17)^14+24*E(17)^15+24*E(17)^16, -32*E(17)-32*E(17)^2-16*E(17)^3-32*E(17)^4-16*E(17)^5-16*E(17)^6-16*E(17)^7-32*E(17)^8-32*E(17)^9-16*E(17)^10-16*E(17)^11-16*E(17)^12-32*E(17)^13-16*E(17)^14-32*E(17)^15-32*E(17)^16, 32*E(17)+32*E(17)^2-16*E(17)^3+32*E(17)^4-16*E(17)^5 -16*E(17)^6-16*E(17)^7+32*E(17)^8+32*E(17)^9-16*E(17)^10-16*E(17)^11-16*E(17)^12+32*E(17)^13-16*E(17)^14+32*E(17)^15+32*E(17)^16, -80*E(17)-80*E(17)^2-48*E(17)^3-80*E(17)^4-48*E(17)^5-48*E(17)^6-48*E(17)^7-80*E(17)^8-80*E(17)^9 -48*E(17)^10-48*E(17)^11-48*E(17)^12-80*E(17)^13-48*E(17)^14-80*E(17)^15-80*E(17)^16 ], [ 1, -7*E(17)-7*E(17)^2-E(17)^3-7*E(17)^4-E(17)^5-E(17)^6-E(17)^7-7*E(17)^8-7*E(17)^9-E(17)^10-E(17)^11-E(17)^12-7*E(17)^13-E(17)^14-7*E(17)^15 -7*E(17)^16, -E(17)-E(17)^2-5*E(17)^3-E(17)^4-5*E(17)^5-5*E(17)^6-5*E(17)^7-E(17)^8-E(17)^9-5*E(17)^10-5*E(17)^11-5*E(17)^12-E(17)^13-5*E(17)^14-E(17)^15-E(17)^16, 25*E(17)+25*E(17)^2+19*E(17)^3+25*E(17)^4+19*E(17)^5+19*E(17)^6 +19*E(17)^7+25*E(17)^8+25*E(17)^9+19*E(17)^10+19*E(17)^11+19*E(17)^12+25*E(17)^13+19*E(17)^14+25*E(17)^15+25*E(17)^16, -4*E(17)-4*E(17)^2-20*E(17)^3-4*E(17)^4-20*E(17)^5-20*E(17)^6-20*E(17)^7-4*E(17)^8-4*E(17)^9-20*E(17)^10-20*E(17)^11 -20*E(17)^12-4*E(17)^13-20*E(17)^14-4*E(17)^15-4*E(17)^16, -12*E(17)-12*E(17)^2-4*E(17)^3-12*E(17)^4-4*E(17)^5-4*E(17)^6-4*E(17)^7-12*E(17)^8-12*E(17)^9-4*E(17)^10-4*E(17)^11-4*E(17)^12-12*E(17)^13-4*E(17)^14-12*E(17)^15-12*E(17)^16, 20*E(17)^3+20*E(17)^5+20*E(17)^6+20*E(17)^7+20*E(17)^10+20*E(17)^11+20*E(17)^12+20*E(17)^14, -64*E(17)-64*E(17)^2-80*E(17)^3-64*E(17)^4-80*E(17)^5-80*E(17)^6-80*E(17)^7-64*E(17)^8-64*E(17)^9-80*E(17)^10-80*E(17)^11-80*E(17)^12-64*E(17)^13 -80*E(17)^14-64*E(17)^15-64*E(17)^16, 40*E(17)+40*E(17)^2+16*E(17)^3+40*E(17)^4+16*E(17)^5+16*E(17)^6+16*E(17)^7+40*E(17)^8+40*E(17)^9+16*E(17)^10+16*E(17)^11+16*E(17)^12+40*E(17)^13+16*E(17)^14+40*E(17)^15+40*E(17)^16, 40*E(17)+40*E(17)^2+16*E(17)^3+40*E(17)^4+16*E(17)^5+16*E(17)^6+16*E(17)^7+40*E(17)^8+40*E(17)^9+16*E(17)^10+16*E(17)^11+16*E(17)^12+40*E(17)^13+16*E(17)^14+40*E(17)^15+40*E(17)^16, 8*E(17)+8*E(17)^2+4*E(17)^3+8*E(17)^4+4*E(17)^5+4*E(17)^6 +4*E(17)^7+8*E(17)^8+8*E(17)^9+4*E(17)^10+4*E(17)^11+4*E(17)^12+8*E(17)^13+4*E(17)^14+8*E(17)^15+8*E(17)^16, -40*E(17)-40*E(17)^2-52*E(17)^3-40*E(17)^4-52*E(17)^5-52*E(17)^6-52*E(17)^7-40*E(17)^8-40*E(17)^9-52*E(17)^10-52*E(17)^11 -52*E(17)^12-40*E(17)^13-52*E(17)^14-40*E(17)^15-40*E(17)^16, -16*E(17)-16*E(17)^2-4*E(17)^3-16*E(17)^4-4*E(17)^5-4*E(17)^6-4*E(17)^7-16*E(17)^8-16*E(17)^9-4*E(17)^10-4*E(17)^11-4*E(17)^12-16*E(17)^13-4*E(17)^14-16*E(17)^15-16*E(17)^16, 80*E(17)+80*E(17)^2+108*E(17)^3+80*E(17)^4+108*E(17)^5+108*E(17)^6+108*E(17)^7+80*E(17)^8+80*E(17)^9+108*E(17)^10+108*E(17)^11+108*E(17)^12+80*E(17)^13+108*E(17)^14+80*E(17)^15+80*E(17)^16, -48*E(17)-48*E(17)^2-16*E(17)^3-48*E(17)^4-16*E(17)^5-16*E(17)^6-16*E(17)^7-48*E(17)^8-48*E(17)^9-16*E(17)^10-16*E(17)^11-16*E(17)^12-48*E(17)^13-16*E(17)^14-48*E(17)^15-48*E(17)^16 ], [ 1, 9, -3, 13, 4, -12, 28, 32, 80, -80, 12, -60, 84, -28, -80 ], [ 1, E(9)^2+3*E(9)^3+2*E(9)^4+2*E(9)^5+3*E(9)^6+E(9)^7, -10*E(9)^2-6*E(9)^3+4*E(9)^4+4*E(9)^5-6*E(9)^6-10*E(9)^7, 12*E(9)^2-E(9)^3+3*E(9)^4+3*E(9)^5-E(9)^6+12*E(9)^7, 14*E(9)^2-10*E(9)^3+22*E(9)^4+22*E(9)^5-10*E(9)^6+14*E(9)^7, -15*E(9)^2-27*E(9)^4-27*E(9)^5-15*E(9)^7, -18*E(9)^2-40*E(9)^3-6*E(9)^4-6*E(9)^5-40*E(9)^6-18*E(9)^7, -2*E(9)^2-14*E(9)^3-10*E(9)^4-10*E(9)^5-14*E(9)^6-2*E(9)^7, -30*E(9)^2+34*E(9)^3-3*E(9)^4-3*E(9)^5+34*E(9)^6-30*E(9)^7, -14*E(9)^2-19*E(9)^3-34*E(9)^4-34*E(9)^5-19*E(9)^6-14*E(9)^7, -11*E(9)^2+30*E(9)^3-7*E(9)^4-7*E(9)^5+30*E(9)^6-11*E(9)^7, 27*E(9)^2+12*E(9)^3+30*E(9)^4+30*E(9)^5+12*E(9)^6 +27*E(9)^7, 36*E(9)^2+6*E(9)^3-18*E(9)^4-18*E(9)^5+6*E(9)^6+36*E(9)^7, 12*E(9)^2-38*E(9)^3+36*E(9)^4+36*E(9)^5-38*E(9)^6+12*E(9)^7, -2*E(9)^2+44*E(9)^3+8*E(9)^4+8*E(9)^5+44*E(9)^6-2*E(9)^7 ], [ 1, E(9)^2+3*E(9)^3-E(9)^4-E(9)^5+3*E(9)^6+E(9)^7, 14*E(9)^2-6*E(9)^3+10*E(9)^4+10*E(9)^5-6*E(9)^6+14*E(9)^7, -9*E(9)^2-E(9)^3-12*E(9)^4-12*E(9)^5-E(9)^6-9*E(9)^7, 8*E(9)^2-10*E(9)^3-14*E(9)^4-14*E(9)^5-10*E(9)^6+8*E(9)^7, -12*E(9)^2+15*E(9)^4+15*E(9)^5-12*E(9)^7, 12*E(9)^2-40*E(9)^3+18*E(9)^4+18*E(9)^5-40*E(9)^6+12*E(9)^7, -8*E(9)^2-14*E(9)^3+2*E(9)^4+2*E(9)^5-14*E(9)^6-8*E(9)^7, 27*E(9)^2+34*E(9)^3+30*E(9)^4+30*E(9)^5+34*E(9)^6+27*E(9)^7, -20*E(9)^2-19*E(9)^3+14*E(9)^4+14*E(9)^5-19*E(9)^6-20*E(9)^7, 4*E(9)^2+30*E(9)^3+11*E(9)^4+11*E(9)^5+30*E(9)^6+4*E(9)^7, 3*E(9)^2+12*E(9)^3-27*E(9)^4-27*E(9)^5+12*E(9)^6+3*E(9)^7, -54*E(9)^2+6*E(9)^3-36*E(9)^4-36*E(9)^5+6*E(9)^6-54*E(9)^7, 24*E(9)^2-38*E(9)^3-12*E(9)^4-12*E(9)^5-38*E(9)^6+24*E(9)^7, 10*E(9)^2+44*E(9)^3+2*E(9)^4+2*E(9)^5+44*E(9)^6+10*E(9)^7 ], [ 1, -2*E(9)^2+3*E(9)^3-E(9)^4-E(9)^5+3*E(9)^6-2*E(9)^7, -4*E(9)^2-6*E(9)^3-14*E(9)^4-14*E(9)^5-6*E(9)^6-4*E(9)^7, -3*E(9)^2-E(9)^3+9*E(9)^4+9*E(9)^5-E(9)^6-3*E(9)^7, -22*E(9)^2-10*E(9)^3-8*E(9)^4-8*E(9)^5-10*E(9)^6-22*E(9)^7, 27*E(9)^2+12*E(9)^4+12*E(9)^5+27*E(9)^7, 6*E(9)^2-40*E(9)^3-12*E(9)^4-12*E(9)^5-40*E(9)^6+6*E(9)^7, 10*E(9)^2-14*E(9)^3+8*E(9)^4+8*E(9)^5-14*E(9)^6+10*E(9)^7, 3*E(9)^2+34*E(9)^3-27*E(9)^4-27*E(9)^5+34*E(9)^6+3*E(9)^7, 34*E(9)^2-19*E(9)^3+20*E(9)^4+20*E(9)^5-19*E(9)^6+34*E(9)^7, 7*E(9)^2+30*E(9)^3-4*E(9)^4-4*E(9)^5+30*E(9)^6+7*E(9)^7, -30*E(9)^2+12*E(9)^3-3*E(9)^4-3*E(9)^5+12*E(9)^6-30*E(9)^7, 18*E(9)^2+6*E(9)^3+54*E(9)^4+54*E(9)^5+6*E(9)^6+18*E(9)^7, -36*E(9)^2-38*E(9)^3-24*E(9)^4-24*E(9)^5-38*E(9)^6-36*E(9)^7, -8*E(9)^2+44*E(9)^3-10*E(9)^4-10*E(9)^5+44*E(9)^6-8*E(9)^7 ], [ 1, 3, -15, -5, -8, -48, -8, 8, 8, 40, 24, -24, -24, 8, 40 ], [ 1, -9, -12, 13, 22, 42, -26, 14, -1, -44, 21, -33, -78, 26, 64 ], [ 1, -7, -15, -15, 12, 12, 12, -72, 48, 0, -36, 36, 36, -12, 0 ], [ 1, -9, 13, 3, -48, -8, -16, -16, -16, -24, 56, 32, 32, 16, -16 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 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672, 544 ], [ 0, 16, 24, 48, 140, 148, 368, 264, 264, 280, 296, 296, 544, 624, 576 ], [ 0, 12, 40, 36, 148, 156, 256, 296, 316, 288, 296, 284, 584, 576, 600 ], [ 0, 4, 46, 22, 184, 128, 292, 304, 280, 288, 312, 276, 604, 572, 576 ], [ 0, 16, 38, 46, 132, 148, 304, 236, 288, 292, 276, 264, 592, 632, 624 ], [ 0, 14, 42, 28, 132, 158, 280, 288, 298, 300, 288, 272, 580, 596, 612 ], [ 0, 16, 34, 32, 140, 144, 288, 292, 300, 278, 292, 288, 596, 604, 584 ], [ 0, 10, 36, 36, 148, 148, 312, 276, 288, 292, 322, 284, 588, 544, 604 ], [ 0, 12, 40, 36, 148, 142, 276, 264, 272, 288, 284, 242, 652, 640, 592 ], [ 0, 14, 29, 45, 136, 146, 302, 296, 290, 298, 294, 326, 570, 566, 576 ], [ 1, 13, 46, 42, 156, 144, 286, 316, 298, 302, 272, 320, 566, 538, 588 ], [ 0, 10, 30, 34, 144, 150, 288, 312, 306, 292, 302, 296, 576, 588, 560 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3888 ], [ 0, 0, 48, 0, 48, 96, 384, 384, 192, 288, 144, 336, 672, 480, 816 ], [ 0, 16, 64, 64, 160, 144, 288, 224, 272, 320, 240, 256, 704, 480, 656 ], [ 0, 0, 64, 64, 176, 160, 256, 224, 336, 368, 304, 256, 512, 544, 624 ], [ 0, 4, 40, 44, 128, 152, 296, 288, 304, 296, 280, 264, 592, 576, 624 ], [ 0, 8, 36, 40, 152, 152, 296, 312, 292, 228, 272, 308, 576, 600, 616 ], [ 0, 16, 36, 32, 148, 148, 280, 288, 284, 292, 304, 316, 584, 576, 584 ], [ 0, 16, 28, 28, 144, 156, 288, 288, 280, 284, 316, 308, 560, 624, 568 ], [ 0, 8, 34, 42, 152, 146, 284, 280, 274, 330, 294, 304, 568, 612, 560 ], [ 0, 12, 40, 46, 148, 114, 292, 284, 330, 284, 290, 284, 604, 584, 576 ], [ 0, 6, 30, 38, 140, 136, 304, 316, 294, 290, 268, 290, 576, 604, 596 ], [ 0, 14, 32, 32, 132, 154, 316, 308, 304, 284, 290, 282, 600, 592, 548 ], [ 0, 14, 44, 32, 148, 144, 292, 280, 284, 302, 288, 300, 584, 576, 600 ], [ 0, 10, 30, 34, 144, 150, 288, 312, 306, 292, 302, 296, 576, 588, 560 ], [ 1, 17, 41, 39, 156, 154, 292, 284, 280, 288, 298, 274, 600, 560, 604 ] ] ] ), rec( name := "M24", sbgname := "M23", degree := 24, rank := 2, permchar := "1a + 23a", charnmbs := [ 1, 2 ], ctbl := [ [ 1, 23 ], [ 1, -1 ] ], mats := [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 23 ], [ 1, 22 ] ] ] ), rec( name := "M24", sbgname := "2^4:A8", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 759, rank := 4, permchar := "1a + 23a + 252a + 483a", charnmbs := [ 1, 2, 7, 9 ], ctbl := [ [ 1, 30, 280, 448 ], [ 1, -15, 70, -56 ], [ 1, 7, 4, -12 ], [ 1, -3, -6, 8 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 30, 0, 0 ], [ 1, 1, 28, 0 ], [ 0, 3, 3, 24 ], [ 0, 0, 15, 15 ] ], [ [ 0, 0, 280, 0 ], [ 0, 28, 28, 224 ], [ 1, 3, 140, 136 ], [ 0, 15, 85, 180 ] ], [ [ 0, 0, 0, 448 ], [ 0, 0, 224, 224 ], [ 0, 24, 136, 288 ], [ 1, 15, 180, 252 ] ] ] ), rec( name := "M24", sbgname := "2^6:3.A6 leq 2^6:3.S6", filename := "2^6:3.A6", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 3542, rank := 5, permchar := "1a + 252a + 483a + 1035a + 1771a", charnmbs := [ 1, 7, 9, 14, 18 ], ctbl := [ [ 1, 1, 180, 480, 2880 ], [ 1, 1, 42, 20, -64 ], [ 1, 1, -18, 40, -24 ], [ 1, 1, -2, -24, 24 ], [ 1, -1, 0, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 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 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 180, 0, 0 ], [ 0, 0, 180, 0, 0 ], [ 1, 1, 34, 48, 96 ], [ 0, 0, 18, 18, 144 ], [ 0, 0, 6, 24, 150 ] ], [ [ 0, 0, 0, 480, 0 ], [ 0, 0, 0, 480, 0 ], [ 0, 0, 48, 48, 384 ], [ 1, 1, 18, 76, 384 ], [ 0, 0, 24, 64, 392 ] ], [ [ 0, 0, 0, 0, 2880 ], [ 0, 0, 0, 0, 2880 ], [ 0, 0, 96, 384, 2400 ], [ 0, 0, 144, 384, 2352 ], [ 1, 1, 150, 392, 2336 ] ] ] ), rec( name := "M24", sbgname := "2^6:3.S6", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. 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Soicher.", degree := 2024, rank := 5, permchar := "1a + 23a + 252a + 483a + 1265a", charnmbs := [ 1, 2, 7, 9, 17 ], ctbl := [ [ 1, 63, 210, 630, 1120 ], [ 1, 39, -30, 150, -160 ], [ 1, 17, 3, -37, 16 ], [ 1, -3, 23, 3, -24 ], [ 1, -3, -9, 3, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 63, 0, 0, 0 ], [ 1, 22, 0, 40, 0 ], [ 0, 0, 6, 9, 48 ], [ 0, 4, 3, 40, 16 ], [ 0, 0, 9, 9, 45 ] ], [ [ 0, 0, 210, 0, 0 ], [ 0, 0, 20, 30, 160 ], [ 1, 6, 32, 75, 96 ], [ 0, 3, 25, 54, 128 ], [ 0, 9, 18, 72, 111 ] ], [ [ 0, 0, 0, 630, 0 ], [ 0, 40, 30, 400, 160 ], [ 0, 9, 75, 162, 384 ], [ 1, 40, 54, 247, 288 ], [ 0, 9, 72, 162, 387 ] ], [ [ 0, 0, 0, 0, 1120 ], [ 0, 0, 160, 160, 800 ], [ 0, 48, 96, 384, 592 ], [ 0, 16, 128, 288, 688 ], [ 1, 45, 111, 387, 576 ] ] ] ), rec( name := "M24", sbgname := "M12.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. 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2160, 2064 ] ] ] ), rec( name := "McL", sbgname := "2.A8", degree := 22275, rank := 6, permchar := "1a + 252a + 1750a + 5103a + 5544a + 9625a", charnmbs := [ 1, 4, 9, 14, 15, 20 ], ctbl := [ [ 1, 210, 2240, 5040, 6720, 8064 ], [ 1, 45, 260, 90, -540, 144 ], [ 1, 39, -28, 72, 60, -144 ], [ 1, -5, 60, -60, 60, -56 ], [ 1, -15, -10, 90, -30, -36 ], [ 1, 3, -28, -36, -12, 72 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 210, 0, 0, 0, 0 ], [ 1, 25, 32, 120, 32, 0 ], [ 0, 3, 36, 54, 27, 90 ], [ 0, 5, 24, 45, 64, 72 ], [ 0, 1, 9, 48, 86, 66 ], [ 0, 0, 25, 45, 55, 85 ] ], [ [ 0, 0, 2240, 0, 0, 0 ], [ 0, 32, 384, 576, 288, 960 ], [ 1, 36, 331, 513, 513, 846 ], [ 0, 24, 228, 512, 636, 840 ], [ 0, 9, 171, 477, 809, 774 ], [ 0, 25, 235, 525, 645, 810 ] ], [ [ 0, 0, 0, 5040, 0, 0 ], [ 0, 120, 576, 1080, 1536, 1728 ], [ 0, 54, 513, 1152, 1431, 1890 ], [ 1, 45, 512, 1170, 1512, 1800 ], [ 0, 48, 477, 1134, 1563, 1818 ], [ 0, 45, 525, 1125, 1515, 1830 ] ], [ [ 0, 0, 0, 0, 6720, 0 ], [ 0, 32, 288, 1536, 2752, 2112 ], [ 0, 27, 513, 1431, 2427, 2322 ], [ 0, 64, 636, 1512, 2084, 2424 ], [ 1, 86, 809, 1563, 1771, 2490 ], [ 0, 55, 645, 1515, 2075, 2430 ] ], [ [ 0, 0, 0, 0, 0, 8064 ], [ 0, 0, 960, 1728, 2112, 3264 ], [ 0, 90, 846, 1890, 2322, 2916 ], [ 0, 72, 840, 1800, 2424, 2928 ], [ 0, 66, 774, 1818, 2490, 2916 ], [ 1, 85, 810, 1830, 2430, 2908 ] ] ] ), rec( name := "McL", sbgname := "3^{1+4}:2S5", filename := "3^1+4:2S5", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 15400, rank := 5, permchar := "1a + 252a + 4500a + 5103a + 5544a", charnmbs := [ 1, 4, 12, 14, 15 ], ctbl := [ [ 1, 90, 1215, 2430, 11664 ], [ 1, 35, 225, -45, -216 ], [ 1, -1, -3, -69, 72 ], [ 1, 10, -25, 30, -16 ], [ 1, -10, 15, 30, -36 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 90, 0, 0, 0 ], [ 1, 8, 54, 27, 0 ], [ 0, 4, 32, 6, 48 ], [ 0, 1, 3, 14, 72 ], [ 0, 0, 5, 15, 70 ] ], [ [ 0, 0, 1215, 0, 0 ], [ 0, 54, 432, 81, 648 ], [ 1, 32, 246, 168, 768 ], [ 0, 3, 84, 192, 936 ], [ 0, 5, 80, 195, 935 ] ], [ [ 0, 0, 0, 2430, 0 ], [ 0, 27, 81, 378, 1944 ], [ 0, 6, 168, 384, 1872 ], [ 1, 14, 192, 351, 1872 ], [ 0, 15, 195, 390, 1830 ] ], [ [ 0, 0, 0, 0, 11664 ], [ 0, 0, 648, 1944, 9072 ], [ 0, 48, 768, 1872, 8976 ], [ 0, 72, 936, 1872, 8784 ], [ 1, 70, 935, 1830, 8828 ] ] ] ), rec( name := "McL", sbgname := "M22", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 2025, rank := 4, permchar := "1a + 22a + 252a + 1750a", permchar2 := "1a + 22a + 252a + 1750a", charnmbs := [ 1, 2, 4, 9 ], charnmbs2 := [ 1, 2, 4, 9 ], ctbl := [ [ 1, 330, 462, 1232 ], [ 1, -120, 147, -28 ], [ 1, 30, 27, -58 ], [ 1, -3, -6, 8 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 330, 0, 0 ], [ 1, 7, 154, 168 ], [ 0, 110, 20, 200 ], [ 0, 45, 75, 210 ] ], [ [ 0, 0, 462, 0 ], [ 0, 154, 28, 280 ], [ 1, 20, 185, 256 ], [ 0, 75, 96, 291 ] ], [ [ 0, 0, 0, 1232 ], [ 0, 168, 280, 784 ], [ 0, 200, 256, 776 ], [ 1, 210, 291, 730 ] ] ] ), rec( name := "McL", sbgname := "U3(5)", filename := "U35", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 7128, rank := 5, permchar := "1a + 22a + 252a + 1750a + 5103a", charnmbs := [ 1, 2, 4, 9, 14 ], ctbl := [ [ 1, 252, 750, 2625, 3500 ], [ 1, -126, 300, -525, 350 ], [ 1, 54, 90, -15, -130 ], [ 1, -18, 12, 51, -46 ], [ 1, 4, -10, -15, 20 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 252, 0, 0, 0 ], [ 1, 1, 125, 0, 125 ], [ 0, 42, 0, 168, 42 ], [ 0, 0, 48, 48, 156 ], [ 0, 9, 9, 117, 117 ] ], [ [ 0, 0, 750, 0, 0 ], [ 0, 125, 0, 500, 125 ], [ 1, 0, 224, 77, 448 ], [ 0, 48, 22, 376, 304 ], [ 0, 9, 96, 228, 417 ] ], [ [ 0, 0, 0, 2625, 0 ], [ 0, 0, 500, 500, 1625 ], [ 0, 168, 77, 1316, 1064 ], [ 1, 48, 376, 808, 1392 ], [ 0, 117, 228, 1044, 1236 ] ], [ [ 0, 0, 0, 0, 3500 ], [ 0, 125, 125, 1625, 1625 ], [ 0, 42, 448, 1064, 1946 ], [ 0, 156, 304, 1392, 1648 ], [ 1, 117, 417, 1236, 1729 ] ] ] ), rec( name := "McL", sbgname := "U4(3)", filename := "U43", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 275, rank := 3, permchar := "1a + 22a + 252a", charnmbs := [ 1, 2, 4 ], ctbl := [ [ 1, 112, 162 ], [ 1, -28, 27 ], [ 1, 2, -3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 112, 0 ], [ 1, 30, 81 ], [ 0, 56, 56 ] ], [ [ 0, 0, 162 ], [ 0, 81, 81 ], [ 1, 56, 105 ] ] ] ), rec( name := "McL.2", sbgname := "U4(3) leq U4(3).2_3", filename := "U43", degree := 550, rank := 6, permchar := "1a^{+-} + 22a^{+-} + 252a^{+-}", charnmbs := [ 1, 2, 3, 4, 7, 8 ], ctbl := [ [ 1, 1, 112, 112, 162, 162 ], [ 1, -1, -112, 112, 162, -162 ], [ 1, 1, -28, -28, 27, 27 ], [ 1, -1, 28, -28, 27, -27 ], [ 1, 1, 2, 2, -3, -3 ], [ 1, -1, -2, 2, -3, 3 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 112, 0, 0, 0 ], [ 0, 0, 0, 112, 0, 0 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mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 180, 0, 0, 0, 0, 0 ], [ 0, 0, 180, 0, 0, 0, 0, 0 ], [ 1, 1, 16, 54, 54, 54, 0, 0 ], [ 0, 0, 8, 32, 32, 12, 48, 48 ], [ 0, 0, 8, 32, 32, 12, 48, 48 ], [ 0, 0, 2, 3, 3, 28, 72, 72 ], [ 0, 0, 0, 5, 5, 30, 70, 70 ], [ 0, 0, 0, 5, 5, 30, 70, 70 ] ], [ [ 0, 0, 0, 1215, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1215, 0, 0, 0 ], [ 0, 0, 54, 216, 216, 81, 324, 324 ], [ 1, 0, 32, 132, 114, 168, 384, 384 ], [ 0, 1, 32, 114, 132, 168, 384, 384 ], [ 0, 0, 3, 42, 42, 192, 468, 468 ], [ 0, 0, 5, 40, 40, 195, 490, 445 ], [ 0, 0, 5, 40, 40, 195, 445, 490 ] ], [ [ 0, 0, 0, 0, 1215, 0, 0, 0 ], [ 0, 0, 0, 1215, 0, 0, 0, 0 ], [ 0, 0, 54, 216, 216, 81, 324, 324 ], [ 0, 1, 32, 114, 132, 168, 384, 384 ], [ 1, 0, 32, 132, 114, 168, 384, 384 ], [ 0, 0, 3, 42, 42, 192, 468, 468 ], [ 0, 0, 5, 40, 40, 195, 445, 490 ], [ 0, 0, 5, 40, 40, 195, 490, 445 ] ], [ [ 0, 0, 0, 0, 0, 4860, 0, 0 ], [ 0, 0, 0, 0, 0, 4860, 0, 0 ], [ 0, 0, 54, 81, 81, 756, 1944, 1944 ], [ 0, 0, 12, 168, 168, 768, 1872, 1872 ], [ 0, 0, 12, 168, 168, 768, 1872, 1872 ], [ 1, 1, 28, 192, 192, 702, 1872, 1872 ], [ 0, 0, 30, 195, 195, 780, 1830, 1830 ], [ 0, 0, 30, 195, 195, 780, 1830, 1830 ] ], [ [ 0, 0, 0, 0, 0, 0, 11664, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 11664 ], [ 0, 0, 0, 324, 324, 1944, 4536, 4536 ], [ 0, 0, 48, 384, 384, 1872, 4704, 4272 ], [ 0, 0, 48, 384, 384, 1872, 4272, 4704 ], [ 0, 0, 72, 468, 468, 1872, 4392, 4392 ], [ 1, 0, 70, 490, 445, 1830, 4828, 4000 ], [ 0, 1, 70, 445, 490, 1830, 4000, 4828 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 11664 ], [ 0, 0, 0, 0, 0, 0, 11664, 0 ], [ 0, 0, 0, 324, 324, 1944, 4536, 4536 ], [ 0, 0, 48, 384, 384, 1872, 4272, 4704 ], [ 0, 0, 48, 384, 384, 1872, 4704, 4272 ], [ 0, 0, 72, 468, 468, 1872, 4392, 4392 ], [ 0, 1, 70, 445, 490, 1830, 4000, 4828 ], [ 1, 0, 70, 490, 445, 1830, 4828, 4000 ] ] ] ), rec( name := "McL.2", sbgname := "2.S8", degree := 22275, rank := 6, permchar := "1a^+ + 252a^+ + 1750a^+ + 5103a^+ + 5544a^+ + 9625a^+", charnmbs := [ 1, 7, 14, 24, 26, 30 ], ctbl := [ [ 1, 210, 2240, 5040, 6720, 8064 ], [ 1, 45, 260, 90, -540, 144 ], [ 1, 39, -28, 72, 60, -144 ], [ 1, -5, 60, -60, 60, -56 ], [ 1, -15, -10, 90, -30, -36 ], [ 1, 3, -28, -36, -12, 72 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 210, 0, 0, 0, 0 ], [ 1, 25, 32, 120, 32, 0 ], [ 0, 3, 36, 54, 27, 90 ], [ 0, 5, 24, 45, 64, 72 ], [ 0, 1, 9, 48, 86, 66 ], [ 0, 0, 25, 45, 55, 85 ] ], [ [ 0, 0, 2240, 0, 0, 0 ], [ 0, 32, 384, 576, 288, 960 ], [ 1, 36, 331, 513, 513, 846 ], [ 0, 24, 228, 512, 636, 840 ], [ 0, 9, 171, 477, 809, 774 ], [ 0, 25, 235, 525, 645, 810 ] ], [ [ 0, 0, 0, 5040, 0, 0 ], [ 0, 120, 576, 1080, 1536, 1728 ], [ 0, 54, 513, 1152, 1431, 1890 ], [ 1, 45, 512, 1170, 1512, 1800 ], [ 0, 48, 477, 1134, 1563, 1818 ], [ 0, 45, 525, 1125, 1515, 1830 ] ], [ [ 0, 0, 0, 0, 6720, 0 ], [ 0, 32, 288, 1536, 2752, 2112 ], [ 0, 27, 513, 1431, 2427, 2322 ], [ 0, 64, 636, 1512, 2084, 2424 ], [ 1, 86, 809, 1563, 1771, 2490 ], [ 0, 55, 645, 1515, 2075, 2430 ] ], [ [ 0, 0, 0, 0, 0, 8064 ], [ 0, 0, 960, 1728, 2112, 3264 ], [ 0, 90, 846, 1890, 2322, 2916 ], [ 0, 72, 840, 1800, 2424, 2928 ], [ 0, 66, 774, 1818, 2490, 2916 ], [ 1, 85, 810, 1830, 2430, 2908 ] ] ] ), rec( name := "McL.2", sbgname := "2.A8 leq 2.S8", filename := "2.A8", degree := 44550, rank := 12, permchar := "1a^{+-} + 252a^{+-} + 1750a^{+-} + 5103a^{+-} + 5544a^{+-} + 9625a^{+-}", charnmbs := [ 1, 2, 7, 8, 14, 15, 24, 25, 26, 27, 30, 31 ], ctbl := [ [ 1, 1, 210, 210, 2240, 2240, 5040, 5040, 6720, 6720, 8064, 8064 ], [ 1, -1, -210, 210, -2240, 2240, 5040, -5040, -6720, 6720, -8064, 8064 ], [ 1, 1, 45, 45, 260, 260, 90, 90, -540, -540, 144, 144 ], [ 1, -1, -45, 45, -260, 260, 90, -90, 540, -540, -144, 144 ], [ 1, 1, 39, 39, -28, -28, 72, 72, 60, 60, -144, -144 ], [ 1, -1, -39, 39, 28, -28, 72, -72, -60, 60, 144, -144 ], [ 1, 1, -5, -5, 60, 60, -60, -60, 60, 60, -56, -56 ], [ 1, -1, 5, -5, -60, 60, -60, 60, -60, 60, 56, -56 ], [ 1, 1, -15, -15, -10, -10, 90, 90, -30, -30, -36, -36 ], [ 1, -1, 15, -15, 10, -10, 90, -90, 30, -30, 36, -36 ], [ 1, 1, 3, 3, -28, -28, -36, -36, -12, -12, 72, 72 ], [ 1, -1, -3, 3, 28, -28, -36, 36, 12, -12, -72, 72 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 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E. Praeger and L. H. Soicher.", degree := 15400, rank := 5, permchar := "1a^+ + 252a^+ + 4500a^+ + 5103a^+ + 5544a^+", charnmbs := [ 1, 7, 20, 24, 26 ], ctbl := [ [ 1, 90, 1215, 2430, 11664 ], [ 1, 35, 225, -45, -216 ], [ 1, -1, -3, -69, 72 ], [ 1, 10, -25, 30, -16 ], [ 1, -10, 15, 30, -36 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 90, 0, 0, 0 ], [ 1, 8, 54, 27, 0 ], [ 0, 4, 32, 6, 48 ], [ 0, 1, 3, 14, 72 ], [ 0, 0, 5, 15, 70 ] ], [ [ 0, 0, 1215, 0, 0 ], [ 0, 54, 432, 81, 648 ], [ 1, 32, 246, 168, 768 ], [ 0, 3, 84, 192, 936 ], [ 0, 5, 80, 195, 935 ] ], [ [ 0, 0, 0, 2430, 0 ], [ 0, 27, 81, 378, 1944 ], [ 0, 6, 168, 384, 1872 ], [ 1, 14, 192, 351, 1872 ], [ 0, 15, 195, 390, 1830 ] ], [ [ 0, 0, 0, 0, 11664 ], [ 0, 0, 648, 1944, 9072 ], [ 0, 48, 768, 1872, 8976 ], [ 0, 72, 936, 1872, 8784 ], [ 1, 70, 935, 1830, 8828 ] ] ] ), rec( name := "McL.2", sbgname := "U3(5).2", filename := "U35.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 7128, rank := 5, permchar := "1a^+ + 22a^- + 252a^+ + 1750a^+ + 5103a^+", charnmbs := [ 1, 4, 7, 14, 24 ], ctbl := [ [ 1, 252, 750, 2625, 3500 ], [ 1, -126, 300, -525, 350 ], [ 1, 54, 90, -15, -130 ], [ 1, -18, 12, 51, -46 ], [ 1, 4, -10, -15, 20 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 252, 0, 0, 0 ], [ 1, 1, 125, 0, 125 ], [ 0, 42, 0, 168, 42 ], [ 0, 0, 48, 48, 156 ], [ 0, 9, 9, 117, 117 ] ], [ [ 0, 0, 750, 0, 0 ], [ 0, 125, 0, 500, 125 ], [ 1, 0, 224, 77, 448 ], [ 0, 48, 22, 376, 304 ], [ 0, 9, 96, 228, 417 ] ], [ [ 0, 0, 0, 2625, 0 ], [ 0, 0, 500, 500, 1625 ], [ 0, 168, 77, 1316, 1064 ], [ 1, 48, 376, 808, 1392 ], [ 0, 117, 228, 1044, 1236 ] ], [ [ 0, 0, 0, 0, 3500 ], [ 0, 125, 125, 1625, 1625 ], [ 0, 42, 448, 1064, 1946 ], [ 0, 156, 304, 1392, 1648 ], [ 1, 117, 417, 1236, 1729 ] ] ] ), rec( name := "McL.2", sbgname := "U4(3).2_3", filename := "U43.2_3", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 275, rank := 3, permchar := "1a^+ + 22a^+ + 252a^+", charnmbs := [ 1, 3, 7 ], ctbl := [ [ 1, 112, 162 ], [ 1, -28, 27 ], [ 1, 2, -3 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 112, 0 ], [ 1, 30, 81 ], [ 0, 56, 56 ] ], [ [ 0, 0, 162 ], [ 0, 81, 81 ], [ 1, 56, 105 ] ] ] ), rec( name := "He", sbgname := "2^2.L3(4).3 leq 2^2.L3(4).S3", filename := "2^2.L34.3", degree := 16660, rank := 10, permchar := "1a + 51ab + 680a + 1029ab + 1275a + 1920a + 4352a + 6272a", charnmbs := [ 1, 2, 3, 6, 7, 8, 9, 12, 14, 15 ], ctbl := [ [ 1, 1, 105, 105, 1344, 1344, 1440, 1680, 1680, 8960 ], [ 1, 1, 35, 35, 224, 224, -240, 280*E(7)^3+280*E(7)^5+280*E(7)^6, 280*E(7)+280*E(7)^2+280*E(7)^4, 0 ], [ 1, 1, 35, 35, 224, 224, -240, 280*E(7)+280*E(7)^2+280*E(7)^4, 280*E(7)^3+280*E(7)^5+280*E(7)^6, 0 ], [ 1, 1, 21, 21, 0, 0, 12, 84, 84, -224 ], [ 1, -1, -5*E(17)-5*E(17)^2+5*E(17)^3-5*E(17)^4+5*E(17)^5+5*E(17)^6+5*E(17)^7-5*E(17)^8-5*E(17)^9+5*E(17)^10+5*E(17)^11+5*E(17)^12-5*E(17)^13+5*E(17)^14 -5*E(17)^15-5*E(17)^16, 5*E(17)+5*E(17)^2-5*E(17)^3+5*E(17)^4-5*E(17)^5-5*E(17)^6-5*E(17)^7+5*E(17)^8+5*E(17)^9-5*E(17)^10-5*E(17)^11-5*E(17)^12+5*E(17)^13-5*E(17)^14+5*E(17)^15+5*E(17)^16, -64, 64, 0, 0, 0, 0 ], [ 1, -1, 5*E(17)+5*E(17)^2-5*E(17)^3+5*E(17)^4-5*E(17)^5-5*E(17)^6-5*E(17)^7+5*E(17)^8+5*E(17)^9-5*E(17)^10-5*E(17)^11-5*E(17)^12+5*E(17)^13-5*E(17)^14+5*E(17)^15+5*E(17)^16, -5*E(17)-5*E(17)^2+5*E(17)^3-5*E(17)^4+5*E(17)^5+5*E(17)^6+5*E(17)^7 -5*E(17)^8-5*E(17)^9+5*E(17)^10+5*E(17)^11+5*E(17)^12-5*E(17)^13+5*E(17)^14-5*E(17)^15-5*E(17)^16, -64, 64, 0, 0, 0, 0 ], [ 1, 1, 7, 7, 0, 0, 96, -56, -56, 0 ], [ 1, 1, -14, -14, 35, 35, 12, 14, 14, -84 ], [ 1, 1, 0, 0, -21, -21, -30, 0, 0, 70 ], [ 1, -1, 0, 0, 21, -21, 0, 0, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 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264, 376, 96, 864 ], [ 0, 0, 9, 9, 135, 135, 144, 162, 162, 924 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 1680, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1680, 0, 0 ], [ 0, 0, 16, 16, 64, 64, 192, 560, 0, 768 ], [ 0, 0, 16, 16, 64, 64, 192, 560, 0, 768 ], [ 0, 0, 5, 5, 105, 105, 180, 330, 50, 900 ], [ 0, 0, 5, 5, 105, 105, 180, 330, 50, 900 ], [ 0, 0, 14, 14, 168, 168, 84, 28, 308, 896 ], [ 0, 0, 0, 0, 40, 40, 264, 96, 376, 864 ], [ 1, 1, 35, 35, 264, 264, 24, 96, 96, 864 ], [ 0, 0, 9, 9, 135, 135, 144, 162, 162, 924 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 8960 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 8960 ], [ 0, 0, 0, 0, 768, 768, 768, 768, 768, 5120 ], [ 0, 0, 0, 0, 768, 768, 768, 768, 768, 5120 ], [ 0, 0, 60, 60, 720, 720, 780, 900, 900, 4820 ], [ 0, 0, 60, 60, 720, 720, 780, 900, 900, 4820 ], [ 0, 0, 56, 56, 728, 728, 784, 896, 896, 4816 ], [ 0, 0, 48, 48, 720, 720, 768, 864, 864, 4928 ], [ 0, 0, 48, 48, 720, 720, 768, 864, 864, 4928 ], [ 1, 1, 60, 60, 723, 723, 774, 924, 924, 4770 ] ] ] ), rec( name := "He", sbgname := "S4(4) leq S4(4).2", filename := "S44", degree := 4116, rank := 7, permchar := "1a + 51ab + 680a + 1029ab + 1275a", charnmbs := [ 1, 2, 3, 6, 7, 8, 9 ], ctbl := [ [ 1, 1, 272, 272, 425, 425, 2720 ], [ 1, 1, 8*E(7)+8*E(7)^2+64*E(7)^3+8*E(7)^4+64*E(7)^5+64*E(7)^6, 64*E(7)+64*E(7)^2+8*E(7)^3+64*E(7)^4+8*E(7)^5+8*E(7)^6, 75, 75, -80 ], [ 1, 1, 64*E(7)+64*E(7)^2+8*E(7)^3+64*E(7)^4+8*E(7)^5+8*E(7)^6, 8*E(7)+8*E(7)^2+64*E(7)^3+8*E(7)^4+64*E(7)^5+64*E(7)^6, 75, 75, -80 ], [ 1, 1, 20, 20, 5, 5, -52 ], [ 1, -1, 0, 0, -5*E(17)-5*E(17)^2+5*E(17)^3-5*E(17)^4+5*E(17)^5+5*E(17)^6+5*E(17)^7-5*E(17)^8-5*E(17)^9+5*E(17)^10+5*E(17)^11+5*E(17)^12 -5*E(17)^13+5*E(17)^14-5*E(17)^15-5*E(17)^16, 5*E(17)+5*E(17)^2-5*E(17)^3+5*E(17)^4-5*E(17)^5-5*E(17)^6-5*E(17)^7+5*E(17)^8+5*E(17)^9-5*E(17)^10-5*E(17)^11-5*E(17)^12+5*E(17)^13-5*E(17)^14+5*E(17)^15+5*E(17)^16, 0 ], [ 1, -1, 0, 0, 5*E(17)+5*E(17)^2-5*E(17)^3+5*E(17)^4-5*E(17)^5-5*E(17)^6-5*E(17)^7+5*E(17)^8+5*E(17)^9-5*E(17)^10-5*E(17)^11-5*E(17)^12+5*E(17)^13-5*E(17)^14+5*E(17)^15+5*E(17)^16, -5*E(17)-5*E(17)^2+5*E(17)^3-5*E(17)^4+5*E(17)^5+5*E(17)^6 +5*E(17)^7-5*E(17)^8-5*E(17)^9+5*E(17)^10+5*E(17)^11+5*E(17)^12-5*E(17)^13+5*E(17)^14-5*E(17)^15-5*E(17)^16, 0 ], [ 1, 1, -8, -8, -9, -9, 32 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 272, 0, 0, 0 ], [ 0, 0, 0, 272, 0, 0, 0 ], [ 1, 1, 0, 0, 75, 75, 120 ], [ 0, 0, 72, 0, 0, 0, 200 ], [ 0, 0, 0, 48, 16, 16, 192 ], [ 0, 0, 0, 48, 16, 16, 192 ], [ 0, 0, 20, 12, 30, 30, 180 ] ], [ [ 0, 0, 272, 0, 0, 0, 0 ], [ 0, 0, 272, 0, 0, 0, 0 ], [ 0, 0, 0, 72, 0, 0, 200 ], [ 1, 1, 0, 0, 75, 75, 120 ], [ 0, 0, 48, 0, 16, 16, 192 ], [ 0, 0, 48, 0, 16, 16, 192 ], [ 0, 0, 12, 20, 30, 30, 180 ] ], [ [ 0, 0, 0, 0, 425, 0, 0 ], [ 0, 0, 0, 0, 0, 425, 0 ], [ 0, 0, 75, 0, 25, 25, 300 ], [ 0, 0, 0, 75, 25, 25, 300 ], [ 1, 0, 16, 16, 68, 68, 256 ], [ 0, 1, 16, 16, 68, 68, 256 ], [ 0, 0, 30, 30, 40, 40, 285 ] ], [ [ 0, 0, 0, 0, 0, 425, 0 ], [ 0, 0, 0, 0, 425, 0, 0 ], [ 0, 0, 75, 0, 25, 25, 300 ], [ 0, 0, 0, 75, 25, 25, 300 ], [ 0, 1, 16, 16, 68, 68, 256 ], [ 1, 0, 16, 16, 68, 68, 256 ], [ 0, 0, 30, 30, 40, 40, 285 ] ], [ [ 0, 0, 0, 0, 0, 0, 2720 ], [ 0, 0, 0, 0, 0, 0, 2720 ], [ 0, 0, 120, 200, 300, 300, 1800 ], [ 0, 0, 200, 120, 300, 300, 1800 ], [ 0, 0, 192, 192, 256, 256, 1824 ], [ 0, 0, 192, 192, 256, 256, 1824 ], [ 1, 1, 180, 180, 285, 285, 1788 ] ] ] ), rec( name := "He", sbgname := "2^2.L3(4).S3", filename := "2^2.L34.S3", degree := 8330, rank := 7, permchar := "1a + 51ab + 680a + 1275a + 1920a + 4352a", charnmbs := [ 1, 2, 3, 6, 9, 12, 14 ], ctbl := [ [ 1, 105, 720, 840, 840, 1344, 4480 ], [ 1, 35, -120, 140*E(7)^3+140*E(7)^5+140*E(7)^6, 140*E(7)+140*E(7)^2+140*E(7)^4, 224, 0 ], [ 1, 35, -120, 140*E(7)+140*E(7)^2+140*E(7)^4, 140*E(7)^3+140*E(7)^5+140*E(7)^6, 224, 0 ], [ 1, 21, 6, 42, 42, 0, -112 ], [ 1, 7, 48, -28, -28, 0, 0 ], [ 1, -14, 6, 7, 7, 35, -42 ], [ 1, 0, -15, 0, 0, -21, 35 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 105, 0, 0, 0, 0, 0 ], [ 1, 8, 0, 16, 16, 64, 0 ], [ 0, 0, 21, 14, 14, 0, 56 ], [ 0, 2, 12, 35, 0, 8, 48 ], [ 0, 2, 12, 0, 35, 8, 48 ], [ 0, 5, 0, 5, 5, 30, 60 ], [ 0, 0, 9, 9, 9, 18, 60 ] ], [ [ 0, 0, 720, 0, 0, 0, 0 ], [ 0, 0, 144, 96, 96, 0, 384 ], [ 1, 21, 54, 42, 42, 168, 392 ], [ 0, 12, 36, 12, 132, 144, 384 ], [ 0, 12, 36, 132, 12, 144, 384 ], [ 0, 0, 90, 90, 90, 60, 390 ], [ 0, 9, 63, 72, 72, 117, 387 ] ], [ [ 0, 0, 0, 0, 840, 0, 0 ], [ 0, 16, 96, 0, 280, 64, 384 ], [ 0, 14, 42, 154, 14, 168, 448 ], [ 1, 35, 12, 48, 48, 264, 432 ], [ 0, 0, 132, 188, 48, 40, 432 ], [ 0, 5, 90, 25, 165, 105, 450 ], [ 0, 9, 72, 81, 81, 135, 462 ] ], [ [ 0, 0, 0, 840, 0, 0, 0 ], [ 0, 16, 96, 280, 0, 64, 384 ], [ 0, 14, 42, 14, 154, 168, 448 ], [ 0, 0, 132, 48, 188, 40, 432 ], [ 1, 35, 12, 48, 48, 264, 432 ], [ 0, 5, 90, 165, 25, 105, 450 ], [ 0, 9, 72, 81, 81, 135, 462 ] ], [ [ 0, 0, 0, 0, 0, 1344, 0 ], [ 0, 64, 0, 64, 64, 384, 768 ], [ 0, 0, 168, 168, 168, 112, 728 ], [ 0, 8, 144, 264, 40, 168, 720 ], [ 0, 8, 144, 40, 264, 168, 720 ], [ 1, 30, 60, 105, 105, 323, 720 ], [ 0, 18, 117, 135, 135, 216, 723 ] ], [ [ 0, 0, 0, 0, 0, 0, 4480 ], [ 0, 0, 384, 384, 384, 768, 2560 ], [ 0, 56, 392, 448, 448, 728, 2408 ], [ 0, 48, 384, 432, 432, 720, 2464 ], [ 0, 48, 384, 432, 432, 720, 2464 ], [ 0, 60, 390, 450, 450, 720, 2410 ], [ 1, 60, 387, 462, 462, 723, 2385 ] ] ] ), rec( name := "He", sbgname := "S4(4).2", filename := "S44.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 2058, rank := 5, permchar := "1a + 51ab + 680a + 1275a", charnmbs := [ 1, 2, 3, 6, 9 ], ctbl := [ [ 1, 136, 136, 425, 1360 ], [ 1, 4*E(7)+4*E(7)^2+32*E(7)^3+4*E(7)^4+32*E(7)^5+32*E(7)^6, 32*E(7)+32*E(7)^2+4*E(7)^3+32*E(7)^4+4*E(7)^5+4*E(7)^6, 75, -40 ], [ 1, 32*E(7)+32*E(7)^2+4*E(7)^3+32*E(7)^4+4*E(7)^5+4*E(7)^6, 4*E(7)+4*E(7)^2+32*E(7)^3+4*E(7)^4+32*E(7)^5+32*E(7)^6, 75, -40 ], [ 1, 10, 10, 5, -26 ], [ 1, -4, -4, -9, 16 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 136, 0, 0 ], [ 1, 0, 0, 75, 60 ], [ 0, 36, 0, 0, 100 ], [ 0, 0, 24, 16, 96 ], [ 0, 10, 6, 30, 90 ] ], [ [ 0, 136, 0, 0, 0 ], [ 0, 0, 36, 0, 100 ], [ 1, 0, 0, 75, 60 ], [ 0, 24, 0, 16, 96 ], [ 0, 6, 10, 30, 90 ] ], [ [ 0, 0, 0, 425, 0 ], [ 0, 75, 0, 50, 300 ], [ 0, 0, 75, 50, 300 ], [ 1, 16, 16, 136, 256 ], [ 0, 30, 30, 80, 285 ] ], [ [ 0, 0, 0, 0, 1360 ], [ 0, 60, 100, 300, 900 ], [ 0, 100, 60, 300, 900 ], [ 0, 96, 96, 256, 912 ], [ 1, 90, 90, 285, 894 ] ] ] ), rec( name := "He.2", sbgname := "S4(4).4", filename := "S44.4", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 2058, rank := 4, permchar := "1a^+ + 51ab + 680a^+ + 1275a^-", charnmbs := [ 1, 3, 5, 9 ], ctbl := [ [ 1, 272, 425, 1360 ], [ 1, -36, 75, -40 ], [ 1, 20, 5, -26 ], [ 1, -8, -9, 16 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 272, 0, 0 ], [ 1, 36, 75, 160 ], [ 0, 48, 32, 192 ], [ 0, 32, 60, 180 ] ], [ [ 0, 0, 425, 0 ], [ 0, 75, 50, 300 ], [ 1, 32, 136, 256 ], [ 0, 60, 80, 285 ] ], [ [ 0, 0, 0, 1360 ], [ 0, 160, 300, 900 ], [ 0, 192, 256, 912 ], [ 1, 180, 285, 894 ] ] ] ), rec( name := "He.2", sbgname := "2^2.L3(4).D12", filename := "2^2.L34.D12", degree := 8330, rank := 6, permchar := "1a^+ + 51ab + 680a^+ + 1275a^+ + 1920a^+ + 4352a^+", charnmbs := [ 1, 3, 5, 8, 11, 15 ], ctbl := [ [ 1, 105, 720, 1344, 1680, 4480 ], [ 1, 35, -120, 224, -140, 0 ], [ 1, 21, 6, 0, 84, -112 ], [ 1, 7, 48, 0, -56, 0 ], [ 1, -14, 6, 35, 14, -42 ], [ 1, 0, -15, -21, 0, 35 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 105, 0, 0, 0, 0 ], [ 1, 8, 0, 64, 32, 0 ], [ 0, 0, 21, 0, 28, 56 ], [ 0, 5, 0, 30, 10, 60 ], [ 0, 2, 12, 8, 35, 48 ], [ 0, 0, 9, 18, 18, 60 ] ], [ [ 0, 0, 720, 0, 0, 0 ], [ 0, 0, 144, 0, 192, 384 ], [ 1, 21, 54, 168, 84, 392 ], [ 0, 0, 90, 60, 180, 390 ], [ 0, 12, 36, 144, 144, 384 ], [ 0, 9, 63, 117, 144, 387 ] ], [ [ 0, 0, 0, 1344, 0, 0 ], [ 0, 64, 0, 384, 128, 768 ], [ 0, 0, 168, 112, 336, 728 ], [ 1, 30, 60, 323, 210, 720 ], [ 0, 8, 144, 168, 304, 720 ], [ 0, 18, 117, 216, 270, 723 ] ], [ [ 0, 0, 0, 0, 1680, 0 ], [ 0, 32, 192, 128, 560, 768 ], [ 0, 28, 84, 336, 336, 896 ], [ 0, 10, 180, 210, 380, 900 ], [ 1, 35, 144, 304, 332, 864 ], [ 0, 18, 144, 270, 324, 924 ] ], [ [ 0, 0, 0, 0, 0, 4480 ], [ 0, 0, 384, 768, 768, 2560 ], [ 0, 56, 392, 728, 896, 2408 ], [ 0, 60, 390, 720, 900, 2410 ], [ 0, 48, 384, 720, 864, 2464 ], [ 1, 60, 387, 723, 924, 2385 ] ] ] ), rec( name := "He.2", sbgname := "2^2.L3(4).S3 leq 2^2.L3(4).D12", filename := "2^2.L34.S3", degree := 16660, rank := 8, permchar := "1a^+ + 51ab + 680a^+ + 1029ab + 1275a^+ + 1920a^+ + 4352a^+ + 6272a^+", charnmbs := [ 1, 3, 5, 7, 8, 11, 15, 17 ], ctbl := [ [ 1, 1, 210, 1344, 1344, 1440, 3360, 8960 ], [ 1, 1, 70, 224, 224, -240, -280, 0 ], [ 1, 1, 42, 0, 0, 12, 168, -224 ], [ 1, -1, 0, -64, 64, 0, 0, 0 ], [ 1, 1, 14, 0, 0, 96, -112, 0 ], [ 1, 1, -28, 35, 35, 12, 28, -84 ], [ 1, 1, 0, -21, -21, -30, 0, 70 ], [ 1, -1, 0, 21, -21, 0, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 210, 0, 0, 0, 0, 0 ], [ 0, 0, 210, 0, 0, 0, 0, 0 ], [ 1, 1, 16, 64, 64, 0, 64, 0 ], [ 0, 0, 10, 30, 30, 0, 20, 120 ], [ 0, 0, 10, 30, 30, 0, 20, 120 ], [ 0, 0, 0, 0, 0, 42, 56, 112 ], [ 0, 0, 4, 8, 8, 24, 70, 96 ], [ 0, 0, 0, 18, 18, 18, 36, 120 ] ], [ [ 0, 0, 0, 1344, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1344, 0, 0, 0 ], [ 0, 0, 64, 192, 192, 0, 128, 768 ], [ 1, 0, 30, 140, 183, 60, 210, 720 ], [ 0, 1, 30, 183, 140, 60, 210, 720 ], [ 0, 0, 0, 56, 56, 168, 336, 728 ], [ 0, 0, 8, 84, 84, 144, 304, 720 ], [ 0, 0, 18, 108, 108, 117, 270, 723 ] ], [ [ 0, 0, 0, 0, 1344, 0, 0, 0 ], [ 0, 0, 0, 1344, 0, 0, 0, 0 ], [ 0, 0, 64, 192, 192, 0, 128, 768 ], [ 0, 1, 30, 183, 140, 60, 210, 720 ], [ 1, 0, 30, 140, 183, 60, 210, 720 ], [ 0, 0, 0, 56, 56, 168, 336, 728 ], [ 0, 0, 8, 84, 84, 144, 304, 720 ], [ 0, 0, 18, 108, 108, 117, 270, 723 ] ], [ [ 0, 0, 0, 0, 0, 1440, 0, 0 ], [ 0, 0, 0, 0, 0, 1440, 0, 0 ], [ 0, 0, 0, 0, 0, 288, 384, 768 ], [ 0, 0, 0, 60, 60, 180, 360, 780 ], [ 0, 0, 0, 60, 60, 180, 360, 780 ], [ 1, 1, 42, 168, 168, 108, 168, 784 ], [ 0, 0, 24, 144, 144, 72, 288, 768 ], [ 0, 0, 18, 117, 117, 126, 288, 774 ] ], [ [ 0, 0, 0, 0, 0, 0, 3360, 0 ], [ 0, 0, 0, 0, 0, 0, 3360, 0 ], [ 0, 0, 64, 128, 128, 384, 1120, 1536 ], [ 0, 0, 20, 210, 210, 360, 760, 1800 ], [ 0, 0, 20, 210, 210, 360, 760, 1800 ], [ 0, 0, 56, 336, 336, 168, 672, 1792 ], [ 1, 1, 70, 304, 304, 288, 664, 1728 ], [ 0, 0, 36, 270, 270, 288, 648, 1848 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 8960 ], [ 0, 0, 0, 0, 0, 0, 0, 8960 ], [ 0, 0, 0, 768, 768, 768, 1536, 5120 ], [ 0, 0, 120, 720, 720, 780, 1800, 4820 ], [ 0, 0, 120, 720, 720, 780, 1800, 4820 ], [ 0, 0, 112, 728, 728, 784, 1792, 4816 ], [ 0, 0, 96, 720, 720, 768, 1728, 4928 ], [ 1, 1, 120, 723, 723, 774, 1848, 4770 ] ] ] ), rec( name := "He.2", sbgname := "2^2.L3(4).6 leq 2^2.L3(4).D12", filename := "2^2.L34.6", degree := 16660, rank := 8, permchar := "1a^+ + 51ab + 680a^+ + 1029ab + 1275a^+ + 1920a^+ + 4352a^+ + 6272a^-", charnmbs := [ 1, 3, 5, 7, 8, 11, 15, 18 ], ctbl := [ [ 1, 1, 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E. Praeger and L. H. Soicher.", degree := 8120, rank := 5, permchar := "1a + 406a + 783a + 3276a + 3654a", charnmbs := [ 1, 4, 5, 6, 7 ], ctbl := [ [ 1, 1, 2304, 2304, 3510 ], [ 1, -1, 144, -144, 0 ], [ 1, 1, 64, 64, -130 ], [ 1, 1, -16, -16, 30 ], [ 1, -1, -16, 16, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 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 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 2304, 0, 0 ], [ 0, 0, 0, 2304, 0 ], [ 1, 0, 728, 600, 975 ], [ 0, 1, 600, 728, 975 ], [ 0, 0, 640, 640, 1024 ] ], [ [ 0, 0, 0, 2304, 0 ], [ 0, 0, 2304, 0, 0 ], [ 0, 1, 600, 728, 975 ], [ 1, 0, 728, 600, 975 ], [ 0, 0, 640, 640, 1024 ] ], [ [ 0, 0, 0, 0, 3510 ], [ 0, 0, 0, 0, 3510 ], [ 0, 0, 975, 975, 1560 ], [ 0, 0, 975, 975, 1560 ], [ 1, 1, 1024, 1024, 1460 ] ] ] ), rec( name := "Ru", sbgname := "^2F4(2)'.2", filename := "^2F42", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 4060, rank := 3, permchar := "1a + 783a + 3276a", charnmbs := [ 1, 5, 6 ], ctbl := [ [ 1, 1755, 2304 ], [ 1, -65, 64 ], [ 1, 15, -16 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 1755, 0 ], [ 1, 730, 1024 ], [ 0, 780, 975 ] ], [ [ 0, 0, 2304 ], [ 0, 1024, 1280 ], [ 1, 975, 1328 ] ] ] ), rec( name := "Ru", sbgname := "(2^2xSz(8)):3", filename := "2^2xSz8:3", degree := 417600, rank := 10, permchar := "1a + 3276a + 20475a + 3654a +34944ab+52780a +65975a + 75400a + 102400a", charnmbs := [ 1, 6, 8, 14, 15, 16, 21, 23, 25, 32 ], ctbl := [ [ 1, 455, 3640, 5824, 29120, 29120, 58240, 87360, 87360, 116480 ], [ 1, -9, 392, -208, 816, 352, -224, -1728, 1056, -448 ], [ 1, 39, -104, 64, 192, 256, -512, 192, 384, -512 ], [ 1, -9, 72, 192, 256, -288, -64, 192, -224, -128 ], [ 1, -2*E(24)-23*E(24)^8+2*E(24)^11-23*E(24)^16+2*E(24)^17-2*E(24)^19, -14*E(24)-16*E(24)^8+14*E(24)^11-16*E(24)^16+14*E(24)^17-14*E(24)^19, 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[ 1, 1, 18, 18, 40, -75, -75, 72 ], [ 1, -1, 18, -18, 0, 63, -63, 0 ], [ 1, -1, -18, 18, 0, -45, 45, 0 ], [ 1, 1, -10, -10, -16, 9, 9, 16 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 486, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 486, 0, 0, 0, 0 ], [ 1, 0, 56, 2, 0, 0, 315, 112 ], [ 0, 1, 2, 56, 0, 315, 0, 112 ], [ 0, 0, 0, 0, 0, 0, 0, 486 ], [ 0, 0, 0, 18, 0, 144, 36, 288 ], [ 0, 0, 18, 0, 0, 36, 144, 288 ], [ 0, 0, 2, 2, 10, 90, 90, 292 ] ], [ [ 0, 0, 0, 486, 0, 0, 0, 0 ], [ 0, 0, 486, 0, 0, 0, 0, 0 ], [ 0, 1, 2, 56, 0, 315, 0, 112 ], [ 1, 0, 56, 2, 0, 0, 315, 112 ], [ 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], [ [ 0, 0, 0, 0, 0, 0, 0, 27216 ], [ 0, 0, 0, 0, 0, 0, 0, 27216 ], [ 0, 0, 112, 112, 560, 5040, 5040, 16352 ], [ 0, 0, 112, 112, 560, 5040, 5040, 16352 ], [ 0, 0, 486, 486, 0, 4374, 4374, 17496 ], [ 0, 0, 288, 288, 288, 4896, 4896, 16560 ], [ 0, 0, 288, 288, 288, 4896, 4896, 16560 ], [ 1, 1, 292, 292, 360, 5175, 5175, 15920 ] ] ] ), rec( name := "Suz", sbgname := "3.U4(3):2", filename := "3.U43:2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 22880, rank := 5, permchar := "1a + 364a + 780a + 5940a + 15795a", charnmbs := [ 1, 3, 4, 9, 15 ], ctbl := [ [ 1, 280, 486, 8505, 13608 ], [ 1, 80, -54, 405, -432 ], [ 1, -28, 90, 189, -252 ], [ 1, 20, 18, -75, 36 ], [ 1, -8, -10, 9, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 280, 0, 0, 0 ], [ 1, 36, 0, 243, 0 ], [ 0, 0, 0, 0, 280 ], [ 0, 8, 0, 128, 144 ], [ 0, 0, 10, 90, 180 ] ], [ [ 0, 0, 486, 0, 0 ], [ 0, 0, 0, 0, 486 ], [ 1, 0, 58, 315, 112 ], [ 0, 0, 18, 180, 288 ], [ 0, 10, 4, 180, 292 ] ], [ [ 0, 0, 0, 8505, 0 ], [ 0, 243, 0, 3888, 4374 ], [ 0, 0, 315, 3150, 5040 ], [ 1, 128, 180, 3300, 4896 ], [ 0, 90, 180, 3060, 5175 ] ], [ [ 0, 0, 0, 0, 13608 ], [ 0, 0, 486, 4374, 8748 ], [ 0, 280, 112, 5040, 8176 ], [ 0, 144, 288, 4896, 8280 ], [ 1, 180, 292, 5175, 7960 ] ] ] ), rec( name := "Suz", sbgname := "G2(4)", filename := "G24", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. 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E. Praeger and L. H. Soicher.", degree := 22880, rank := 5, permchar := "1a^+ + 364a^+ + 780a^+ + 5940a^+ + 15795a^+", charnmbs := [ 1, 5, 7, 14, 23 ], ctbl := [ [ 1, 280, 486, 8505, 13608 ], [ 1, 80, -54, 405, -432 ], [ 1, -28, 90, 189, -252 ], [ 1, 20, 18, -75, 36 ], [ 1, -8, -10, 9, 8 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 280, 0, 0, 0 ], [ 1, 36, 0, 243, 0 ], [ 0, 0, 0, 0, 280 ], [ 0, 8, 0, 128, 144 ], [ 0, 0, 10, 90, 180 ] ], [ [ 0, 0, 486, 0, 0 ], [ 0, 0, 0, 0, 486 ], [ 1, 0, 58, 315, 112 ], [ 0, 0, 18, 180, 288 ], [ 0, 10, 4, 180, 292 ] ], [ [ 0, 0, 0, 8505, 0 ], [ 0, 243, 0, 3888, 4374 ], [ 0, 0, 315, 3150, 5040 ], [ 1, 128, 180, 3300, 4896 ], [ 0, 90, 180, 3060, 5175 ] ], [ [ 0, 0, 0, 0, 13608 ], [ 0, 0, 486, 4374, 8748 ], [ 0, 280, 112, 5040, 8176 ], [ 0, 144, 288, 4896, 8280 ], [ 1, 180, 292, 5175, 7960 ] ] ] ), rec( name := "Suz.2", sbgname := "G2(4).2", filename := "G24.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 1782, rank := 3, permchar := "1a^+ + 780a^+ + 1001a^+", charnmbs := [ 1, 7, 9 ], ctbl := [ [ 1, 416, 1365 ], [ 1, 20, -21 ], [ 1, -16, 15 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 416, 0 ], [ 1, 100, 315 ], [ 0, 96, 320 ] ], [ [ 0, 0, 1365 ], [ 0, 315, 1050 ], [ 1, 320, 1044 ] ] ] ), rec( name := "Suz.2", sbgname := "3.U4(3).2_3^{prime} leq 3.U4(3).2^2", filename := "3.U43.2_3-", degree := 45760, rank := 10, permchar := "1a^{+-} + 364a^{+-} + 780a^{+-} + 5940a^{+-} + 15795a^{+-}", charnmbs := [ 1, 2, 5, 6, 7, 8, 14, 15, 23, 24 ], ctbl := [ [ 1, 1, 280, 280, 486, 486, 8505, 8505, 13608, 13608 ], [ 1, -1, -280, 280, 486, -486, -8505, 8505, -13608, 13608 ], [ 1, 1, 80, 80, -54, -54, 405, 405, -432, -432 ], [ 1, -1, -80, 80, -54, 54, -405, 405, 432, -432 ], [ 1, 1, -28, -28, 90, 90, 189, 189, -252, -252 ], [ 1, -1, 28, -28, 90, -90, -189, 189, 252, -252 ], [ 1, 1, 20, 20, 18, 18, -75, -75, 36, 36 ], [ 1, -1, -20, 20, 18, -18, 75, -75, -36, 36 ], 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name := "Suz.2", sbgname := "3.U4(3).2_3 leq 3.U4(3).2^2", filename := "3.U43.2_3", degree := 45760, rank := 8, permchar := "1a^+ + 143a^+ + 364a^+ + 780a^+ + 5940a^+ + 10725a^+ + 12012a^+ + 15795a^+", charnmbs := [ 1, 3, 5, 7, 14, 16, 18, 23 ], ctbl := [ [ 1, 1, 486, 486, 560, 8505, 8505, 27216 ], [ 1, -1, -162, 162, 0, 945, -945, 0 ], [ 1, 1, -54, -54, 160, 405, 405, -864 ], [ 1, 1, 90, 90, -56, 189, 189, -504 ], [ 1, 1, 18, 18, 40, -75, -75, 72 ], [ 1, -1, -18, 18, 0, -63, 63, 0 ], [ 1, -1, 18, -18, 0, 45, -45, 0 ], [ 1, 1, -10, -10, -16, 9, 9, 16 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 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5040, 0, 0, 16352 ], [ 0, 0, 0, 0, 112, 0, 112, 0, 0, 560, 5040, 0, 0, 5040, 16352, 0 ], [ 0, 0, 0, 0, 0, 112, 0, 112, 560, 0, 0, 5040, 5040, 0, 0, 16352 ], [ 0, 0, 0, 0, 112, 0, 112, 0, 0, 560, 5040, 0, 0, 5040, 16352, 0 ], [ 0, 0, 0, 0, 486, 0, 486, 0, 0, 0, 4374, 0, 0, 4374, 17496, 0 ], [ 0, 0, 0, 0, 0, 486, 0, 486, 0, 0, 0, 4374, 4374, 0, 0, 17496 ], [ 0, 0, 0, 0, 0, 288, 0, 288, 288, 0, 0, 4896, 4896, 0, 0, 16560 ], [ 0, 0, 0, 0, 288, 0, 288, 0, 0, 288, 4896, 0, 0, 4896, 16560, 0 ], [ 0, 0, 0, 0, 288, 0, 288, 0, 0, 288, 4896, 0, 0, 4896, 16560, 0 ], [ 0, 0, 0, 0, 0, 288, 0, 288, 288, 0, 0, 4896, 4896, 0, 0, 16560 ], [ 1, 0, 1, 0, 0, 292, 0, 292, 360, 0, 0, 5175, 5175, 0, 0, 15920 ], [ 0, 1, 0, 1, 292, 0, 292, 0, 0, 360, 5175, 0, 0, 5175, 15920, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27216 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27216, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27216 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27216, 0 ], [ 0, 0, 0, 0, 112, 0, 112, 0, 0, 560, 5040, 0, 0, 5040, 16352, 0 ], [ 0, 0, 0, 0, 0, 112, 0, 112, 560, 0, 0, 5040, 5040, 0, 0, 16352 ], [ 0, 0, 0, 0, 112, 0, 112, 0, 0, 560, 5040, 0, 0, 5040, 16352, 0 ], [ 0, 0, 0, 0, 0, 112, 0, 112, 560, 0, 0, 5040, 5040, 0, 0, 16352 ], [ 0, 0, 0, 0, 0, 486, 0, 486, 0, 0, 0, 4374, 4374, 0, 0, 17496 ], [ 0, 0, 0, 0, 486, 0, 486, 0, 0, 0, 4374, 0, 0, 4374, 17496, 0 ], [ 0, 0, 0, 0, 288, 0, 288, 0, 0, 288, 4896, 0, 0, 4896, 16560, 0 ], [ 0, 0, 0, 0, 0, 288, 0, 288, 288, 0, 0, 4896, 4896, 0, 0, 16560 ], [ 0, 0, 0, 0, 0, 288, 0, 288, 288, 0, 0, 4896, 4896, 0, 0, 16560 ], [ 0, 0, 0, 0, 288, 0, 288, 0, 0, 288, 4896, 0, 0, 4896, 16560, 0 ], [ 0, 1, 0, 1, 292, 0, 292, 0, 0, 360, 5175, 0, 0, 5175, 15920, 0 ], [ 1, 0, 1, 0, 0, 292, 0, 292, 360, 0, 0, 5175, 5175, 0, 0, 15920 ] ] ] ), rec( name := "Suz.2", sbgname := "U5(2).2", filename := "U52.2", degree := 32760, rank := 6, permchar := "1a^+ + 143a^- + 364a^+ + 5940a^+ + 12012a^- + 14300a^-", charnmbs := [ 1, 4, 5, 14, 19, 21 ], ctbl := [ [ 1, 891, 1980, 2816, 6336, 20736 ], [ 1, 243, -180, 512, -576, 0 ], [ 1, -99, 330, 176, -264, -144 ], [ 1, 33, 30, 8, 96, -168 ], [ 1, -27, -30, 32, 24, 0 ], [ 1, 9, 6, -40, -48, 72 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 891, 0, 0, 0, 0 ], [ 1, 82, 40, 256, 0, 512 ], [ 0, 18, 9, 0, 288, 576 ], [ 0, 81, 0, 162, 81, 567 ], [ 0, 0, 90, 36, 225, 540 ], [ 0, 22, 55, 77, 165, 572 ] ], [ [ 0, 0, 1980, 0, 0, 0 ], [ 0, 40, 20, 0, 640, 1280 ], [ 1, 9, 306, 320, 192, 1152 ], [ 0, 0, 225, 135, 405, 1215 ], [ 0, 90, 60, 180, 390, 1260 ], [ 0, 55, 110, 165, 385, 1265 ] ], [ [ 0, 0, 0, 2816, 0, 0 ], [ 0, 256, 0, 512, 256, 1792 ], [ 0, 0, 320, 192, 576, 1728 ], [ 1, 162, 135, 466, 270, 1782 ], [ 0, 36, 180, 120, 680, 1800 ], [ 0, 77, 165, 242, 550, 1782 ] ], [ [ 0, 0, 0, 0, 6336, 0 ], [ 0, 0, 640, 256, 1600, 3840 ], [ 0, 288, 192, 576, 1248, 4032 ], [ 0, 81, 405, 270, 1530, 4050 ], [ 1, 225, 390, 680, 1080, 3960 ], [ 0, 165, 385, 550, 1210, 4026 ] ], [ [ 0, 0, 0, 0, 0, 20736 ], [ 0, 512, 1280, 1792, 3840, 13312 ], [ 0, 576, 1152, 1728, 4032, 13248 ], [ 0, 567, 1215, 1782, 4050, 13122 ], [ 0, 540, 1260, 1800, 3960, 13176 ], [ 1, 572, 1265, 1782, 4026, 13090 ] ] ] ), rec( name := "Suz.2", sbgname := "U5(2) leq U5(2).2", filename := "U52", degree := 65520, rank := 12, permchar := "1a^{+-} + 143a^{+-} + 364a^{+-} + 5940a^{+-} + 12012a^{+-} + 14300a^{+-}", charnmbs := [ 1, 2, 3, 4, 5, 6, 14, 15, 18, 19, 20, 21 ], ctbl := [ [ 1, 1, 891, 891, 1980, 1980, 2816, 2816, 6336, 6336, 20736, 20736 ], [ 1, -1, 891, -891, 1980, -1980, -2816, 2816, 6336, -6336, 20736, -20736 ], [ 1, -1, 243, -243, -180, 180, -512, 512, -576, 576, 0, 0 ], [ 1, 1, 243, 243, -180, -180, 512, 512, -576, -576, 0, 0 ], [ 1, 1, -99, -99, 330, 330, 176, 176, -264, -264, -144, -144 ], [ 1, -1, -99, 99, 330, -330, -176, 176, -264, 264, -144, 144 ], [ 1, 1, 33, 33, 30, 30, 8, 8, 96, 96, -168, -168 ], [ 1, -1, 33, -33, 30, -30, -8, 8, 96, -96, -168, 168 ], [ 1, -1, -27, 27, -30, 30, -32, 32, 24, -24, 0, 0 ], [ 1, 1, -27, -27, -30, -30, 32, 32, 24, 24, 0, 0 ], [ 1, -1, 9, -9, 6, -6, 40, -40, -48, 48, 72, -72 ], [ 1, 1, 9, 9, 6, 6, -40, -40, -48, -48, 72, 72 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 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0, 0, 0, 0, 55296, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7168, 10240, 0, 0, 20480, 0, 17408 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7168, 0, 0, 10240, 20480, 0, 17408, 0 ], [ 0, 0, 0, 0, 0, 0, 1536, 0, 0, 3072, 3072, 0, 0, 4608, 18432, 0, 24576, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1536, 3072, 0, 0, 3072, 4608, 0, 0, 18432, 0, 24576 ], [ 0, 0, 0, 0, 320, 0, 1024, 0, 0, 2560, 3008, 0, 0, 5120, 16640, 0, 26624, 0 ], [ 0, 0, 0, 0, 0, 320, 0, 1024, 2560, 0, 0, 3008, 5120, 0, 0, 16640, 0, 26624 ], [ 0, 0, 0, 0, 0, 216, 0, 864, 2376, 0, 0, 3024, 5832, 0, 0, 17928, 0, 25056 ], [ 0, 0, 0, 0, 216, 0, 864, 0, 0, 2376, 3024, 0, 0, 5832, 17928, 0, 25056, 0 ], [ 0, 0, 0, 42, 120, 0, 564, 0, 0, 1680, 4374, 0, 0, 8160, 19200, 0, 21156, 0 ], [ 0, 0, 42, 0, 0, 120, 0, 564, 1680, 0, 0, 4374, 8160, 0, 0, 19200, 0, 21156 ], [ 0, 0, 32, 0, 0, 96, 0, 512, 1728, 0, 0, 4352, 8000, 0, 0, 19520, 0, 21056 ], [ 0, 0, 0, 32, 96, 0, 512, 0, 0, 1728, 4352, 0, 0, 8000, 19520, 0, 21056, 0 ], [ 0, 0, 0, 24, 144, 0, 624, 0, 0, 1992, 3840, 0, 0, 7320, 19080, 0, 22272, 0 ], [ 0, 0, 24, 0, 0, 144, 0, 624, 1992, 0, 0, 3840, 7320, 0, 0, 19080, 0, 22272 ], [ 0, 1, 0, 17, 160, 0, 832, 0, 0, 2320, 3526, 0, 0, 6580, 18560, 0, 23300, 0 ], [ 1, 0, 17, 0, 0, 160, 0, 832, 2320, 0, 0, 3526, 6580, 0, 0, 18560, 0, 23300 ] ] ] ), rec( name := "Suz.2", sbgname := "3^5:(M11x2)", filename := "3^5:M11x2", degree := 232960, rank := 10, permchar := "1a^+ + 364a^{+-} + 5940a^+ + 12012a^- + 14300a^- + 15015ab + 15795a^+ + 54054a^+ + 100100a^-", charnmbs := [ 1, 5, 6, 14, 19, 21, 22, 23, 33, 48 ], ctbl := [ [ 1, 165, 891, 2916, 5346, 17820, 32076, 40095, 53460, 80190 ], [ 1, 65, 291, 36, -594, 1020, -1764, 3195, -540, -1710 ], [ 1, -55, 99, -540, 198, 1980, -1188, -1485, -1980, 2970 ], [ 1, 35, 111, -48, 198, -120, 408, -75, -360, -150 ], [ 1, -25, 39, 0, -162, 120, 432, -135, 0, -270 ], [ 1, 11, -33, 144, 54, 264, 72, -99, -216, -198 ], [ 1, -19, 27, 36, 90, -36, -180, -9, 180, -90 ], [ 1, 21, 27, 36, -110, -36, -180, -369, 340, 270 ], [ 1, 5, -21, -60, 18, 60, 12, 15, 180, -210 ], [ 1, -1, -9, 0, -18, -72, 0, 81, -144, 162 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 165, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 2, 54, 0, 0, 108, 0, 0, 0, 0 ], [ 0, 10, 20, 0, 0, 0, 0, 135, 0, 0 ], [ 0, 0, 0, 0, 0, 55, 0, 0, 0, 110 ], [ 0, 0, 0, 0, 10, 0, 90, 0, 20, 45 ], [ 0, 1, 0, 9, 0, 2, 18, 63, 54, 18 ], [ 0, 0, 0, 0, 15, 10, 25, 10, 30, 75 ], [ 0, 0, 3, 0, 0, 28, 8, 54, 24, 48 ], [ 0, 0, 0, 0, 2, 18, 18, 18, 37, 72 ], [ 0, 0, 0, 4, 3, 4, 30, 24, 48, 52 ] ], [ [ 0, 0, 891, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 54, 108, 0, 0, 0, 0, 729, 0, 0 ], [ 1, 20, 90, 0, 0, 240, 0, 540, 0, 0 ], [ 0, 0, 0, 11, 0, 0, 110, 220, 330, 220 ], [ 0, 0, 0, 0, 90, 0, 216, 0, 180, 405 ], [ 0, 0, 12, 0, 0, 123, 54, 216, 162, 324 ], [ 0, 0, 0, 10, 36, 30, 205, 80, 210, 320 ], [ 0, 3, 12, 16, 0, 96, 64, 284, 192, 224 ], [ 0, 0, 0, 18, 18, 54, 126, 144, 225, 306 ], [ 0, 0, 0, 8, 27, 72, 128, 112, 204, 340 ] ], [ [ 0, 0, 0, 2916, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 972, 0, 0, 0, 1944 ], [ 0, 0, 0, 36, 0, 0, 360, 720, 1080, 720 ], [ 1, 0, 11, 0, 132, 660, 242, 220, 330, 1320 ], [ 0, 0, 0, 72, 72, 180, 432, 540, 720, 900 ], [ 0, 9, 0, 108, 54, 72, 522, 639, 810, 702 ], [ 0, 0, 10, 22, 72, 290, 372, 450, 600, 1100 ], [ 0, 0, 16, 16, 72, 284, 360, 480, 600, 1088 ], [ 0, 0, 18, 18, 72, 270, 360, 450, 612, 1116 ], [ 0, 4, 8, 48, 60, 156, 440, 544, 744, 912 ] ], [ [ 0, 0, 0, 0, 5346, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 324, 0, 2916, 0, 648, 1458 ], [ 0, 0, 0, 0, 540, 0, 1296, 0, 1080, 2430 ], [ 0, 0, 0, 132, 132, 330, 792, 990, 1320, 1650 ], [ 1, 10, 90, 72, 62, 540, 666, 1125, 1160, 1620 ], [ 0, 0, 0, 54, 162, 432, 756, 702, 1188, 2052 ], [ 0, 15, 36, 72, 111, 420, 642, 1095, 1200, 1755 ], [ 0, 0, 0, 72, 150, 312, 876, 672, 1320, 1944 ], [ 0, 2, 18, 72, 116, 396, 720, 990, 1250, 1782 ], [ 0, 3, 27, 60, 108, 456, 702, 972, 1188, 1830 ] ], [ [ 0, 0, 0, 0, 0, 17820, 0, 0, 0, 0 ], [ 0, 108, 0, 972, 0, 216, 1944, 6804, 5832, 1944 ], [ 0, 0, 240, 0, 0, 2460, 1080, 4320, 3240, 6480 ], [ 0, 55, 0, 660, 330, 440, 3190, 3905, 4950, 4290 ], [ 0, 0, 0, 180, 540, 1440, 2520, 2340, 3960, 6840 ], [ 1, 2, 123, 72, 432, 2196, 1926, 2826, 3294, 6948 ], [ 0, 10, 30, 290, 420, 1070, 2760, 2940, 4380, 5920 ], [ 0, 28, 96, 284, 312, 1256, 2352, 3636, 4272, 5584 ], [ 0, 18, 54, 270, 396, 1098, 2628, 3204, 4320, 5832 ], [ 0, 4, 72, 156, 456, 1544, 2368, 2792, 3888, 6540 ] ], [ [ 0, 0, 0, 0, 0, 0, 32076, 0, 0, 0 ], [ 0, 0, 0, 0, 2916, 1944, 4860, 1944, 5832, 14580 ], [ 0, 0, 0, 360, 1296, 1080, 7380, 2880, 7560, 11520 ], [ 0, 0, 110, 242, 792, 3190, 4092, 4950, 6600, 12100 ], [ 0, 90, 216, 432, 666, 2520, 3852, 6570, 7200, 10530 ], [ 0, 18, 54, 522, 756, 1926, 4968, 5292, 7884, 10656 ], [ 1, 25, 205, 372, 642, 2760, 4216, 5825, 7140, 10890 ], [ 0, 8, 64, 360, 876, 2352, 4660, 4688, 7392, 11676 ], [ 0, 18, 126, 360, 720, 2628, 4284, 5544, 7200, 11196 ], [ 0, 30, 128, 440, 702, 2368, 4356, 5838, 7464, 10750 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 40095, 0, 0 ], [ 0, 0, 729, 0, 0, 6804, 1944, 13122, 5832, 11664 ], [ 0, 135, 540, 720, 0, 4320, 2880, 12780, 8640, 10080 ], [ 0, 0, 220, 220, 990, 3905, 4950, 6600, 8250, 14960 ], [ 0, 0, 0, 540, 1125, 2340, 6570, 5040, 9900, 14580 ], [ 0, 63, 216, 639, 702, 2826, 5292, 8181, 9612, 12564 ], [ 0, 10, 80, 450, 1095, 2940, 5825, 5860, 9240, 14595 ], [ 1, 54, 284, 480, 672, 3636, 4688, 7960, 8880, 13440 ], [ 0, 18, 144, 450, 990, 3204, 5544, 6660, 9009, 14076 ], [ 0, 24, 112, 544, 972, 2792, 5838, 6720, 9384, 13709 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 53460, 0 ], [ 0, 0, 0, 0, 648, 5832, 5832, 5832, 11988, 23328 ], [ 0, 0, 0, 1080, 1080, 3240, 7560, 8640, 13500, 18360 ], [ 0, 0, 330, 330, 1320, 4950, 6600, 8250, 11220, 20460 ], [ 0, 20, 180, 720, 1160, 3960, 7200, 9900, 12500, 17820 ], [ 0, 54, 162, 810, 1188, 3294, 7884, 9612, 12960, 17496 ], [ 0, 30, 210, 600, 1200, 4380, 7140, 9240, 12000, 18660 ], [ 0, 24, 192, 600, 1320, 4272, 7392, 8880, 12012, 18768 ], [ 1, 37, 225, 612, 1250, 4320, 7200, 9009, 12068, 18738 ], [ 0, 48, 204, 744, 1188, 3888, 7464, 9384, 12492, 18048 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 80190 ], [ 0, 0, 0, 1944, 1458, 1944, 14580, 11664, 23328, 25272 ], [ 0, 0, 0, 720, 2430, 6480, 11520, 10080, 18360, 30600 ], [ 0, 110, 220, 1320, 1650, 4290, 12100, 14960, 20460, 25080 ], [ 0, 45, 405, 900, 1620, 6840, 10530, 14580, 17820, 27450 ], [ 0, 18, 324, 702, 2052, 6948, 10656, 12564, 17496, 29430 ], [ 0, 75, 320, 1100, 1755, 5920, 10890, 14595, 18660, 26875 ], [ 0, 48, 224, 1088, 1944, 5584, 11676, 13440, 18768, 27418 ], [ 0, 72, 306, 1116, 1782, 5832, 11196, 14076, 18738, 27072 ], [ 1, 52, 340, 912, 1830, 6540, 10750, 13709, 18048, 28008 ] ] ] ), rec( name := "Suz.2", sbgname := "2_^{1+6}.U4(2).2", filename := "2_^1+6.U42.2", degree := 135135, rank := 9, permchar := "1a^+ + 143a^- + 780a^+ + 3432a^+ + 5940a^+ + 14300a^- + 18954a^- + 25025a^+ + 66560a^+", charnmbs := [ 1, 4, 7, 11, 14, 21, 26, 27, 38 ], ctbl := [ [ 1, 54, 360, 1728, 5120, 9216, 17280, 46080, 55296 ], [ 1, -27, 90, 432, 800, -1152, -2160, -1440, 3456 ], [ 1, 21, 30, 276, -160, 768, 120, -1440, 384 ], [ 1, 3, -60, 132, 200, 48, -60, 360, -624 ], [ 1, 15, 48, 12, 128, -144, 276, -96, -240 ], [ 1, -9, 24, -36, 80, 144, -108, 48, -144 ], [ 1, -11, 10, 48, -80, -64, 80, 80, -64 ], [ 1, 9, 6, 0, -64, 0, -144, 192, 0 ], [ 1, 0, -12, -18, 8, -9, 36, -96, 90 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 54, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 20, 32, 0, 0, 0, 0, 0 ], [ 0, 3, 3, 0, 0, 0, 48, 0, 0 ], [ 0, 1, 0, 1, 0, 32, 20, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 27, 27, 0 ], [ 0, 0, 0, 6, 0, 6, 0, 0, 42 ], [ 0, 0, 1, 2, 8, 0, 3, 8, 32 ], [ 0, 0, 0, 0, 3, 0, 3, 24, 24 ], [ 0, 0, 0, 0, 0, 7, 10, 20, 17 ] ], [ [ 0, 0, 360, 0, 0, 0, 0, 0, 0 ], [ 0, 20, 20, 0, 0, 0, 320, 0, 0 ], [ 1, 3, 4, 48, 128, 0, 48, 128, 0 ], [ 0, 0, 10, 10, 0, 0, 20, 0, 320 ], [ 0, 0, 9, 0, 27, 0, 27, 81, 216 ], [ 0, 0, 0, 0, 0, 60, 60, 120, 120 ], [ 0, 1, 1, 2, 8, 32, 84, 136, 96 ], [ 0, 0, 1, 0, 9, 24, 51, 131, 144 ], [ 0, 0, 0, 10, 20, 20, 30, 120, 160 ] ], [ [ 0, 0, 0, 1728, 0, 0, 0, 0, 0 ], [ 0, 32, 0, 32, 0, 1024, 640, 0, 0 ], [ 0, 0, 48, 48, 0, 0, 96, 0, 1536 ], [ 1, 1, 10, 180, 160, 192, 0, 160, 1024 ], [ 0, 0, 0, 54, 162, 0, 54, 594, 864 ], [ 0, 6, 0, 36, 0, 282, 360, 480, 564 ], [ 0, 2, 2, 0, 16, 192, 348, 656, 512 ], [ 0, 0, 0, 6, 66, 96, 246, 690, 624 ], [ 0, 0, 10, 32, 80, 94, 160, 520, 832 ] ], [ [ 0, 0, 0, 0, 5120, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 2560, 2560, 0 ], [ 0, 0, 128, 0, 384, 0, 384, 1152, 3072 ], [ 0, 0, 0, 160, 480, 0, 160, 1760, 2560 ], [ 1, 0, 27, 162, 340, 216, 378, 1620, 2376 ], [ 0, 0, 0, 0, 120, 440, 840, 2040, 1680 ], [ 0, 8, 8, 16, 112, 448, 896, 1904, 1728 ], [ 0, 3, 9, 66, 180, 408, 714, 1748, 1992 ], [ 0, 0, 20, 80, 220, 280, 540, 1660, 2320 ] ], [ [ 0, 0, 0, 0, 0, 9216, 0, 0, 0 ], [ 0, 0, 0, 1024, 0, 1024, 0, 0, 7168 ], [ 0, 0, 0, 0, 0, 1536, 1536, 3072, 3072 ], [ 0, 32, 0, 192, 0, 1504, 1920, 2560, 3008 ], [ 0, 0, 0, 0, 216, 792, 1512, 3672, 3024 ], [ 1, 6, 60, 282, 440, 753, 900, 2400, 4374 ], [ 0, 0, 32, 192, 448, 480, 832, 2880, 4352 ], [ 0, 0, 24, 96, 408, 480, 1080, 3288, 3840 ], [ 0, 7, 20, 94, 280, 729, 1360, 3200, 3526 ] ], [ [ 0, 0, 0, 0, 0, 0, 17280, 0, 0 ], [ 0, 0, 320, 640, 2560, 0, 960, 2560, 10240 ], [ 0, 48, 48, 96, 384, 1536, 4032, 6528, 4608 ], [ 0, 20, 20, 0, 160, 1920, 3480, 6560, 5120 ], [ 0, 27, 27, 54, 378, 1512, 3024, 6426, 5832 ], [ 0, 0, 60, 360, 840, 900, 1560, 5400, 8160 ], [ 1, 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832, 2320, 3526, 6580, 18560, 23300 ] ] ] ), rec( name := "Suz.2", sbgname := "2^{4+6}:3S6", filename := "2^4+6:3S6", degree := 405405, rank := 13, permchar := "1a^+ + 364a^+ + 780a^+ + 1001a^+ + 5940a^+ + 12012a^- + 14300a^- + 15795a^+ + 25025a^+ + 66560a^+ + 75075a^+ + 88452a^+ + 100100a^+", charnmbs := [ 1, 5, 7, 9, 14, 19, 21, 23, 27, 38, 40, 44, 47 ], ctbl := [ [ 1, 60, 480, 1536, 1920, 6144, 6144, 20480, 23040, 23040, 46080, 92160, 184320 ], [ 1, -15, 30, 336, 120, -96, 1104, -1120, -360, -2160, 2880, -5040, 4320 ], [ 1, 27, 84, 216, 336, 864, -192, 1472, 864, 72, -1440, -2880, 576 ], [ 1, 15, -60, -156, 300, 1104, 96, -1120, -720, -180, 720, 1440, -1440 ], [ 1, 21, 90, -24, 48, -96, 216, -112, 576, -360, -96, 744, -1008 ], [ 1, -15, 30, -96, 120, -96, 96, 320, -360, 0, 0, 0, 0 ], [ 1, -3, 18, 24, -96, 96, 264, -16, -144, 360, -288, -72, -144 ], [ 1, 7, -36, 116, 76, -96, 48, 112, -96, 172, 240, 240, -784 ], [ 1, 15, 36, -12, 12, -48, -96, -160, -144, 252, 144, -288, 288 ], [ 1, 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82656 ], [ 0, 24, 168, 696, 912, 2976, 2688, 9360, 10224, 10728, 20736, 42048, 83760 ], [ 0, 40, 240, 536, 848, 2840, 2400, 9600, 10728, 11168, 19872, 43824, 82224 ], [ 0, 24, 240, 768, 864, 2688, 3072, 9024, 10368, 9936, 21576, 40704, 85056 ], [ 0, 24, 204, 624, 804, 2748, 2532, 9576, 10512, 10956, 20352, 42900, 83088 ], [ 1, 29, 222, 736, 906, 2798, 2916, 9184, 10470, 10278, 21264, 41544, 83972 ] ] ] ), rec( name := "Suz.2", sbgname := "2^{4+6}:3A6 leq 2^{4+6}:3S6", filename := "2^4+6:3A6", degree := 810810, rank := 26, permchar := "1a^{+-} + 364a^{+-} + 780a^{+-} + 1001a^{+-} + 5940a^{+-} + 12012a^{+-} + 14300a^{+-} + 15795a^{+-} + 25025a^{+-} + 66560a^{+-} + 75075a^{+-} + 88452a^{+-} + 100100a^{+-}", charnmbs := [ 1, 2, 5, 6, 7, 8, 9, 10, 14, 15, 18, 19, 20, 21, 23, 24, 27, 28, 38, 39, 40, 41, 44, 45, 47, 48 ], ctbl := [ [ 1, 1, 60, 60, 480, 480, 1536, 1536, 1920, 1920, 6144, 6144, 6144, 6144, 20480, 20480, 23040, 23040, 23040, 23040, 46080, 46080, 92160, 92160, 184320, 184320 ], [ 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24, 0, 168, 0, 0, 696, 0, 912, 2976, 0, 0, 2688, 9360, 0, 10224, 0, 0, 10728, 0, 20736, 42048, 0, 83760, 0 ], [ 0, 0, 0, 24, 0, 168, 696, 0, 912, 0, 0, 2976, 2688, 0, 0, 9360, 0, 10224, 10728, 0, 20736, 0, 0, 42048, 0, 83760 ], [ 0, 0, 0, 40, 0, 240, 536, 0, 848, 0, 0, 2840, 2400, 0, 0, 9600, 0, 10728, 11168, 0, 19872, 0, 0, 43824, 0, 82224 ], [ 0, 0, 40, 0, 240, 0, 0, 536, 0, 848, 2840, 0, 0, 2400, 9600, 0, 10728, 0, 0, 11168, 0, 19872, 43824, 0, 82224, 0 ], [ 0, 0, 0, 24, 0, 240, 768, 0, 864, 0, 0, 2688, 3072, 0, 0, 9024, 0, 10368, 9936, 0, 21576, 0, 0, 40704, 0, 85056 ], [ 0, 0, 24, 0, 240, 0, 0, 768, 0, 864, 2688, 0, 0, 3072, 9024, 0, 10368, 0, 0, 9936, 0, 21576, 40704, 0, 85056, 0 ], [ 0, 0, 24, 0, 204, 0, 0, 624, 0, 804, 2748, 0, 0, 2532, 9576, 0, 10512, 0, 0, 10956, 0, 20352, 42900, 0, 83088, 0 ], [ 0, 0, 0, 24, 0, 204, 624, 0, 804, 0, 0, 2748, 2532, 0, 0, 9576, 0, 10512, 10956, 0, 20352, 0, 0, 42900, 0, 83088 ], [ 0, 1, 29, 0, 222, 0, 0, 736, 0, 906, 2798, 0, 0, 2916, 9184, 0, 10470, 0, 0, 10278, 0, 21264, 41544, 0, 83972, 0 ], [ 1, 0, 0, 29, 0, 222, 736, 0, 906, 0, 0, 2798, 2916, 0, 0, 9184, 0, 10470, 10278, 0, 21264, 0, 0, 41544, 0, 83972 ] ] ] ), rec( name := "ON", sbgname := "L3(7).2", filename := "L37.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 122760, rank := 5, permchar := "1a + 10944a + 26752a + 32395a + 52668a", permchar2 := "1a + 10944a + 26752a + 32395b + 52668a", charnmbs := [ 1, 2, 7, 8, 11 ], charnmbs2 := [ 1, 2, 7, 9, 11 ], ctbl := [ [ 1, 5586, 6384, 52136, 58653 ], [ 1, 196, -106, 161, -252 ], [ 1, -21, 111, 161, -252 ], [ 1, 42, 48, -280, 189 ], [ 1, -56, -64, 56, 63 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 5586, 0, 0, 0 ], [ 1, 364, 216, 2464, 2541 ], [ 0, 189, 301, 2303, 2793 ], [ 0, 264, 282, 2394, 2646 ], [ 0, 242, 304, 2352, 2688 ] ], [ [ 0, 0, 6384, 0, 0 ], [ 0, 216, 344, 2632, 3192 ], [ 1, 301, 349, 2793, 2940 ], [ 0, 282, 342, 2736, 3024 ], [ 0, 304, 320, 2688, 3072 ] ], [ [ 0, 0, 0, 52136, 0 ], [ 0, 2464, 2632, 22344, 24696 ], [ 0, 2303, 2793, 22344, 24696 ], [ 1, 2394, 2736, 22057, 24948 ], [ 0, 2352, 2688, 22176, 24920 ] ], [ [ 0, 0, 0, 0, 58653 ], [ 0, 2541, 3192, 24696, 28224 ], [ 0, 2793, 2940, 24696, 28224 ], [ 0, 2646, 3024, 24948, 28035 ], [ 1, 2688, 3072, 24920, 27972 ] ] ] ), rec( name := "ON", sbgname := "L3(7) leq L3(7).2", filename := "L37", degree := 245520, rank := 7, permchar := "1a + 10944a + 26752a + 32395a + 37696a + 52668a + 85064a", permchar2 := "1a + 10944a + 26752a + 32395b + 37696a + 52668a + 85064a", charnmbs := [ 1, 2, 7, 8, 10, 11, 18 ], charnmbs2 := [ 1, 2, 7, 9, 10, 11, 18 ], ctbl := [ [ 1, 1, 11172, 12768, 52136, 52136, 117306 ], [ 1, 1, 392, -212, 161, 161, -504 ], [ 1, 1, -42, 222, 161, 161, -504 ], [ 1, 1, 84, 96, -280, -280, 378 ], [ 1, -1, 0, 0, -343, 343, 0 ], [ 1, 1, -112, -128, 56, 56, 126 ], [ 1, -1, 0, 0, 152, -152, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 11172, 0, 0, 0, 0 ], [ 0, 0, 11172, 0, 0, 0, 0 ], [ 1, 1, 728, 432, 2464, 2464, 5082 ], [ 0, 0, 378, 602, 2303, 2303, 5586 ], [ 0, 0, 528, 564, 2394, 2394, 5292 ], [ 0, 0, 528, 564, 2394, 2394, 5292 ], [ 0, 0, 484, 608, 2352, 2352, 5376 ] ], [ [ 0, 0, 0, 12768, 0, 0, 0 ], [ 0, 0, 0, 12768, 0, 0, 0 ], [ 0, 0, 432, 688, 2632, 2632, 6384 ], [ 1, 1, 602, 698, 2793, 2793, 5880 ], [ 0, 0, 564, 684, 2736, 2736, 6048 ], [ 0, 0, 564, 684, 2736, 2736, 6048 ], [ 0, 0, 608, 640, 2688, 2688, 6144 ] ], [ [ 0, 0, 0, 0, 52136, 0, 0 ], [ 0, 0, 0, 0, 0, 52136, 0 ], [ 0, 0, 2464, 2632, 11172, 11172, 24696 ], [ 0, 0, 2303, 2793, 11172, 11172, 24696 ], [ 1, 0, 2394, 2736, 10933, 11124, 24948 ], [ 0, 1, 2394, 2736, 11124, 10933, 24948 ], [ 0, 0, 2352, 2688, 11088, 11088, 24920 ] ], [ [ 0, 0, 0, 0, 0, 52136, 0 ], [ 0, 0, 0, 0, 52136, 0, 0 ], [ 0, 0, 2464, 2632, 11172, 11172, 24696 ], [ 0, 0, 2303, 2793, 11172, 11172, 24696 ], [ 0, 1, 2394, 2736, 11124, 10933, 24948 ], [ 1, 0, 2394, 2736, 10933, 11124, 24948 ], [ 0, 0, 2352, 2688, 11088, 11088, 24920 ] ], [ [ 0, 0, 0, 0, 0, 0, 117306 ], [ 0, 0, 0, 0, 0, 0, 117306 ], [ 0, 0, 5082, 6384, 24696, 24696, 56448 ], [ 0, 0, 5586, 5880, 24696, 24696, 56448 ], [ 0, 0, 5292, 6048, 24948, 24948, 56070 ], [ 0, 0, 5292, 6048, 24948, 24948, 56070 ], [ 1, 1, 5376, 6144, 24920, 24920, 55944 ] ] ] ), rec( name := "ON.2", sbgname := "L3(7).2", filename := "L37.2", degree := 245520, rank := 9, permchar := "1a^{+-} + 10944a^{+-} + 26752a^{+-} + 32395ab + 52668a^{+-}", charnmbs := [ 1, 2, 3, 4, 7, 8, 9, 12, 13 ], ctbl := [ [ 1, 456, 5586, 6384, 11172, 32928, 52136, 58653, 78204 ], [ 1, -456, 5586, 6384, -11172, -32928, 52136, 58653, -78204 ], [ 1, 49, 196, -106, 238, -28, 161, -252, -259 ], [ 1, -49, 196, -106, -238, 28, 161, -252, 259 ], [ 1, -21*E(8)+21*E(8)^3, -21, 111, 84*E(8)-84*E(8)^3, 105*E(8)-105*E(8)^3, 161, -252, -168*E(8)+168*E(8)^3 ], [ 1, 21*E(8)-21*E(8)^3, -21, 111, -84*E(8)+84*E(8)^3, 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9180, 8640, 15820 ], [ 0, 0, 220, 20, 360, 20, 8640, 2160, 9180, 8400, 15820, 8640 ], [ 0, 0, 60, 120, 180, 720, 4500, 8280, 7740, 9360, 10260, 12240 ], [ 0, 0, 120, 60, 720, 180, 8280, 4500, 9360, 7740, 12240, 10260 ], [ 0, 0, 60, 144, 560, 612, 6192, 7488, 8640, 7776, 9792, 12196 ], [ 0, 0, 144, 60, 612, 560, 7488, 6192, 7776, 8640, 12196, 9792 ], [ 0, 1, 137, 84, 432, 791, 6156, 7344, 7344, 9147, 11548, 10476 ], [ 1, 0, 84, 137, 791, 432, 7344, 6156, 9147, 7344, 10476, 11548 ] ] ] ), rec( name := "Co3", sbgname := "2.S6(2)", filename := "2.S62", degree := 170775, rank := 7, permchar := "1a + 275a + 7084a + 8855a + 23000a + 57960a + 73600a", charnmbs := [ 1, 5, 14, 15, 20, 27, 29 ], ctbl := [ [ 1, 630, 1920, 8960, 30240, 48384, 80640 ], [ 1, 147, -288, 1232, 1260, 2016, -4368 ], [ 1, -45, 120, -40, 540, -216, -360 ], [ 1, 75, 0, 80, 180, -576, 240 ], [ 1, 3, 72, 116, -252, 72, -12 ], [ 1, 15, 0, -100, 0, 144, -60 ], [ 1, -18, -33, 32, 0, -54, 72 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 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35, 741, 2268, -1305, -1740 ], [ 1, -55, 123, -324, 495, -240 ], [ 1, 35, 93, -324, -225, 420 ], [ 1, 35, -15, 0, 207, -228 ], [ 1, -9, -15, 44, -57, 36 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 495, 0, 0, 0, 0 ], [ 1, 8, 54, 0, 324, 108 ], [ 0, 10, 20, 180, 45, 240 ], [ 0, 0, 15, 135, 165, 180 ], [ 0, 4, 3, 132, 152, 204 ], [ 0, 1, 12, 108, 153, 221 ] ], [ [ 0, 0, 2673, 0, 0, 0 ], [ 0, 54, 108, 972, 243, 1296 ], [ 1, 20, 430, 1512, 330, 380 ], [ 0, 15, 126, 957, 675, 900 ], [ 0, 3, 22, 540, 936, 1172 ], [ 0, 12, 19, 540, 879, 1223 ] ], [ [ 0, 0, 0, 32076, 0, 0 ], [ 0, 0, 972, 8748, 10692, 11664 ], [ 0, 180, 1512, 11484, 8100, 10800 ], [ 1, 135, 957, 8648, 9555, 12780 ], [ 0, 132, 540, 7644, 10080, 13680 ], [ 0, 108, 540, 7668, 10260, 13500 ] ], [ [ 0, 0, 0, 0, 40095, 0 ], [ 0, 324, 243, 10692, 12312, 16524 ], [ 0, 45, 330, 8100, 14040, 17580 ], [ 0, 165, 675, 9555, 12600, 17100 ], [ 1, 152, 936, 10080, 12510, 16416 ], [ 0, 153, 879, 10260, 12312, 16491 ] ], [ [ 0, 0, 0, 0, 0, 53460 ], [ 0, 108, 1296, 11664, 16524, 23868 ], [ 0, 240, 380, 10800, 17580, 24460 ], [ 0, 180, 900, 12780, 17100, 22500 ], [ 0, 204, 1172, 13680, 16416, 21988 ], [ 1, 221, 1223, 13500, 16491, 22024 ] ] ] ), rec( name := "Co3", sbgname := "HS", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 11178, rank := 5, permchar := "1a + 23a + 275a + 2024a + 8855a", charnmbs := [ 1, 2, 5, 9, 15 ], ctbl := [ [ 1, 352, 1100, 4125, 5600 ], [ 1, -176, 440, -825, 560 ], [ 1, 76, 134, -15, -196 ], [ 1, -26, 20, 75, -70 ], [ 1, 4, -10, -15, 20 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 352, 0, 0, 0 ], [ 1, 1, 175, 0, 175 ], [ 0, 56, 0, 240, 56 ], [ 0, 0, 64, 64, 224 ], [ 0, 11, 11, 165, 165 ] ], [ [ 0, 0, 1100, 0, 0 ], [ 0, 175, 0, 750, 175 ], [ 1, 0, 322, 105, 672 ], [ 0, 64, 28, 560, 448 ], [ 0, 11, 132, 330, 627 ] ], [ [ 0, 0, 0, 4125, 0 ], [ 0, 0, 750, 750, 2625 ], [ 0, 240, 105, 2100, 1680 ], [ 1, 64, 560, 1260, 2240 ], [ 0, 165, 330, 1650, 1980 ] ], [ [ 0, 0, 0, 0, 5600 ], [ 0, 175, 175, 2625, 2625 ], [ 0, 56, 672, 1680, 3192 ], [ 0, 224, 448, 2240, 2688 ], [ 1, 165, 627, 1980, 2827 ] ] ] ), rec( name := "Co3", sbgname := "M23", degree := 48600, rank := 8, permchar := "1a + 23a + 253b + 275a + 2024a + 5544a + 8855a + 31625c", charnmbs := [ 1, 2, 4, 5, 9, 13, 15, 24 ], ctbl := [ [ 1, 253, 506, 1771, 7590, 8855, 14168, 15456 ], [ 1, 55, -286, 847, -330, -2695, 3080, -672 ], [ 1, -85, -86, 147, 870, 105, -280, -672 ], [ 1, 1, 146, 343, -330, 455, 56, -672 ], [ 1, 10, -61, 97, -105, 80, -250, 228 ], [ 1, -22, 31, 21, 15, -120, -82, 156 ], [ 1, 28, 11, 1, 75, -40, -52, -24 ], [ 1, -4, -5, -15, -21, 24, 44, -24 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 253, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 42, 210, 0, 0, 0 ], [ 0, 0, 0, 0, 120, 105, 28, 0 ], [ 0, 6, 0, 16, 0, 15, 120, 96 ], [ 0, 7, 8, 0, 0, 42, 84, 112 ], [ 0, 0, 6, 3, 36, 64, 48, 96 ], [ 0, 0, 1, 15, 45, 30, 90, 72 ], [ 0, 0, 0, 11, 55, 55, 66, 66 ] ], [ [ 0, 0, 506, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 240, 210, 56, 0 ], [ 1, 0, 0, 210, 15, 0, 280, 0 ], [ 0, 0, 60, 0, 30, 320, 0, 96 ], [ 0, 8, 1, 7, 42, 56, 168, 224 ], [ 0, 6, 0, 64, 48, 4, 288, 96 ], [ 0, 1, 10, 0, 90, 180, 45, 180 ], [ 0, 0, 0, 11, 110, 55, 165, 165 ] ], [ [ 0, 0, 0, 1771, 0, 0, 0, 0 ], [ 0, 42, 0, 112, 0, 105, 840, 672 ], [ 0, 0, 210, 0, 105, 1120, 0, 336 ], [ 1, 16, 0, 386, 120, 0, 1056, 192 ], [ 0, 0, 7, 28, 392, 336, 448, 560 ], [ 0, 3, 64, 0, 288, 704, 136, 576 ], [ 0, 15, 0, 132, 240, 85, 807, 492 ], [ 0, 11, 11, 22, 275, 330, 451, 671 ] ], [ [ 0, 0, 0, 0, 7590, 0, 0, 0 ], [ 0, 210, 240, 0, 0, 1260, 2520, 3360 ], [ 0, 120, 15, 105, 630, 840, 2520, 3360 ], [ 0, 0, 30, 120, 1680, 1440, 1920, 2400 ], [ 1, 0, 42, 392, 1611, 1456, 2072, 2016 ], [ 0, 36, 48, 288, 1248, 1218, 2352, 2400 ], [ 0, 45, 90, 240, 1110, 1470, 2115, 2520 ], [ 0, 55, 110, 275, 990, 1375, 2310, 2475 ] ], [ [ 0, 0, 0, 0, 0, 8855, 0, 0 ], [ 0, 0, 210, 105, 1260, 2240, 1680, 3360 ], [ 0, 105, 0, 1120, 840, 70, 5040, 1680 ], [ 0, 15, 320, 0, 1440, 3520, 680, 2880 ], [ 0, 42, 56, 336, 1456, 1421, 2744, 2800 ], [ 1, 64, 4, 704, 1218, 608, 3760, 2496 ], [ 0, 30, 180, 85, 1470, 2350, 1740, 3000 ], [ 0, 55, 55, 330, 1375, 1430, 2750, 2860 ] ], [ [ 0, 0, 0, 0, 0, 0, 14168, 0 ], [ 0, 0, 56, 840, 2520, 1680, 5040, 4032 ], [ 0, 28, 280, 0, 2520, 5040, 1260, 5040 ], [ 0, 120, 0, 1056, 1920, 680, 6456, 3936 ], [ 0, 84, 168, 448, 2072, 2744, 3948, 4704 ], [ 0, 48, 288, 136, 2352, 3760, 2784, 4800 ], [ 1, 90, 45, 807, 2115, 1740, 5050, 4320 ], [ 0, 66, 165, 451, 2310, 2750, 3960, 4466 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 15456 ], [ 0, 0, 0, 672, 3360, 3360, 4032, 4032 ], [ 0, 0, 0, 336, 3360, 1680, 5040, 5040 ], [ 0, 96, 96, 192, 2400, 2880, 3936, 5856 ], [ 0, 112, 224, 560, 2016, 2800, 4704, 5040 ], [ 0, 96, 96, 576, 2400, 2496, 4800, 4992 ], [ 0, 72, 180, 492, 2520, 3000, 4320, 4872 ], [ 1, 66, 165, 671, 2475, 2860, 4466, 4752 ] ] ] ), rec( name := "Co3", sbgname := "McL leq McL.2", filename := "McL", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 552, rank := 4, permchar := "1a + 23a + 253b + 275a", charnmbs := [ 1, 2, 4, 5 ], ctbl := [ [ 1, 1, 275, 275 ], [ 1, -1, 55, -55 ], [ 1, -1, -5, 5 ], [ 1, 1, -1, -1 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ], [ [ 0, 0, 275, 0 ], [ 0, 0, 0, 275 ], [ 1, 0, 162, 112 ], [ 0, 1, 112, 162 ] ], [ [ 0, 0, 0, 275 ], [ 0, 0, 275, 0 ], [ 0, 1, 112, 162 ], [ 1, 0, 162, 112 ] ] ] ), rec( name := "Co2", sbgname := "2^{1+8}:S6(2)", filename := "2^1+8:S62", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 56925, rank := 5, permchar := "1a + 275a + 2024a + 23000a + 31625b", charnmbs := [ 1, 4, 6, 15, 17 ], ctbl := [ [ 1, 1008, 1260, 14336, 40320 ], [ 1, -234, 225, 1088, -1080 ], [ 1, 108, 135, -64, -180 ], [ 1, 18, -27, 80, -72 ], [ 1, -18, 9, -64, 72 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 1008, 0, 0, 0 ], [ 1, 0, 135, 512, 360 ], [ 0, 108, 36, 0, 864 ], [ 0, 36, 0, 162, 810 ], [ 0, 9, 27, 288, 684 ] ], [ [ 0, 0, 1260, 0, 0 ], [ 0, 135, 45, 0, 1080 ], [ 1, 36, 135, 512, 576 ], [ 0, 0, 45, 405, 810 ], [ 0, 27, 18, 288, 927 ] ], [ [ 0, 0, 0, 14336, 0 ], [ 0, 512, 0, 2304, 11520 ], [ 0, 0, 512, 4608, 9216 ], [ 1, 162, 405, 4048, 9720 ], [ 0, 288, 288, 3456, 10304 ] ], [ [ 0, 0, 0, 0, 40320 ], [ 0, 360, 1080, 11520, 27360 ], [ 0, 864, 576, 9216, 29664 ], [ 0, 810, 810, 9720, 28980 ], [ 1, 684, 927, 10304, 28404 ] ] ] ), rec( name := "Co2", sbgname := "U5(2).2 leq U6(2).2", filename := 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E. Praeger and L. H. Soicher.", degree := 46575, rank := 5, permchar := "1a + 275a + 2024a + 12650a + 31625b", charnmbs := [ 1, 4, 6, 14, 17 ], ctbl := [ [ 1, 462, 2464, 21120, 22528 ], [ 1, -21, 532, -960, 448 ], [ 1, 87, 64, 120, -272 ], [ 1, -21, 28, 120, -128 ], [ 1, 3, -20, -48, 64 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 462, 0, 0, 0 ], [ 1, 61, 80, 320, 0 ], [ 0, 15, 15, 240, 192 ], [ 0, 7, 28, 203, 224 ], [ 0, 0, 21, 210, 231 ] ], [ [ 0, 0, 2464, 0, 0 ], [ 0, 80, 80, 1280, 1024 ], [ 1, 15, 496, 480, 1472 ], [ 0, 28, 56, 1260, 1120 ], [ 0, 21, 161, 1050, 1232 ] ], [ [ 0, 0, 0, 21120, 0 ], [ 0, 320, 1280, 9280, 10240 ], [ 0, 240, 480, 10800, 9600 ], [ 1, 203, 1260, 9352, 10304 ], [ 0, 210, 1050, 9660, 10200 ] ], [ [ 0, 0, 0, 0, 22528 ], [ 0, 0, 1024, 10240, 11264 ], [ 0, 192, 1472, 9600, 11264 ], [ 0, 224, 1120, 10304, 10880 ], [ 1, 231, 1232, 10200, 10864 ] ] ] ), rec( name := "Co2", sbgname := "2^{10}:M22 leq 2^{10}:M22:2", filename := "2^10:M22", degree := 93150, rank := 8, permchar := "1a + 23a + 275a + 2024a + 2277a + 12650a + 31625b + 44275a", charnmbs := [ 1, 2, 4, 6, 7, 14, 17, 20 ], ctbl := [ [ 1, 1, 924, 2464, 2464, 22528, 22528, 42240 ], [ 1, -1, 0, 1232, -1232, -5632, 5632, 0 ], [ 1, 1, -42, 532, 532, 448, 448, -1920 ], [ 1, 1, 174, 64, 64, -272, -272, 240 ], [ 1, -1, 0, 182, -182, 368, -368, 0 ], [ 1, 1, -42, 28, 28, -128, -128, 240 ], [ 1, 1, 6, -20, -20, 64, 64, -96 ], [ 1, -1, 0, -10, 10, -16, 16, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 924, 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[ 0, 0, 192, 1472, 0, 1472, 9792, 9600 ], [ 1, 0, 231, 1071, 161, 3528, 7336, 10200 ], [ 0, 1, 231, 161, 1071, 7336, 3528, 10200 ], [ 0, 0, 224, 560, 560, 5440, 5440, 10304 ] ], [ [ 0, 0, 0, 0, 0, 0, 22528, 0 ], [ 0, 0, 0, 0, 0, 22528, 0, 0 ], [ 0, 0, 0, 512, 512, 5632, 5632, 10240 ], [ 0, 0, 192, 1472, 0, 1472, 9792, 9600 ], [ 0, 0, 192, 0, 1472, 9792, 1472, 9600 ], [ 0, 1, 231, 161, 1071, 7336, 3528, 10200 ], [ 1, 0, 231, 1071, 161, 3528, 7336, 10200 ], [ 0, 0, 224, 560, 560, 5440, 5440, 10304 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 42240 ], [ 0, 0, 0, 0, 0, 0, 0, 42240 ], [ 0, 0, 640, 1280, 1280, 10240, 10240, 18560 ], [ 0, 0, 480, 480, 480, 9600, 9600, 21600 ], [ 0, 0, 480, 480, 480, 9600, 9600, 21600 ], [ 0, 0, 420, 1050, 1050, 10200, 10200, 19320 ], [ 0, 0, 420, 1050, 1050, 10200, 10200, 19320 ], [ 1, 1, 406, 1260, 1260, 10304, 10304, 18704 ] ] ] ), rec( name := "Co2", sbgname := "McL", degree := 47104, rank := 6, permchar := "1a + 23a + 275a + 2277a + 12650a + 31878a", charnmbs := [ 1, 2, 4, 7, 14, 18 ], ctbl := [ [ 1, 275, 2025, 7128, 15400, 22275 ], [ 1, -165, 945, -2376, 3080, -1485 ], [ 1, 91, 369, 504, -56, -909 ], [ 1, -45, 105, 24, -280, 195 ], [ 1, 19, 9, -72, -56, 99 ], [ 1, -5, -15, 24, 40, -45 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 275, 0, 0, 0, 0 ], [ 1, 0, 162, 0, 112, 0 ], [ 0, 22, 0, 176, 0, 77 ], [ 0, 0, 50, 0, 175, 50 ], [ 0, 2, 0, 81, 30, 162 ], [ 0, 0, 7, 16, 112, 140 ] ], [ [ 0, 0, 2025, 0, 0, 0 ], [ 0, 162, 0, 1296, 0, 567 ], [ 1, 0, 462, 0, 1232, 330 ], [ 0, 50, 0, 750, 175, 1050 ], [ 0, 0, 162, 81, 972, 810 ], [ 0, 7, 30, 336, 560, 1092 ] ], [ [ 0, 0, 0, 7128, 0, 0 ], [ 0, 0, 1296, 0, 4536, 1296 ], [ 0, 176, 0, 2640, 616, 3696 ], [ 1, 0, 750, 252, 3500, 2625 ], [ 0, 81, 81, 1620, 1620, 3726 ], [ 0, 16, 336, 840, 2576, 3360 ] ], [ [ 0, 0, 0, 0, 15400, 0 ], [ 0, 112, 0, 4536, 1680, 9072 ], [ 0, 0, 1232, 616, 7392, 6160 ], [ 0, 175, 175, 3500, 3500, 8050 ], [ 1, 30, 972, 1620, 5892, 6885 ], [ 0, 112, 560, 2576, 4760, 7392 ] ], [ [ 0, 0, 0, 0, 0, 22275 ], [ 0, 0, 567, 1296, 9072, 11340 ], [ 0, 77, 330, 3696, 6160, 12012 ], [ 0, 50, 1050, 2625, 8050, 10500 ], [ 0, 162, 810, 3726, 6885, 10692 ], [ 1, 140, 1092, 3360, 7392, 10290 ] ] ] ), rec( name := "Co2", sbgname := "U6(2).2", filename := "U62.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 2300, rank := 3, permchar := "1a + 275a + 2024a", charnmbs := [ 1, 4, 6 ], ctbl := [ [ 1, 891, 1408 ], [ 1, 63, -64 ], [ 1, -9, 8 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 891, 0 ], [ 1, 378, 512 ], [ 0, 324, 567 ] ], [ [ 0, 0, 1408 ], [ 0, 512, 896 ], [ 1, 567, 840 ] ] ] ), rec( name := "Co2", sbgname := "U6(2) leq U6(2).2", filename := "U62", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 4600, rank := 5, permchar := "1a + 23a + 275a + 2024a + 2277a", charnmbs := [ 1, 2, 4, 6, 7 ], ctbl := [ [ 1, 1, 891, 891, 2816 ], [ 1, -1, 297, -297, 0 ], [ 1, 1, 63, 63, -128 ], [ 1, 1, -9, -9, 16 ], [ 1, -1, -3, 3, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 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 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 891, 0, 0 ], [ 0, 0, 0, 891, 0 ], [ 1, 0, 336, 42, 512 ], [ 0, 1, 42, 336, 512 ], [ 0, 0, 162, 162, 567 ] ], [ [ 0, 0, 0, 891, 0 ], [ 0, 0, 891, 0, 0 ], [ 0, 1, 42, 336, 512 ], [ 1, 0, 336, 42, 512 ], [ 0, 0, 162, 162, 567 ] ], [ [ 0, 0, 0, 0, 2816 ], [ 0, 0, 0, 0, 2816 ], [ 0, 0, 512, 512, 1792 ], [ 0, 0, 512, 512, 1792 ], [ 1, 1, 567, 567, 1680 ] ] ] ), rec( name := "Co2", sbgname := "HS.2", degree := 476928, rank := 7, permchar := "1a + 275a + 2024a + 23000a + 31625b + 184437a + 245916a", charnmbs := [ 1, 4, 6, 14, 17, 27, 33 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63616, 63616, 91840 ], [ 0, 0, 1050, 1050, 510, 510, 13980, 13980, 26640, 64440, 64440, 77400 ], [ 0, 0, 1050, 1050, 510, 510, 13980, 13980, 26640, 64440, 64440, 77400 ], [ 0, 0, 750, 750, 1250, 1250, 18500, 18500, 26000, 64000, 64000, 69000 ], [ 0, 0, 1040, 1040, 1136, 1136, 17184, 17184, 24576, 64000, 64000, 72704 ], [ 0, 0, 1040, 1040, 1136, 1136, 17184, 17184, 24576, 64000, 64000, 72704 ], [ 1, 1, 1204, 1204, 1435, 1435, 18060, 18060, 23184, 63616, 63616, 72184 ] ] ] ), rec( name := "Fi22", sbgname := "2.U6(2)", filename := "2.U62", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 3510, rank := 3, permchar := "1a + 429a + 3080a", charnmbs := [ 1, 3, 7 ], ctbl := [ [ 1, 693, 2816 ], [ 1, 63, -64 ], [ 1, -9, 8 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 693, 0 ], [ 1, 180, 512 ], [ 0, 126, 567 ] ], [ [ 0, 0, 2816 ], [ 0, 512, 2304 ], [ 1, 567, 2248 ] ] ] ), rec( name := "Fi22", sbgname := "2^{10}:M22", filename := "2^10:M22", degree := 142155, rank := 8, permchar := "1a + 78a + 429a + 1430a + 3080a + 30030a + 32032a + 75075a", charnmbs := [ 1, 2, 3, 5, 7, 10, 11, 17 ], ctbl := [ [ 1, 154, 1024, 3696, 4928, 11264, 42240, 78848 ], [ 1, -77, -320, 924, 1232, -1408, -5280, 4928 ], [ 1, 49, -176, 546, -532, 1184, -960, -112 ], [ 1, -35, 160, 294, -364, -400, 120, 224 ], [ 1, 37, 88, 186, 248, 32, 120, -712 ], [ 1, 13, -32, 6, -28, -112, 120, 32 ], [ 1, -17, -20, 24, 32, 32, 120, -172 ], [ 1, 1, 16, -30, -4, 32, -96, 80 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 154, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 120, 32, 0, 0, 0 ], [ 0, 0, 0, 0, 77, 0, 0, 77 ], [ 0, 5, 0, 5, 0, 64, 80, 0 ], [ 0, 1, 16, 0, 1, 0, 120, 16 ], [ 0, 0, 0, 21, 0, 21, 0, 112 ], [ 0, 0, 0, 7, 14, 0, 21, 112 ], [ 0, 0, 1, 0, 1, 16, 60, 76 ] ], [ [ 0, 0, 1024, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 512, 0, 0, 512 ], [ 1, 0, 22, 231, 0, 0, 0, 770 ], [ 0, 0, 64, 0, 0, 0, 640, 320 ], [ 0, 16, 0, 0, 16, 256, 480, 256 ], [ 0, 0, 0, 0, 112, 0, 240, 672 ], [ 0, 0, 0, 56, 56, 64, 176, 672 ], [ 0, 1, 10, 15, 16, 96, 360, 526 ] ], [ [ 0, 0, 0, 3696, 0, 0, 0, 0 ], [ 0, 120, 0, 120, 0, 1536, 1920, 0 ], [ 0, 0, 231, 0, 0, 0, 2310, 1155 ], [ 1, 5, 0, 450, 120, 320, 240, 2560 ], [ 0, 0, 0, 90, 510, 0, 600, 2496 ], [ 0, 21, 0, 105, 0, 630, 1260, 1680 ], [ 0, 7, 56, 21, 70, 336, 1470, 1736 ], [ 0, 0, 15, 120, 156, 240, 930, 2235 ] ], [ [ 0, 0, 0, 0, 4928, 0, 0, 0 ], [ 0, 32, 512, 0, 32, 0, 3840, 512 ], [ 0, 77, 0, 0, 77, 1232, 2310, 1232 ], [ 0, 0, 0, 120, 680, 0, 800, 3328 ], [ 1, 1, 16, 510, 256, 256, 480, 3408 ], [ 0, 0, 112, 0, 112, 252, 2100, 2352 ], [ 0, 14, 56, 70, 56, 560, 1876, 2296 ], [ 0, 1, 16, 156, 213, 336, 1230, 2976 ] ], [ [ 0, 0, 0, 0, 0, 11264, 0, 0 ], [ 0, 0, 0, 1536, 0, 1536, 0, 8192 ], [ 0, 0, 0, 0, 1232, 0, 2640, 7392 ], [ 0, 64, 0, 320, 0, 1920, 3840, 5120 ], [ 0, 0, 256, 0, 256, 576, 4800, 5376 ], [ 1, 21, 0, 630, 252, 1120, 2520, 6720 ], [ 0, 0, 64, 336, 560, 672, 2912, 6720 ], [ 0, 16, 96, 240, 336, 960, 3600, 6016 ] ], [ [ 0, 0, 0, 0, 0, 0, 42240, 0 ], [ 0, 0, 0, 1920, 3840, 0, 5760, 30720 ], [ 0, 0, 0, 2310, 2310, 2640, 7260, 27720 ], [ 0, 80, 640, 240, 800, 3840, 16800, 19840 ], [ 0, 120, 480, 600, 480, 4800, 16080, 19680 ], [ 0, 0, 240, 1260, 2100, 2520, 10920, 25200 ], [ 1, 21, 176, 1470, 1876, 2912, 10584, 25200 ], [ 0, 60, 360, 930, 1230, 3600, 13500, 22560 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 78848 ], [ 0, 0, 512, 0, 512, 8192, 30720, 38912 ], [ 0, 77, 770, 1155, 1232, 7392, 27720, 40502 ], [ 0, 0, 320, 2560, 3328, 5120, 19840, 47680 ], [ 0, 16, 256, 2496, 3408, 5376, 19680, 47616 ], [ 0, 112, 672, 1680, 2352, 6720, 25200, 42112 ], [ 0, 112, 672, 1736, 2296, 6720, 25200, 42112 ], [ 1, 76, 526, 2235, 2976, 6016, 22560, 44458 ] ] ] ), rec( name := "Fi22", sbgname := "O7(3)", filename := "O73", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 14080, rank := 3, permchar := "1a + 429a + 13650a", permchar2 := "1a + 429a + 13650a", charnmbs := [ 1, 3, 9 ], charnmbs2 := [ 1, 3, 9 ], ctbl := [ [ 1, 3159, 10920 ], [ 1, 279, -280 ], [ 1, -9, 8 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 3159, 0 ], [ 1, 918, 2240 ], [ 0, 648, 2511 ] ], [ [ 0, 0, 10920 ], [ 0, 2240, 8680 ], [ 1, 2511, 8408 ] ] ] ), rec( name := "Fi22", sbgname := "O8^+(2).3.2", filename := "O8+2.3.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 61776, rank := 4, permchar := "1a + 3080a + 13650a + 45045a", charnmbs := [ 1, 7, 9, 13 ], ctbl := [ [ 1, 1575, 22400, 37800 ], [ 1, 171, -64, -108 ], [ 1, -9, 224, -216 ], [ 1, -9, -64, 72 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1575, 0, 0 ], [ 1, 198, 512, 864 ], [ 0, 36, 567, 972 ], [ 0, 36, 576, 963 ] ], [ [ 0, 0, 22400, 0 ], [ 0, 512, 8064, 13824 ], [ 1, 567, 8224, 13608 ], [ 0, 576, 8064, 13760 ] ], [ [ 0, 0, 0, 37800 ], [ 0, 864, 13824, 23112 ], [ 0, 972, 13608, 23220 ], [ 1, 963, 13760, 23076 ] ] ] ), rec( name := "Fi22", sbgname := "O8^+(2).3 leq O8^+(2).3.2", filename := "O8+2.3", degree := 123552, rank := 7, permchar := "1a + 1001a + 3080a + 10725a + 13650a + 45045a + 50050a", charnmbs := [ 1, 4, 7, 8, 9, 13, 15 ], ctbl := [ [ 1, 1, 1575, 1575, 22400, 22400, 75600 ], [ 1, -1, 225, -225, 800, -800, 0 ], [ 1, 1, 171, 171, -64, -64, -216 ], [ 1, -1, -63, 63, 224, -224, 0 ], [ 1, 1, -9, -9, 224, 224, -432 ], [ 1, 1, -9, -9, -64, -64, 144 ], [ 1, -1, 9, -9, -64, 64, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1575, 0, 0, 0, 0 ], [ 0, 0, 0, 1575, 0, 0, 0 ], [ 1, 0, 144, 54, 512, 0, 864 ], [ 0, 1, 54, 144, 0, 512, 864 ], [ 0, 0, 36, 0, 324, 243, 972 ], [ 0, 0, 0, 36, 243, 324, 972 ], [ 0, 0, 18, 18, 288, 288, 963 ] ], [ [ 0, 0, 0, 1575, 0, 0, 0 ], [ 0, 0, 1575, 0, 0, 0, 0 ], [ 0, 1, 54, 144, 0, 512, 864 ], [ 1, 0, 144, 54, 512, 0, 864 ], [ 0, 0, 0, 36, 243, 324, 972 ], [ 0, 0, 36, 0, 324, 243, 972 ], [ 0, 0, 18, 18, 288, 288, 963 ] ], [ [ 0, 0, 0, 0, 22400, 0, 0 ], [ 0, 0, 0, 0, 0, 22400, 0 ], [ 0, 0, 512, 0, 4608, 3456, 13824 ], [ 0, 0, 0, 512, 3456, 4608, 13824 ], [ 1, 0, 324, 243, 4336, 3888, 13608 ], [ 0, 1, 243, 324, 3888, 4336, 13608 ], [ 0, 0, 288, 288, 4032, 4032, 13760 ] ], [ [ 0, 0, 0, 0, 0, 22400, 0 ], [ 0, 0, 0, 0, 22400, 0, 0 ], [ 0, 0, 0, 512, 3456, 4608, 13824 ], [ 0, 0, 512, 0, 4608, 3456, 13824 ], [ 0, 1, 243, 324, 3888, 4336, 13608 ], [ 1, 0, 324, 243, 4336, 3888, 13608 ], [ 0, 0, 288, 288, 4032, 4032, 13760 ] ], [ [ 0, 0, 0, 0, 0, 0, 75600 ], [ 0, 0, 0, 0, 0, 0, 75600 ], [ 0, 0, 864, 864, 13824, 13824, 46224 ], [ 0, 0, 864, 864, 13824, 13824, 46224 ], [ 0, 0, 972, 972, 13608, 13608, 46440 ], [ 0, 0, 972, 972, 13608, 13608, 46440 ], [ 1, 1, 963, 963, 13760, 13760, 46152 ] ] ] ), rec( name := "Fi22", sbgname := "O8^+(2).2 leq O8^+(2).3.2", filename := "O8+2.2", degree := 185328, rank := 7, permchar := "1a + 429a + 3080a + 13650a + 45045a + 48048a + 75075a", charnmbs := [ 1, 3, 7, 9, 13, 14, 17 ], ctbl := [ [ 1, 2, 1575, 3150, 22400, 44800, 113400 ], [ 1, -1, 315, -315, 2240, -2240, 0 ], [ 1, 2, 171, 342, -64, -128, -324 ], [ 1, 2, -9, -18, 224, 448, -648 ], [ 1, 2, -9, -18, -64, -128, 216 ], [ 1, -1, -45, 45, 80, -80, 0 ], [ 1, -1, 27, -27, -64, 64, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 2, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], [ [ 0, 0, 1575, 0, 0, 0, 0 ], [ 0, 0, 0, 1575, 0, 0, 0 ], [ 1, 0, 102, 96, 512, 0, 864 ], [ 0, 1, 48, 150, 0, 512, 864 ], [ 0, 0, 36, 0, 351, 216, 972 ], [ 0, 0, 0, 36, 108, 459, 972 ], [ 0, 0, 12, 24, 192, 384, 963 ] ], [ [ 0, 0, 0, 3150, 0, 0, 0 ], [ 0, 0, 1575, 1575, 0, 0, 0 ], [ 0, 2, 96, 300, 0, 1024, 1728 ], [ 1, 1, 150, 246, 512, 512, 1728 ], [ 0, 0, 0, 72, 216, 918, 1944 ], [ 0, 0, 36, 36, 459, 675, 1944 ], [ 0, 0, 24, 48, 384, 768, 1926 ] ], [ [ 0, 0, 0, 0, 22400, 0, 0 ], [ 0, 0, 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E. Praeger and L. H. Soicher.", degree := 3510, rank := 3, permchar := "1a^+ + 429a^+ + 3080a^+", charnmbs := [ 1, 5, 13 ], ctbl := [ [ 1, 693, 2816 ], [ 1, 63, -64 ], [ 1, -9, 8 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 693, 0 ], [ 1, 180, 512 ], [ 0, 126, 567 ] ], [ [ 0, 0, 2816 ], [ 0, 512, 2304 ], [ 1, 567, 2248 ] ] ] ), rec( name := "Fi22.2", sbgname := "2.U6(2) leq 2.U6(2).2", filename := "2.U62", degree := 7020, rank := 6, permchar := "1a^{+-} + 429a^{+-} + 3080a^{+-}", charnmbs := [ 1, 2, 5, 6, 13, 14 ], ctbl := [ [ 1, 1, 693, 693, 2816, 2816 ], [ 1, -1, -693, 693, 2816, -2816 ], [ 1, 1, 63, 63, -64, -64 ], [ 1, -1, -63, 63, -64, 64 ], [ 1, 1, -9, -9, 8, 8 ], [ 1, -1, 9, -9, 8, -8 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 693, 0, 0, 0 ], [ 0, 0, 0, 693, 0, 0 ], [ 1, 0, 0, 180, 512, 0 ], [ 0, 1, 180, 0, 0, 512 ], [ 0, 0, 126, 0, 0, 567 ], [ 0, 0, 0, 126, 567, 0 ] ], [ [ 0, 0, 0, 693, 0, 0 ], [ 0, 0, 693, 0, 0, 0 ], [ 0, 1, 180, 0, 0, 512 ], [ 1, 0, 0, 180, 512, 0 ], [ 0, 0, 0, 126, 567, 0 ], [ 0, 0, 126, 0, 0, 567 ] ], [ [ 0, 0, 0, 0, 2816, 0 ], [ 0, 0, 0, 0, 0, 2816 ], [ 0, 0, 512, 0, 0, 2304 ], [ 0, 0, 0, 512, 2304, 0 ], [ 1, 0, 0, 567, 2248, 0 ], [ 0, 1, 567, 0, 0, 2248 ] ], [ [ 0, 0, 0, 0, 0, 2816 ], [ 0, 0, 0, 0, 2816, 0 ], [ 0, 0, 0, 512, 2304, 0 ], [ 0, 0, 512, 0, 0, 2304 ], [ 0, 1, 567, 0, 0, 2248 ], [ 1, 0, 0, 567, 2248, 0 ] ] ] ), rec( name := "Fi22.2", sbgname := "O7(3)", filename := "O73", degree := 28160, rank := 6, permchar := "1a^{+-} + 429a^{+-} + 13650a^{+-}", charnmbs := [ 1, 2, 5, 6, 17, 18 ], ctbl := [ [ 1, 364, 1080, 3159, 10920, 12636 ], [ 1, -364, -1080, 3159, 10920, -12636 ], [ 1, 84, -120, 279, -280, 36 ], [ 1, -84, 120, 279, -280, -36 ], [ 1, 12, 24, -9, 8, -36 ], [ 1, -12, -24, -9, 8, 36 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 364, 0, 0, 0, 0 ], [ 1, 0, 0, 243, 120, 0 ], [ 0, 0, 0, 0, 364, 0 ], [ 0, 28, 0, 0, 0, 336 ], [ 0, 4, 36, 0, 0, 324 ], [ 0, 0, 0, 84, 280, 0 ] ], [ [ 0, 0, 1080, 0, 0, 0 ], [ 0, 0, 0, 0, 1080, 0 ], [ 1, 0, 0, 351, 728, 0 ], [ 0, 0, 120, 0, 0, 960 ], [ 0, 36, 72, 0, 0, 972 ], [ 0, 0, 0, 240, 840, 0 ] ], [ [ 0, 0, 0, 3159, 0, 0 ], [ 0, 243, 0, 0, 0, 2916 ], [ 0, 0, 351, 0, 0, 2808 ], [ 1, 0, 0, 918, 2240, 0 ], [ 0, 0, 0, 648, 2511, 0 ], [ 0, 84, 240, 0, 0, 2835 ] ], [ [ 0, 0, 0, 0, 10920, 0 ], [ 0, 120, 1080, 0, 0, 9720 ], [ 0, 364, 728, 0, 0, 9828 ], [ 0, 0, 0, 2240, 8680, 0 ], [ 1, 0, 0, 2511, 8408, 0 ], [ 0, 280, 840, 0, 0, 9800 ] ], [ [ 0, 0, 0, 0, 0, 12636 ], [ 0, 0, 0, 2916, 9720, 0 ], [ 0, 0, 0, 2808, 9828, 0 ], [ 0, 336, 960, 0, 0, 11340 ], [ 0, 324, 972, 0, 0, 11340 ], [ 1, 0, 0, 2835, 9800, 0 ] ] ] ), rec( name := "Fi22.2", sbgname := "O8^+(2).3.2x2", filename := "O8+2.3.2x2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 61776, rank := 4, permchar := "1a^+ + 3080a^+ + 13650a^+ + 45045a^+", charnmbs := [ 1, 13, 17, 25 ], ctbl := [ [ 1, 1575, 22400, 37800 ], [ 1, 171, -64, -108 ], [ 1, -9, 224, -216 ], [ 1, -9, -64, 72 ] ], mats := [ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], [ [ 0, 1575, 0, 0 ], [ 1, 198, 512, 864 ], [ 0, 36, 567, 972 ], [ 0, 36, 576, 963 ] ], [ [ 0, 0, 22400, 0 ], [ 0, 512, 8064, 13824 ], [ 1, 567, 8224, 13608 ], [ 0, 576, 8064, 13760 ] ], [ [ 0, 0, 0, 37800 ], [ 0, 864, 13824, 23112 ], [ 0, 972, 13608, 23220 ], [ 1, 963, 13760, 23076 ] ] ] ), rec( name := "Fi22.2", sbgname := "O8^+(2).3.2 leq O8^+(2).3.2x2", filename := "O8+2.3.2", degree := 123552, rank := 8, permchar := "1a^{+-} + 3080a^{+-} + 13650a^{+-} + 45045a^{+-}", charnmbs := [ 1, 2, 13, 14, 17, 18, 25, 26 ], ctbl := [ [ 1, 1, 1575, 1575, 22400, 22400, 37800, 37800 ], [ 1, -1, 1575, -1575, -22400, 22400, 37800, -37800 ], [ 1, 1, 171, 171, -64, -64, -108, -108 ], [ 1, -1, 171, -171, 64, -64, -108, 108 ], [ 1, 1, -9, -9, 224, 224, -216, -216 ], [ 1, -1, -9, 9, -224, 224, -216, 216 ], [ 1, 1, -9, -9, -64, -64, 72, 72 ], [ 1, -1, -9, 9, 64, -64, 72, -72 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 1575, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1575, 0, 0, 0, 0 ], [ 1, 0, 198, 0, 0, 512, 864, 0 ], [ 0, 1, 0, 198, 512, 0, 0, 864 ], [ 0, 0, 0, 36, 567, 0, 0, 972 ], [ 0, 0, 36, 0, 0, 567, 972, 0 ], [ 0, 0, 36, 0, 0, 576, 963, 0 ], [ 0, 0, 0, 36, 576, 0, 0, 963 ] ], [ [ 0, 0, 0, 1575, 0, 0, 0, 0 ], [ 0, 0, 1575, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 198, 512, 0, 0, 864 ], [ 1, 0, 198, 0, 0, 512, 864, 0 ], [ 0, 0, 36, 0, 0, 567, 972, 0 ], [ 0, 0, 0, 36, 567, 0, 0, 972 ], [ 0, 0, 0, 36, 576, 0, 0, 963 ], [ 0, 0, 36, 0, 0, 576, 963, 0 ] ], [ [ 0, 0, 0, 0, 22400, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 22400, 0, 0 ], [ 0, 0, 0, 512, 8064, 0, 0, 13824 ], [ 0, 0, 512, 0, 0, 8064, 13824, 0 ], [ 1, 0, 567, 0, 0, 8224, 13608, 0 ], [ 0, 1, 0, 567, 8224, 0, 0, 13608 ], [ 0, 0, 0, 576, 8064, 0, 0, 13760 ], [ 0, 0, 576, 0, 0, 8064, 13760, 0 ] ], [ [ 0, 0, 0, 0, 0, 22400, 0, 0 ], [ 0, 0, 0, 0, 22400, 0, 0, 0 ], [ 0, 0, 512, 0, 0, 8064, 13824, 0 ], [ 0, 0, 0, 512, 8064, 0, 0, 13824 ], [ 0, 1, 0, 567, 8224, 0, 0, 13608 ], [ 1, 0, 567, 0, 0, 8224, 13608, 0 ], [ 0, 0, 576, 0, 0, 8064, 13760, 0 ], [ 0, 0, 0, 576, 8064, 0, 0, 13760 ] ], [ [ 0, 0, 0, 0, 0, 0, 37800, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 37800 ], [ 0, 0, 864, 0, 0, 13824, 23112, 0 ], [ 0, 0, 0, 864, 13824, 0, 0, 23112 ], [ 0, 0, 0, 972, 13608, 0, 0, 23220 ], [ 0, 0, 972, 0, 0, 13608, 23220, 0 ], [ 1, 0, 963, 0, 0, 13760, 23076, 0 ], [ 0, 1, 0, 963, 13760, 0, 0, 23076 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 37800 ], [ 0, 0, 0, 0, 0, 0, 37800, 0 ], [ 0, 0, 0, 864, 13824, 0, 0, 23112 ], [ 0, 0, 864, 0, 0, 13824, 23112, 0 ], [ 0, 0, 972, 0, 0, 13608, 23220, 0 ], [ 0, 0, 0, 972, 13608, 0, 0, 23220 ], [ 0, 1, 0, 963, 13760, 0, 0, 23076 ], [ 1, 0, 963, 0, 0, 13760, 23076, 0 ] ] ] ), rec( name := "Fi22.2", sbgname := "O8^+(2).S3 leq O8^+(2).3.2x2", filename := "O8+2.S3", degree := 123552, rank := 7, permchar := "1a^+ + 1001a^+ + 3080a^+ + 10725a^- + 13650a^+ + 45045a^+ + 50050a^-", charnmbs := [ 1, 7, 13, 16, 17, 25, 30 ], ctbl := [ [ 1, 1, 1575, 1575, 22400, 22400, 75600 ], [ 1, -1, -225, 225, -800, 800, 0 ], [ 1, 1, 171, 171, -64, -64, -216 ], [ 1, -1, 63, -63, -224, 224, 0 ], [ 1, 1, -9, -9, 224, 224, -432 ], [ 1, 1, -9, -9, -64, -64, 144 ], [ 1, -1, -9, 9, 64, -64, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1575, 0, 0, 0, 0 ], [ 0, 0, 0, 1575, 0, 0, 0 ], [ 1, 0, 54, 144, 0, 512, 864 ], [ 0, 1, 144, 54, 512, 0, 864 ], [ 0, 0, 0, 36, 243, 324, 972 ], [ 0, 0, 36, 0, 324, 243, 972 ], [ 0, 0, 18, 18, 288, 288, 963 ] ], [ [ 0, 0, 0, 1575, 0, 0, 0 ], [ 0, 0, 1575, 0, 0, 0, 0 ], [ 0, 1, 144, 54, 512, 0, 864 ], [ 1, 0, 54, 144, 0, 512, 864 ], [ 0, 0, 36, 0, 324, 243, 972 ], [ 0, 0, 0, 36, 243, 324, 972 ], [ 0, 0, 18, 18, 288, 288, 963 ] ], [ [ 0, 0, 0, 0, 22400, 0, 0 ], [ 0, 0, 0, 0, 0, 22400, 0 ], [ 0, 0, 0, 512, 3456, 4608, 13824 ], [ 0, 0, 512, 0, 4608, 3456, 13824 ], [ 1, 0, 243, 324, 3888, 4336, 13608 ], [ 0, 1, 324, 243, 4336, 3888, 13608 ], [ 0, 0, 288, 288, 4032, 4032, 13760 ] ], [ [ 0, 0, 0, 0, 0, 22400, 0 ], [ 0, 0, 0, 0, 22400, 0, 0 ], [ 0, 0, 512, 0, 4608, 3456, 13824 ], [ 0, 0, 0, 512, 3456, 4608, 13824 ], [ 0, 1, 324, 243, 4336, 3888, 13608 ], [ 1, 0, 243, 324, 3888, 4336, 13608 ], [ 0, 0, 288, 288, 4032, 4032, 13760 ] ], [ [ 0, 0, 0, 0, 0, 0, 75600 ], [ 0, 0, 0, 0, 0, 0, 75600 ], [ 0, 0, 864, 864, 13824, 13824, 46224 ], [ 0, 0, 864, 864, 13824, 13824, 46224 ], [ 0, 0, 972, 972, 13608, 13608, 46440 ], [ 0, 0, 972, 972, 13608, 13608, 46440 ], [ 1, 1, 963, 963, 13760, 13760, 46152 ] ] ] ), rec( name := "Fi22.2", sbgname := "O8^+(2).3x2 leq O8^+(2).3.2x2", filename := "O8+2.3x2", degree := 123552, rank := 7, permchar := "1a^+ + 1001a^- + 3080a^+ + 10725a^+ + 13650a^+ + 45045a^+ + 50050a^+", charnmbs := [ 1, 8, 13, 15, 17, 25, 29 ], ctbl := [ [ 1, 1, 1575, 1575, 22400, 22400, 75600 ], [ 1, -1, 225, -225, -800, 800, 0 ], [ 1, 1, 171, 171, -64, -64, -216 ], [ 1, -1, -63, 63, -224, 224, 0 ], [ 1, 1, -9, -9, 224, 224, -432 ], [ 1, 1, -9, -9, -64, -64, 144 ], [ 1, -1, 9, -9, 64, -64, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 1575, 0, 0, 0, 0 ], [ 0, 0, 0, 1575, 0, 0, 0 ], [ 1, 0, 144, 54, 0, 512, 864 ], [ 0, 1, 54, 144, 512, 0, 864 ], [ 0, 0, 0, 36, 324, 243, 972 ], [ 0, 0, 36, 0, 243, 324, 972 ], [ 0, 0, 18, 18, 288, 288, 963 ] ], [ [ 0, 0, 0, 1575, 0, 0, 0 ], [ 0, 0, 1575, 0, 0, 0, 0 ], [ 0, 1, 54, 144, 512, 0, 864 ], [ 1, 0, 144, 54, 0, 512, 864 ], [ 0, 0, 36, 0, 243, 324, 972 ], [ 0, 0, 0, 36, 324, 243, 972 ], [ 0, 0, 18, 18, 288, 288, 963 ] ], [ [ 0, 0, 0, 0, 22400, 0, 0 ], [ 0, 0, 0, 0, 0, 22400, 0 ], [ 0, 0, 0, 512, 4608, 3456, 13824 ], [ 0, 0, 512, 0, 3456, 4608, 13824 ], [ 1, 0, 324, 243, 3888, 4336, 13608 ], [ 0, 1, 243, 324, 4336, 3888, 13608 ], [ 0, 0, 288, 288, 4032, 4032, 13760 ] ], [ [ 0, 0, 0, 0, 0, 22400, 0 ], [ 0, 0, 0, 0, 22400, 0, 0 ], [ 0, 0, 512, 0, 3456, 4608, 13824 ], [ 0, 0, 0, 512, 4608, 3456, 13824 ], [ 0, 1, 243, 324, 4336, 3888, 13608 ], [ 1, 0, 324, 243, 3888, 4336, 13608 ], [ 0, 0, 288, 288, 4032, 4032, 13760 ] ], [ [ 0, 0, 0, 0, 0, 0, 75600 ], [ 0, 0, 0, 0, 0, 0, 75600 ], [ 0, 0, 864, 864, 13824, 13824, 46224 ], [ 0, 0, 864, 864, 13824, 13824, 46224 ], [ 0, 0, 972, 972, 13608, 13608, 46440 ], [ 0, 0, 972, 972, 13608, 13608, 46440 ], [ 1, 1, 963, 963, 13760, 13760, 46152 ] ] ] ), rec( name := "Fi22.2", sbgname := "O8^+(2).2x2 leq O8^+(2).3.2x2", filename := "O8+2.2x2", degree := 185328, rank := 7, permchar := "1a^+ + 429a^+ + 3080a^+ + 13650a^+ + 45045a^+ + 48048a^+ + 75075a^+", charnmbs := [ 1, 5, 13, 17, 25, 27, 33 ], ctbl := [ [ 1, 2, 1575, 3150, 22400, 44800, 113400 ], [ 1, -1, 315, -315, 2240, -2240, 0 ], [ 1, 2, 171, 342, -64, -128, -324 ], [ 1, 2, -9, -18, 224, 448, -648 ], [ 1, 2, -9, -18, -64, -128, 216 ], [ 1, -1, -45, 45, 80, -80, 0 ], [ 1, -1, 27, -27, -64, 64, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 2, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 2, 0, 0, 0 ], [ 0, 0, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 0 ], [ 0, 0, 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 2 ] ], [ [ 0, 0, 1575, 0, 0, 0, 0 ], [ 0, 0, 0, 1575, 0, 0, 0 ], [ 1, 0, 102, 96, 512, 0, 864 ], [ 0, 1, 48, 150, 0, 512, 864 ], [ 0, 0, 36, 0, 351, 216, 972 ], [ 0, 0, 0, 36, 108, 459, 972 ], [ 0, 0, 12, 24, 192, 384, 963 ] ], [ [ 0, 0, 0, 3150, 0, 0, 0 ], [ 0, 0, 1575, 1575, 0, 0, 0 ], [ 0, 2, 96, 300, 0, 1024, 1728 ], [ 1, 1, 150, 246, 512, 512, 1728 ], [ 0, 0, 0, 72, 216, 918, 1944 ], [ 0, 0, 36, 36, 459, 675, 1944 ], [ 0, 0, 24, 48, 384, 768, 1926 ] ], [ [ 0, 0, 0, 0, 22400, 0, 0 ], [ 0, 0, 0, 0, 0, 22400, 0 ], [ 0, 0, 512, 0, 4992, 3072, 13824 ], [ 0, 0, 0, 512, 1536, 6528, 13824 ], [ 1, 0, 351, 216, 3904, 4320, 13608 ], [ 0, 1, 108, 459, 2160, 6064, 13608 ], [ 0, 0, 192, 384, 2688, 5376, 13760 ] ], [ [ 0, 0, 0, 0, 0, 44800, 0 ], [ 0, 0, 0, 0, 22400, 22400, 0 ], [ 0, 0, 0, 1024, 3072, 13056, 27648 ], [ 0, 0, 512, 512, 6528, 9600, 27648 ], [ 0, 2, 216, 918, 4320, 12128, 27216 ], [ 1, 1, 459, 675, 6064, 10384, 27216 ], [ 0, 0, 384, 768, 5376, 10752, 27520 ] ], [ [ 0, 0, 0, 0, 0, 0, 113400 ], [ 0, 0, 0, 0, 0, 0, 113400 ], [ 0, 0, 864, 1728, 13824, 27648, 69336 ], [ 0, 0, 864, 1728, 13824, 27648, 69336 ], [ 0, 0, 972, 1944, 13608, 27216, 69660 ], [ 0, 0, 972, 1944, 13608, 27216, 69660 ], [ 1, 2, 963, 1926, 13760, 27520, 69228 ] ] ] ), rec( name := "Fi22.2", sbgname := "O8^+(2).3 leq O8^+(2).3.2x2", filename := "O8+2.3", degree := 247104, rank := 14, permchar := "1a^{+-} + 1001a^{+-} + 3080a^{+-} + 10725a^{+-} + 13650a^{+-} + 45045a^{+-} + 50050a^{+-}", charnmbs := [ 1, 2, 7, 8, 13, 14, 15, 16, 17, 18, 25, 26, 29, 30 ], ctbl := [ [ 1, 1, 1, 1, 1575, 1575, 1575, 1575, 22400, 22400, 22400, 22400, 75600, 75600 ], [ 1, -1, 1, -1, -1575, 1575, -1575, 1575, 22400, -22400, 22400, -22400, 75600, -75600 ], [ 1, 1, -1, -1, -225, -225, 225, 225, 800, 800, -800, -800, 0, 0 ], [ 1, -1, -1, 1, 225, -225, -225, 225, 800, -800, -800, 800, 0, 0 ], [ 1, 1, 1, 1, 171, 171, 171, 171, -64, -64, -64, -64, -216, -216 ], [ 1, -1, 1, -1, -171, 171, -171, 171, -64, 64, -64, 64, -216, 216 ], [ 1, -1, -1, 1, -63, 63, 63, -63, 224, -224, -224, 224, 0, 0 ], [ 1, 1, -1, -1, 63, 63, -63, -63, 224, 224, -224, -224, 0, 0 ], [ 1, 1, 1, 1, -9, -9, -9, -9, 224, 224, 224, 224, -432, -432 ], [ 1, -1, 1, -1, 9, -9, 9, -9, 224, -224, 224, -224, -432, 432 ], [ 1, 1, 1, 1, -9, -9, -9, -9, -64, -64, -64, -64, 144, 144 ], [ 1, -1, 1, -1, 9, -9, 9, -9, -64, 64, -64, 64, 144, -144 ], [ 1, -1, -1, 1, 9, -9, -9, 9, -64, 64, 64, -64, 0, 0 ], [ 1, 1, -1, -1, -9, -9, 9, 9, -64, -64, 64, 64, 0, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 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1926, 13760, 0, 27520, 0, 0, 69228 ] ] ] ), rec( name := "Fi22.2", sbgname := "O8^+(2).2 leq O8^+(2).3.2x2 (Rank 13)", filename := "O8+2.2-13", degree := 370656, rank := 13, permchar := "1a^+ + 429a^{+-} + 1001a^+ + 3080a^+ + 10725a^- + 13650a^+ + 45045a^+ + 48048a^{+-} + 50050a^- + 75075a^{+-}", charnmbs := [ 1, 5, 6, 7, 13, 16, 17, 25, 27, 28, 30, 33, 34 ], ctbl := [ [ 1, 1, 2, 2, 1575, 1575, 3150, 3150, 22400, 22400, 44800, 44800, 226800 ], [ 1, 1, -1, -1, 315, 315, -315, -315, 2240, 2240, -2240, -2240, 0 ], [ 1, -1, -1, 1, 315, -315, 315, -315, -2240, 2240, -2240, 2240, 0 ], [ 1, -1, 2, -2, -225, 225, 450, -450, -800, 800, 1600, -1600, 0 ], [ 1, 1, 2, 2, 171, 171, 342, 342, -64, -64, -128, -128, -648 ], [ 1, -1, 2, -2, 63, -63, -126, 126, -224, 224, 448, -448, 0 ], [ 1, 1, 2, 2, -9, -9, -18, -18, 224, 224, 448, 448, -1296 ], [ 1, 1, 2, 2, -9, -9, -18, -18, -64, -64, -128, -128, 432 ], [ 1, 1, -1, -1, -45, -45, 45, 45, 80, 80, -80, -80, 0 ], [ 1, -1, -1, 1, -45, 45, -45, 45, -80, 80, -80, 80, 0 ], [ 1, -1, 2, -2, -9, 9, 18, -18, 64, -64, -128, 128, 0 ], [ 1, 1, -1, -1, 27, 27, -27, -27, -64, -64, 64, 64, 0 ], [ 1, -1, -1, 1, 27, -27, 27, -27, 64, -64, 64, -64, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 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432, 3472, 2592, 5184, 5200, 27216 ], [ 1, 0, 1, 0, 243, 216, 432, 243, 2592, 3472, 5200, 5184, 27216 ], [ 0, 0, 0, 0, 192, 192, 384, 384, 2688, 2688, 5376, 5376, 27520 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 226800 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 226800 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 226800 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 226800 ], [ 0, 0, 0, 0, 864, 864, 1728, 1728, 13824, 13824, 27648, 27648, 138672 ], [ 0, 0, 0, 0, 864, 864, 1728, 1728, 13824, 13824, 27648, 27648, 138672 ], [ 0, 0, 0, 0, 864, 864, 1728, 1728, 13824, 13824, 27648, 27648, 138672 ], [ 0, 0, 0, 0, 864, 864, 1728, 1728, 13824, 13824, 27648, 27648, 138672 ], [ 0, 0, 0, 0, 972, 972, 1944, 1944, 13608, 13608, 27216, 27216, 139320 ], [ 0, 0, 0, 0, 972, 972, 1944, 1944, 13608, 13608, 27216, 27216, 139320 ], [ 0, 0, 0, 0, 972, 972, 1944, 1944, 13608, 13608, 27216, 27216, 139320 ], [ 0, 0, 0, 0, 972, 972, 1944, 1944, 13608, 13608, 27216, 27216, 139320 ], [ 1, 1, 2, 2, 963, 963, 1926, 1926, 13760, 13760, 27520, 27520, 138456 ] ] ] ), rec( name := "Fi22.2", sbgname := "2^{10}:M22.2", filename := "2^10:M22.2", degree := 142155, rank := 8, permchar := "1a^+ + 78a^+ + 429a^+ + 1430a^+ + 3080a^+ + 30030a^+ + 32032a^+ + 75075a^+", charnmbs := [ 1, 3, 5, 9, 13, 19, 21, 33 ], ctbl := [ [ 1, 154, 1024, 3696, 4928, 11264, 42240, 78848 ], [ 1, -77, -320, 924, 1232, -1408, -5280, 4928 ], [ 1, 49, -176, 546, -532, 1184, -960, -112 ], [ 1, -35, 160, 294, -364, -400, 120, 224 ], [ 1, 37, 88, 186, 248, 32, 120, -712 ], [ 1, 13, -32, 6, -28, -112, 120, 32 ], [ 1, -17, -20, 24, 32, 32, 120, -172 ], [ 1, 1, 16, -30, -4, 32, -96, 80 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 154, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 120, 32, 0, 0, 0 ], [ 0, 0, 0, 0, 77, 0, 0, 77 ], [ 0, 5, 0, 5, 0, 64, 80, 0 ], [ 0, 1, 16, 0, 1, 0, 120, 16 ], [ 0, 0, 0, 21, 0, 21, 0, 112 ], [ 0, 0, 0, 7, 14, 0, 21, 112 ], [ 0, 0, 1, 0, 1, 16, 60, 76 ] ], [ [ 0, 0, 1024, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 512, 0, 0, 512 ], [ 1, 0, 22, 231, 0, 0, 0, 770 ], [ 0, 0, 64, 0, 0, 0, 640, 320 ], [ 0, 16, 0, 0, 16, 256, 480, 256 ], [ 0, 0, 0, 0, 112, 0, 240, 672 ], [ 0, 0, 0, 56, 56, 64, 176, 672 ], [ 0, 1, 10, 15, 16, 96, 360, 526 ] ], [ [ 0, 0, 0, 3696, 0, 0, 0, 0 ], [ 0, 120, 0, 120, 0, 1536, 1920, 0 ], [ 0, 0, 231, 0, 0, 0, 2310, 1155 ], [ 1, 5, 0, 450, 120, 320, 240, 2560 ], [ 0, 0, 0, 90, 510, 0, 600, 2496 ], [ 0, 21, 0, 105, 0, 630, 1260, 1680 ], [ 0, 7, 56, 21, 70, 336, 1470, 1736 ], [ 0, 0, 15, 120, 156, 240, 930, 2235 ] ], [ [ 0, 0, 0, 0, 4928, 0, 0, 0 ], [ 0, 32, 512, 0, 32, 0, 3840, 512 ], [ 0, 77, 0, 0, 77, 1232, 2310, 1232 ], [ 0, 0, 0, 120, 680, 0, 800, 3328 ], [ 1, 1, 16, 510, 256, 256, 480, 3408 ], [ 0, 0, 112, 0, 112, 252, 2100, 2352 ], [ 0, 14, 56, 70, 56, 560, 1876, 2296 ], [ 0, 1, 16, 156, 213, 336, 1230, 2976 ] ], [ [ 0, 0, 0, 0, 0, 11264, 0, 0 ], [ 0, 0, 0, 1536, 0, 1536, 0, 8192 ], [ 0, 0, 0, 0, 1232, 0, 2640, 7392 ], [ 0, 64, 0, 320, 0, 1920, 3840, 5120 ], [ 0, 0, 256, 0, 256, 576, 4800, 5376 ], [ 1, 21, 0, 630, 252, 1120, 2520, 6720 ], [ 0, 0, 64, 336, 560, 672, 2912, 6720 ], [ 0, 16, 96, 240, 336, 960, 3600, 6016 ] ], [ [ 0, 0, 0, 0, 0, 0, 42240, 0 ], [ 0, 0, 0, 1920, 3840, 0, 5760, 30720 ], [ 0, 0, 0, 2310, 2310, 2640, 7260, 27720 ], [ 0, 80, 640, 240, 800, 3840, 16800, 19840 ], [ 0, 120, 480, 600, 480, 4800, 16080, 19680 ], [ 0, 0, 240, 1260, 2100, 2520, 10920, 25200 ], [ 1, 21, 176, 1470, 1876, 2912, 10584, 25200 ], [ 0, 60, 360, 930, 1230, 3600, 13500, 22560 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 78848 ], [ 0, 0, 512, 0, 512, 8192, 30720, 38912 ], [ 0, 77, 770, 1155, 1232, 7392, 27720, 40502 ], [ 0, 0, 320, 2560, 3328, 5120, 19840, 47680 ], [ 0, 16, 256, 2496, 3408, 5376, 19680, 47616 ], [ 0, 112, 672, 1680, 2352, 6720, 25200, 42112 ], [ 0, 112, 672, 1736, 2296, 6720, 25200, 42112 ], [ 1, 76, 526, 2235, 2976, 6016, 22560, 44458 ] ] ] ), rec( name := "Fi22.2", sbgname := "2^{10}:M22 leq 2^{10}:M22.2", filename := "2^10:M22", degree := 284310, rank := 16, permchar := "1a^{+-} + 78a^{+-} + 429a^{+-} + 1430a^{+-} + 3080a^{+-} + 30030a^{+-} + 32032a^{+-} + 75075a^{+-}", charnmbs := [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 19, 20, 21, 22, 33, 34 ], ctbl := [ [ 1, 1, 154, 154, 1024, 1024, 3696, 3696, 4928, 4928, 11264, 11264, 42240, 42240, 78848, 78848 ], [ 1, -1, -154, 154, 1024, -1024, 3696, -3696, -4928, 4928, -11264, 11264, 42240, -42240, -78848, 78848 ], [ 1, 1, -77, -77, -320, -320, 924, 924, 1232, 1232, -1408, -1408, -5280, -5280, 4928, 4928 ], [ 1, -1, 77, -77, -320, 320, 924, -924, -1232, 1232, 1408, -1408, -5280, 5280, -4928, 4928 ], [ 1, 1, 49, 49, -176, -176, 546, 546, -532, -532, 1184, 1184, -960, -960, -112, -112 ], [ 1, -1, -49, 49, -176, 176, 546, -546, 532, -532, -1184, 1184, -960, 960, 112, -112 ], [ 1, 1, -35, -35, 160, 160, 294, 294, -364, -364, 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[ 1, 45, 510, 960, 2808, 4080, 15948, 51968, 84096, 81504 ] ] ] ), rec( name := "Fi22.2", sbgname := "2^6:S6(2) leq 2^7:S6(2)", filename := "2^6:S62", degree := 1389960, rank := 20, permchar := "1a^{+-} + 429a^{+-} + 1430a^{+-} + 3080a^{+-} + 13650a^{+-} + 30030a^{+-} + 45045a^{+-} + 75075a^{+-} + 205920a^{+-} + 320320a^{+-}", charnmbs := [ 1, 2, 5, 6, 9, 10, 13, 14, 17, 18, 19, 20, 25, 26, 33, 34, 46, 47, 52, 53 ], ctbl := [ [ 1, 1, 135, 135, 1260, 1260, 2304, 2304, 8640, 8640, 10080, 10080, 45360, 45360, 143360, 143360, 241920, 241920, 241920, 241920 ], [ 1, -1, 135, -135, -1260, 1260, 2304, -2304, 8640, -8640, -10080, 10080, -45360, 45360, 143360, -143360, 241920, 241920, -241920, -241920 ], [ 1, 1, -15, -15, 210, 210, 624, 624, -960, -960, 1680, 1680, 1260, 1260, 8960, 8960, -10080, -1680, -1680, -10080 ], [ 1, -1, -15, 15, -210, 210, 624, -624, -960, 960, -1680, 1680, -1260, 1260, 8960, -8960, -10080, -1680, 1680, 10080 ], [ 1, 1, -27, -27, 126, 126, -288, -288, 216, 216, 1008, 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sbgname := "A12", degree := 1140000, rank := 12, permchar := "1a + 133ab + 760a + 3344a + 8910a + 16929a + 35112ab + 267520a + 365750a + 406296a", charnmbs := [ 1, 2, 3, 4, 5, 8, 10, 11, 12, 18, 20, 23 ], ctbl := [ [ 1, 462, 2520, 2520, 10395, 16632, 30800, 69300, 166320, 166320, 311850, 362880 ], [ 1, -198, 360*E(5)-360*E(5)^2-360*E(5)^3+360*E(5)^4, -360*E(5)+360*E(5)^2+360*E(5)^3-360*E(5)^4, 2475, 792, 4400, -9900, -7920*E(5)+7920*E(5)^2+7920*E(5)^3-7920*E(5)^4, 7920*E(5)-7920*E(5)^2-7920*E(5)^3+7920*E(5)^4, -14850, 17280 ], [ 1, -198, -360*E(5)+360*E(5)^2+360*E(5)^3-360*E(5)^4, 360*E(5)-360*E(5)^2-360*E(5)^3+360*E(5)^4, 2475, 792, 4400, -9900, 7920*E(5)-7920*E(5)^2-7920*E(5)^3+7920*E(5)^4, -7920*E(5)+7920*E(5)^2+7920*E(5)^3-7920*E(5)^4, -14850, 17280 ], [ 1, 132, -540, -540, 1485, -1188, 1100, 4950, -5940, -5940, 0, 6480 ], [ 1, 12, 120, 120, 495, 1332, -2200, 300, -1080, -1080, -900, 2880 ], [ 1, 82, 240, 240, 515, -88, 400, 900, 640, 640, -1650, -1920 ], [ 1, 62, -120, -120, 155, 632, 400, -300, 80, 80, 1050, -1920 ], [ 1, -48, 60*E(5)-60*E(5)^2-60*E(5)^3+60*E(5)^4, -60*E(5)+60*E(5)^2+60*E(5)^3-60*E(5)^4, 225, -108, -100, -150, 180*E(5)-180*E(5)^2-180*E(5)^3+180*E(5)^4, -180*E(5)+180*E(5)^2+180*E(5)^3-180*E(5)^4, 900, -720 ], [ 1, -48, -60*E(5)+60*E(5)^2+60*E(5)^3-60*E(5)^4, 60*E(5)-60*E(5)^2-60*E(5)^3+60*E(5)^4, 225, -108, -100, -150, -180*E(5)+180*E(5)^2+180*E(5)^3-180*E(5)^4, 180*E(5)-180*E(5)^2-180*E(5)^3+180*E(5)^4, 900, -720 ], [ 1, 12, 30, 30, -45, -18, 50, -150, -270, -270, 450, 180 ], [ 1, -18, 0, 0, -45, 72, 80, 180, 0, 0, -270, 0 ], [ 1, 12, -20, -20, 5, -68, -100, -50, 180, 180, -200, 80 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 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[ 0, 54, 972, 0, 1458, 2916, 3888, 9558, 14472, 35316, 45198, 52488 ], [ 0, 36, 72, 1008, 1116, 2736, 4248, 8748, 36432, 15480, 45468, 50976 ], [ 0, 180, 300, 300, 640, 1936, 2680, 15180, 23400, 23400, 51960, 46344 ], [ 1, 0, 300, 300, 2845, 2620, 6540, 6450, 23400, 23400, 39000, 61464 ], [ 0, 64, 192, 528, 1512, 2448, 4464, 10104, 27712, 20800, 45504, 52992 ], [ 0, 55, 561, 231, 1386, 2475, 4455, 9735, 21241, 28171, 45540, 52470 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 311850, 0 ], [ 0, 0, 0, 0, 4050, 8100, 16200, 2700, 43200, 43200, 64800, 129600 ], [ 0, 0, 0, 990, 1980, 3960, 7920, 17820, 65340, 23760, 87120, 102960 ], [ 0, 0, 990, 0, 1980, 3960, 7920, 17820, 23760, 65340, 87120, 102960 ], [ 0, 180, 480, 480, 720, 3840, 4800, 26400, 45360, 45360, 99750, 84480 ], [ 0, 225, 600, 600, 2400, 4500, 8400, 20400, 45900, 45900, 88125, 94800 ], [ 0, 243, 648, 648, 1620, 4536, 5832, 23652, 45198, 45198, 92907, 91368 ], [ 0, 18, 648, 648, 3960, 4896, 10512, 13932, 45468, 45468, 78012, 108288 ], [ 0, 120, 990, 360, 2835, 4590, 8370, 18945, 39000, 51960, 85320, 99360 ], [ 0, 120, 360, 990, 2835, 4590, 8370, 18945, 51960, 39000, 85320, 99360 ], [ 1, 96, 704, 704, 3325, 4700, 9176, 17336, 45504, 45504, 82976, 101824 ], [ 0, 165, 715, 715, 2420, 4345, 7755, 20680, 45540, 45540, 87505, 96470 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 362880 ], [ 0, 0, 0, 0, 0, 0, 0, 43200, 43200, 43200, 129600, 103680 ], [ 0, 0, 1584, 144, 1584, 7920, 7920, 15840, 33264, 80784, 102960, 110880 ], [ 0, 0, 144, 1584, 1584, 7920, 7920, 15840, 80784, 33264, 102960, 110880 ], [ 0, 0, 384, 384, 6144, 5760, 13440, 15360, 48384, 48384, 84480, 140160 ], [ 0, 0, 1200, 1200, 3600, 6000, 8400, 19200, 54000, 54000, 94800, 120480 ], [ 0, 0, 648, 648, 4536, 4536, 13608, 16848, 52488, 52488, 91368, 125712 ], [ 0, 288, 576, 576, 2304, 4608, 7488, 29088, 50976, 50976, 108288, 107712 ], [ 0, 120, 504, 1224, 3024, 5400, 9720, 21240, 61464, 46344, 99360, 114480 ], [ 0, 120, 1224, 504, 3024, 5400, 9720, 21240, 46344, 61464, 99360, 114480 ], [ 0, 192, 832, 832, 2816, 5056, 9024, 24064, 52992, 52992, 101824, 112256 ], [ 1, 132, 770, 770, 4015, 5522, 10670, 20570, 52470, 52470, 96470, 119020 ] ] ] ), rec( name := "HN", sbgname := "A11", degree := 13680000, rank := 19, permchar := "1a + 133ab + 760a + 3344a + 8910a + 9405a + 16929a + 35112ab + 267520a + 365750a + 406296a + 653125a + 1185030a + 2031480a + 2375000a + 2407680a + 3878280a", charnmbs := [ 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 18, 20, 23, 24, 32, 39, 40, 41, 47 ], ctbl := [ [ 1, 11, 2772, 2772, 16632, 20790, 30240, 30240, 83160, 99792, 103950, 362880, 369600, 831600, 1247400, 1995840, 1995840, 2494800, 3991680 ], [ 1, 11, -1188, -1188, 792, 4950, -4320*E(5)+4320*E(5)^2+4320*E(5)^3-4320*E(5)^4, 4320*E(5)-4320*E(5)^2-4320*E(5)^3+4320*E(5)^4, 3960, 4752, 24750, 17280, 52800, -118800, -59400, 95040*E(5)-95040*E(5)^2-95040*E(5)^3+95040*E(5)^4, -95040*E(5)+95040*E(5)^2+95040*E(5)^3-95040*E(5)^4, -118800, 190080 ], [ 1, 11, -1188, -1188, 792, 4950, 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41328, 64800, 169344 ], [ 0, 1, 56, 300, 550, 1375, 2600, 5650, 28700, 33300, 48384, 63750, 170150 ], [ 1, 0, 300, 56, 550, 1375, 5650, 2600, 28700, 48384, 33300, 63750, 170150 ], [ 0, 0, 160, 160, 480, 1280, 3920, 3920, 28800, 40800, 40800, 64416, 170080 ], [ 0, 0, 156, 156, 504, 1380, 4062, 4062, 28224, 40836, 40836, 63780, 170820 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 554400, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 554400, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 63000, 63000, 63000, 113400, 252000 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 63000, 63000, 63000, 113400, 252000 ], [ 0, 0, 0, 0, 2520, 2520, 10080, 10080, 30240, 60480, 60480, 115920, 262080 ], [ 0, 0, 0, 0, 960, 960, 3840, 3840, 49920, 61440, 61440, 118560, 253440 ], [ 0, 0, 0, 0, 1260, 1260, 5040, 5040, 46620, 61740, 61740, 114660, 257040 ], [ 0, 0, 0, 0, 1260, 1260, 5040, 5040, 46620, 61740, 61740, 114660, 257040 ], [ 0, 0, 360, 360, 540, 2340, 6660, 6660, 44280, 64800, 64800, 93240, 270360 ], [ 0, 0, 250, 250, 750, 2000, 6125, 6125, 45000, 63750, 63750, 100650, 265750 ], [ 0, 0, 250, 250, 750, 2000, 6125, 6125, 45000, 63750, 63750, 100650, 265750 ], [ 1, 1, 288, 288, 920, 2470, 7280, 7280, 41440, 64416, 64416, 97920, 267680 ], [ 0, 0, 240, 240, 780, 1980, 6120, 6120, 45060, 63780, 63780, 100380, 265920 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1478400 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1478400 ], [ 0, 0, 0, 0, 2100, 10500, 16800, 16800, 96600, 163800, 163800, 252000, 756000 ], [ 0, 0, 0, 0, 2100, 10500, 16800, 16800, 96600, 163800, 163800, 252000, 756000 ], [ 0, 0, 672, 672, 672, 6720, 13776, 13776, 121632, 169344, 169344, 262080, 719712 ], [ 0, 0, 1280, 1280, 2560, 3840, 21120, 21120, 121600, 176640, 176640, 253440, 698880 ], [ 0, 0, 672, 672, 1722, 6930, 17136, 17136, 114492, 170604, 170604, 257040, 721392 ], [ 0, 0, 672, 672, 1722, 6930, 17136, 17136, 114492, 170604, 170604, 257040, 721392 ], [ 0, 0, 552, 552, 2172, 5700, 16356, 16356, 117912, 169344, 169344, 270360, 709752 ], [ 0, 0, 650, 650, 2100, 5750, 16925, 16925, 117600, 170150, 170150, 265750, 711750 ], [ 0, 0, 650, 650, 2100, 5750, 16925, 16925, 117600, 170150, 170150, 265750, 711750 ], [ 0, 0, 640, 640, 2080, 5280, 16320, 16320, 120160, 170080, 170080, 267680, 709120 ], [ 1, 1, 720, 720, 2142, 5460, 17176, 17176, 118292, 170820, 170820, 265920, 709152 ] ] ] ), rec( name := "Ly", sbgname := "3.McL.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 9606125, rank := 5, permchar := "1a + 45694a + 1534500a + 3028266a + 4997664a", charnmbs := [ 1, 4, 11, 12, 15 ], ctbl := [ [ 1, 15400, 534600, 1871100, 7185024 ], [ 1, -325, 10125, -2025, -7776 ], [ 1, -10, -60, 2805, -2736 ], [ 1, 175, 125, -525, 224 ], [ 1, -100, -150, -525, 774 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 15400, 0, 0, 0 ], [ 1, 90, 1215, 2430, 11664 ], [ 0, 35, 560, 3045, 11760 ], [ 0, 20, 870, 2990, 11520 ], [ 0, 25, 875, 3000, 11500 ] ], [ [ 0, 0, 534600, 0, 0 ], [ 0, 1215, 19440, 105705, 408240 ], [ 1, 560, 38985, 102270, 392784 ], [ 0, 870, 29220, 104190, 400320 ], [ 0, 875, 29225, 104250, 400250 ] ], [ [ 0, 0, 0, 1871100, 0 ], [ 0, 2430, 105705, 363285, 1399680 ], [ 0, 3045, 102270, 364665, 1401120 ], [ 1, 2990, 104190, 366255, 1397664 ], [ 0, 3000, 104250, 363975, 1399875 ] ], [ [ 0, 0, 0, 0, 7185024 ], [ 0, 11664, 408240, 1399680, 5365440 ], [ 0, 11760, 392784, 1401120, 5379360 ], [ 0, 11520, 400320, 1397664, 5375520 ], [ 1, 11500, 400250, 1399875, 5373398 ] ] ] ), rec( name := "Ly", sbgname := "G2(5)", filename := "G25", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 8835156, rank := 5, permchar := "1a + 45694a + 1534500a + 3028266a + 4226695a", charnmbs := [ 1, 4, 11, 12, 14 ], ctbl := [ [ 1, 19530, 968750, 2034375, 5812500 ], [ 1, 549, 11375, 3075, -15000 ], [ 1, 234, -70, -1755, 1590 ], [ 1, 49, -625, 1575, -1000 ], [ 1, -126, 350, -525, 300 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 19530, 0, 0, 0 ], [ 1, 154, 3125, 3750, 12500 ], [ 0, 63, 2520, 4599, 12348 ], [ 0, 36, 2190, 4584, 12720 ], [ 0, 42, 2058, 4452, 12978 ] ], [ [ 0, 0, 968750, 0, 0 ], [ 0, 3125, 125000, 228125, 612500 ], [ 1, 2520, 114013, 225372, 626844 ], [ 0, 2190, 107320, 223080, 636160 ], [ 0, 2058, 104474, 222656, 639562 ] ], [ [ 0, 0, 0, 2034375, 0 ], [ 0, 3750, 228125, 477500, 1325000 ], [ 0, 4599, 225372, 468468, 1335936 ], [ 1, 4584, 223080, 468670, 1338040 ], [ 0, 4452, 222656, 468314, 1338953 ] ], [ [ 0, 0, 0, 0, 5812500 ], [ 0, 12500, 612500, 1325000, 3862500 ], [ 0, 12348, 626844, 1335936, 3837372 ], [ 0, 12720, 636160, 1338040, 3825580 ], [ 1, 12978, 639562, 1338953, 3821006 ] ] ] ), rec( name := "Fi23", sbgname := "2.Fi22", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 31671, rank := 3, permchar := "1a + 782a + 30888a", charnmbs := [ 1, 2, 6 ], ctbl := [ [ 1, 3510, 28160 ], [ 1, 351, -352 ], [ 1, -9, 8 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 3510, 0 ], [ 1, 693, 2816 ], [ 0, 351, 3159 ] ], [ [ 0, 0, 28160 ], [ 0, 2816, 25344 ], [ 1, 3159, 25000 ] ] ] ), rec( name := "Fi23", sbgname := "O8^+(3).3 leq O8^+(3).3.2", filename := "O8+3.3", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 275264, rank := 5, permchar := "1a + 25806a + 30888a + 106743a + 111826a", charnmbs := [ 1, 5, 6, 8, 9 ], ctbl := [ [ 1, 1, 28431, 28431, 218400 ], [ 1, -1, -351, 351, 0 ], [ 1, 1, 279, 279, -560 ], [ 1, 1, -81, -81, 160 ], [ 1, -1, 81, -81, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 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 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 28431, 0, 0 ], [ 0, 0, 0, 28431, 0 ], [ 1, 0, 2880, 3150, 22400 ], [ 0, 1, 3150, 2880, 22400 ], [ 0, 0, 2916, 2916, 22599 ] ], [ [ 0, 0, 0, 28431, 0 ], [ 0, 0, 28431, 0, 0 ], [ 0, 1, 3150, 2880, 22400 ], [ 1, 0, 2880, 3150, 22400 ], [ 0, 0, 2916, 2916, 22599 ] ], [ [ 0, 0, 0, 0, 218400 ], [ 0, 0, 0, 0, 218400 ], [ 0, 0, 22400, 22400, 173600 ], [ 0, 0, 22400, 22400, 173600 ], [ 1, 1, 22599, 22599, 173200 ] ] ] ), rec( name := "Fi23", sbgname := "O8^+(3).3.2", filename := "O8+3.3.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 137632, rank := 3, permchar := "1a + 30888a + 106743a", charnmbs := [ 1, 6, 8 ], ctbl := [ [ 1, 28431, 109200 ], [ 1, 279, -280 ], [ 1, -81, 80 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 28431, 0 ], [ 1, 6030, 22400 ], [ 0, 5832, 22599 ] ], [ [ 0, 0, 109200 ], [ 0, 22400, 86800 ], [ 1, 22599, 86600 ] ] ] ), rec( name := "Fi23", sbgname := "O8^+(3).2_2 leq O8^+(3).3.2", filename := "O8+3.3.2_2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 412896, rank := 5, permchar := "1a + 782a + 30888a + 106743a + 274482a", charnmbs := [ 1, 2, 6, 8, 10 ], ctbl := [ [ 1, 2, 28431, 56862, 327600 ], [ 1, -1, 3159, -3159, 0 ], [ 1, 2, 279, 558, -840 ], [ 1, 2, -81, -162, 240 ], [ 1, -1, -9, 9, 0 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 2, 0, 0, 0 ], [ 1, 1, 0, 0, 0 ], [ 0, 0, 0, 2, 0 ], [ 0, 0, 1, 1, 0 ], [ 0, 0, 0, 0, 2 ] ], [ [ 0, 0, 28431, 0, 0 ], [ 0, 0, 0, 28431, 0 ], [ 1, 0, 4110, 1920, 22400 ], [ 0, 1, 960, 5070, 22400 ], [ 0, 0, 1944, 3888, 22599 ] ], [ [ 0, 0, 0, 56862, 0 ], [ 0, 0, 28431, 28431, 0 ], [ 0, 2, 1920, 10140, 44800 ], [ 1, 1, 5070, 6990, 44800 ], [ 0, 0, 3888, 7776, 45198 ] ], [ [ 0, 0, 0, 0, 327600 ], [ 0, 0, 0, 0, 327600 ], [ 0, 0, 22400, 44800, 260400 ], [ 0, 0, 22400, 44800, 260400 ], [ 1, 2, 22599, 45198, 259800 ] ] ] ), rec( name := "Fi23", sbgname := "2^{11}.M23", filename := "2^11.M23", degree := 195747435, 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E. Praeger and L. H. 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7368704 ] , [ 0, 0, 3840, 11520, 13056, 110592, 175104, 536832, 1370112, 3538944, 6626304 ], [ 1, 35, 4600, 12040, 13860, 112960, 183520, 551800, 1382400, 3524288, 6600800 ], [ 0, 96, 2880, 7680, 17568, 138624, 137856, 690816, 1242432, 3168384, 6979968 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25804800 ], [ 0, 0, 0, 0, 0, 0, 286720, 286720, 3440640, 9175040, 12615680 ], [ 0, 0, 2048, 0, 24576, 393216, 178176, 1579008, 2187264, 5898240, 15542272 ], [ 0, 0, 0, 4480, 53760, 286720, 170240, 1635200, 2338560, 5734400, 15581440 ], [ 0, 0, 5120, 30720, 23040, 245760, 360960, 1113600, 2734080, 7495680, 13795840 ], [ 0, 0, 10080, 20160, 30240, 221760, 372960, 1118880, 2933280, 7277760, 13819680 ], [ 0, 135, 3915, 10260, 38070, 319680, 239760, 1533060, 2423520, 6203520, 15032880 ], [ 0, 32, 8224, 23360, 27840, 227328, 363392, 1126208, 2868096, 7368704, 13791616 ], [ 0, 192, 5696, 16704, 34176, 297984, 287232, 1434048, 2563200, 6626304, 14539264 ], [ 0, 200, 6000, 16000, 36600, 288800, 287200, 1439200, 2588400, 6600800, 14541600 ], [ 1, 132, 7589, 20868, 32334, 263232, 334064, 1292964, 2726112, 6979968, 14147536 ] ] ] ), rec( name := "J4", sbgname := "2^{11}:M24", filename := "2^11:M24", degree := 173067389, rank := 7, permchar := "1a + 889111a + 1776888a + 4290927a + 35411145ab + 95288172a", charnmbs := [ 1, 8, 11, 14, 19, 20, 21 ], ctbl := [ [ 1, 15180, 28336, 3400320, 32643072, 54405120, 82575360 ], [ 1, 825, 1166, 14520, 19008, 10560, -46080 ], [ 1, 517, -990, -1496, 32560, -23936, -6656 ], [ 1, -253, 0, 7084, 0, -28336, 21504 ], [ 1, 49*E(33)+49*E(33)^2+49*E(33)^4+83*E(33)^5+83*E(33)^7+49*E(33)^8+83*E(33)^10+83*E(33)^13+83*E(33)^14+49*E(33)^16+49*E(33)^17+83*E(33)^19+83*E(33)^20+83*E(33)^23+49*E(33)^25+83*E(33)^26+83*E(33)^28+49*E(33)^29+49*E(33)^31+49*E(33)^32, 118*E(33)+118*E(33)^2+118*E(33)^4+80*E(33)^5+80*E(33)^7+118*E(33)^8+80*E(33)^10+80*E(33)^13+80*E(33)^14+118*E(33)^16+118*E(33)^17+80*E(33)^19+80*E(33)^20+80*E(33)^23+118*E(33)^25+80*E(33)^26+80*E(33)^28+118*E(33)^29+118*E(33)^31 +118*E(33)^32, -1320*E(33)-1320*E(33)^2-1320*E(33)^4-1012*E(33)^5-1012*E(33)^7-1320*E(33)^8-1012*E(33)^10-1012*E(33)^13-1012*E(33)^14-1320*E(33)^16-1320*E(33)^17-1012*E(33)^19-1012*E(33)^20-1012*E(33)^23-1320*E(33)^25-1012*E(33)^26 -1012*E(33)^28-1320*E(33)^29-1320*E(33)^31-1320*E(33)^32, -64*E(33)-64*E(33)^2-64*E(33)^4-2048*E(33)^5-2048*E(33)^7-64*E(33)^8-2048*E(33)^10-2048*E(33)^13-2048*E(33)^14-64*E(33)^16-64*E(33)^17-2048*E(33)^19-2048*E(33)^20-2048*E(33)^23 -64*E(33)^25-2048*E(33)^26-2048*E(33)^28-64*E(33)^29-64*E(33)^31-64*E(33)^32, -2880*E(33)-2880*E(33)^2-2880*E(33)^4-2224*E(33)^5-2224*E(33)^7-2880*E(33)^8-2224*E(33)^10-2224*E(33)^13-2224*E(33)^14-2880*E(33)^16-2880*E(33)^17 -2224*E(33)^19-2224*E(33)^20-2224*E(33)^23-2880*E(33)^25-2224*E(33)^26-2224*E(33)^28-2880*E(33)^29-2880*E(33)^31-2880*E(33)^32, 4096*E(33)+4096*E(33)^2+4096*E(33)^4+5120*E(33)^5+5120*E(33)^7+4096*E(33)^8+5120*E(33)^10+5120*E(33)^13 +5120*E(33)^14+4096*E(33)^16+4096*E(33)^17+5120*E(33)^19+5120*E(33)^20+5120*E(33)^23+4096*E(33)^25+5120*E(33)^26+5120*E(33)^28+4096*E(33)^29+4096*E(33)^31+4096*E(33)^32 ], [ 1, 83*E(33)+83*E(33)^2+83*E(33)^4+49*E(33)^5+49*E(33)^7+83*E(33)^8+49*E(33)^10+49*E(33)^13+49*E(33)^14+83*E(33)^16+83*E(33)^17+49*E(33)^19+49*E(33)^20+49*E(33)^23+83*E(33)^25+49*E(33)^26+49*E(33)^28+83*E(33)^29+83*E(33)^31+83*E(33)^32, 80*E(33)+80*E(33)^2+80*E(33)^4+118*E(33)^5+118*E(33)^7+80*E(33)^8+118*E(33)^10+118*E(33)^13+118*E(33)^14+80*E(33)^16+80*E(33)^17+118*E(33)^19+118*E(33)^20+118*E(33)^23+80*E(33)^25+118*E(33)^26+118*E(33)^28+80*E(33)^29+80*E(33)^31 +80*E(33)^32, -1012*E(33)-1012*E(33)^2-1012*E(33)^4-1320*E(33)^5-1320*E(33)^7-1012*E(33)^8-1320*E(33)^10-1320*E(33)^13-1320*E(33)^14-1012*E(33)^16-1012*E(33)^17-1320*E(33)^19-1320*E(33)^20-1320*E(33)^23-1012*E(33)^25-1320*E(33)^26 -1320*E(33)^28-1012*E(33)^29-1012*E(33)^31-1012*E(33)^32, -2048*E(33)-2048*E(33)^2-2048*E(33)^4-64*E(33)^5-64*E(33)^7-2048*E(33)^8-64*E(33)^10-64*E(33)^13-64*E(33)^14-2048*E(33)^16-2048*E(33)^17-64*E(33)^19-64*E(33)^20-64*E(33)^23 -2048*E(33)^25-64*E(33)^26-64*E(33)^28-2048*E(33)^29-2048*E(33)^31-2048*E(33)^32, -2224*E(33)-2224*E(33)^2-2224*E(33)^4-2880*E(33)^5-2880*E(33)^7-2224*E(33)^8-2880*E(33)^10-2880*E(33)^13-2880*E(33)^14-2224*E(33)^16-2224*E(33)^17 -2880*E(33)^19-2880*E(33)^20-2880*E(33)^23-2224*E(33)^25-2880*E(33)^26-2880*E(33)^28-2224*E(33)^29-2224*E(33)^31-2224*E(33)^32, 5120*E(33)+5120*E(33)^2+5120*E(33)^4+4096*E(33)^5+4096*E(33)^7+5120*E(33)^8+4096*E(33)^10+4096*E(33)^13 +4096*E(33)^14+5120*E(33)^16+5120*E(33)^17+4096*E(33)^19+4096*E(33)^20+4096*E(33)^23+5120*E(33)^25+4096*E(33)^26+4096*E(33)^28+5120*E(33)^29+5120*E(33)^31+5120*E(33)^32 ], [ 1, -55, -66, 440, 0, 3520, -3840 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 15180, 0, 0, 0, 0, 0 ], [ 1, 311, 84, 4032, 10752, 0, 0 ], [ 0, 45, 375, 3240, 0, 11520, 0 ], [ 0, 18, 27, 463, 3168, 5360, 6144 ], [ 0, 5, 0, 330, 3125, 4680, 7040 ], [ 0, 0, 6, 335, 2808, 4735, 7296 ], [ 0, 0, 0, 253, 2783, 4807, 7337 ] ], [ [ 0, 0, 28336, 0, 0, 0, 0 ], [ 0, 84, 700, 6048, 0, 21504, 0 ], [ 1, 375, 0, 3000, 23040, 1920, 0 ], [ 0, 27, 25, 972, 5856, 9168, 12288 ], [ 0, 0, 20, 610, 5106, 9160, 13440 ], [ 0, 6, 1, 573, 5496, 8820, 13440 ], [ 0, 0, 0, 506, 5313, 8855, 13662 ] ], [ [ 0, 0, 0, 3400320, 0, 0, 0 ], [ 0, 4032, 6048, 103712, 709632, 1200640, 1376256 ], [ 0, 3240, 3000, 116640, 702720, 1100160, 1474560 ], [ 1, 463, 972, 73508, 648768, 1060736, 1615872 ], [ 0, 330, 610, 67580, 641320, 1070000, 1620480 ], [ 0, 335, 573, 66296, 642000, 1071404, 1619712 ], [ 0, 253, 506, 66539, 640596, 1067154, 1625272 ] ], [ [ 0, 0, 0, 0, 32643072, 0, 0 ], [ 0, 10752, 0, 709632, 6720000, 10063872, 15138816 ], [ 0, 0, 23040, 702720, 5882112, 10552320, 15482880 ], [ 0, 3168, 5856, 648768, 6156672, 10272000, 15556608 ], [ 1, 3125, 5106, 641320, 6167600, 10253440, 15572480 ], [ 0, 2808, 5496, 642000, 6152064, 10265664, 15575040 ], [ 0, 2783, 5313, 640596, 6155996, 10261680, 15576704 ] ], [ [ 0, 0, 0, 0, 0, 54405120, 0 ], [ 0, 0, 21504, 1200640, 10063872, 16970240, 26148864 ], [ 0, 11520, 1920, 1100160, 10552320, 16934400, 25804800 ], [ 0, 5360, 9168, 1060736, 10272000, 17142464, 25915392 ], [ 0, 4680, 9160, 1070000, 10253440, 17109440, 25958400 ], [ 1, 4735, 8820, 1071404, 10265664, 17089952, 25964544 ], [ 0, 4807, 8855, 1067154, 10261680, 17106848, 25955776 ] ], [ [ 0, 0, 0, 0, 0, 0, 82575360 ], [ 0, 0, 0, 1376256, 15138816, 26148864, 39911424 ], [ 0, 0, 0, 1474560, 15482880, 25804800, 39813120 ], [ 0, 6144, 12288, 1615872, 15556608, 25915392, 39469056 ], [ 0, 7040, 13440, 1620480, 15572480, 25958400, 39403520 ], [ 0, 7296, 13440, 1619712, 15575040, 25964544, 39395328 ], [ 1, 7337, 13662, 1625272, 15576704, 25955776, 39396608 ] ] ] ), rec( name := "Fi24'", groupfilename := "F24", sbgname := "Fi23", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 306936, rank := 3, permchar := "1a + 57477a + 249458a", charnmbs := [ 1, 3, 4 ], ctbl := [ [ 1, 31671, 275264 ], [ 1, 351, -352 ], [ 1, -81, 80 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 31671, 0 ], [ 1, 3510, 28160 ], [ 0, 3240, 28431 ] ], [ [ 0, 0, 275264 ], [ 0, 28160, 247104 ], [ 1, 28431, 246832 ] ] ] ), rec( name := "Fi24'.2", groupfilename := "Fi24", sbgname := "Fi23x2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 306936, rank := 3, permchar := "1a^+ + 57477a^+ + 249458a^+", charnmbs := [ 1, 5, 7 ], ctbl := [ [ 1, 31671, 275264 ], [ 1, 351, -352 ], [ 1, -81, 80 ] ], mats := [ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], [ [ 0, 31671, 0 ], [ 1, 3510, 28160 ], [ 0, 3240, 28431 ] ], [ [ 0, 0, 275264 ], [ 0, 28160, 247104 ], [ 1, 28431, 246832 ] ] ] ), rec( name := "Fi24'.2", groupfilename := "Fi24", sbgname := "Fi23 leq Fi23x2", filename := "Fi23", degree := 613872, rank := 6, permchar := "1a^{+-} + 57477a^{+-} + 249458a^{+-}", charnmbs := [ 1, 2, 5, 6, 7, 8 ], ctbl := [ [ 1, 1, 31671, 31671, 275264, 275264 ], [ 1, -1, 31671, -31671, -275264, 275264 ], [ 1, 1, 351, 351, -352, -352 ], [ 1, -1, 351, -351, 352, -352 ], [ 1, 1, -81, -81, 80, 80 ], [ 1, -1, -81, 81, -80, 80 ] ], mats := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], [ [ 0, 0, 31671, 0, 0, 0 ], [ 0, 0, 0, 31671, 0, 0 ], [ 1, 0, 3510, 0, 0, 28160 ], [ 0, 1, 0, 3510, 28160, 0 ], [ 0, 0, 0, 3240, 28431, 0 ], [ 0, 0, 3240, 0, 0, 28431 ] ], [ [ 0, 0, 0, 31671, 0, 0 ], [ 0, 0, 31671, 0, 0, 0 ], [ 0, 1, 0, 3510, 28160, 0 ], [ 1, 0, 3510, 0, 0, 28160 ], [ 0, 0, 3240, 0, 0, 28431 ], [ 0, 0, 0, 3240, 28431, 0 ] ], [ [ 0, 0, 0, 0, 275264, 0 ], [ 0, 0, 0, 0, 0, 275264 ], [ 0, 0, 0, 28160, 247104, 0 ], [ 0, 0, 28160, 0, 0, 247104 ], [ 1, 0, 28431, 0, 0, 246832 ], [ 0, 1, 0, 28431, 246832, 0 ] ], [ [ 0, 0, 0, 0, 0, 275264 ], [ 0, 0, 0, 0, 275264, 0 ], [ 0, 0, 28160, 0, 0, 247104 ], [ 0, 0, 0, 28160, 247104, 0 ], [ 0, 1, 0, 28431, 246832, 0 ], [ 1, 0, 28431, 0, 0, 246832 ] ] ] ), rec( name := "B", sbgname := "2.^2E6(2).2", filename := "2.^2E62.2", origin := "The collapsed adjacency matrices were computed by C. E. Praeger and L. H. Soicher.", degree := 13571955000, rank := 5, permchar := "1a + 96255a + 9458750a + 4275362520a + 9287037474a", charnmbs := [ 1, 3, 5, 13, 15 ], ctbl := [ [ 1, 3968055, 23113728, 2370830336, 11174042880 ], [ 1, 228735, -709632, 14483456, -14002560 ], [ 1, 50895, 133056, 124928, -308880 ], [ 1, 1935, -4032, -31744, 33840 ], [ 1, -945, 1728, 14336, -15120 ] ], mats := [ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], [ [ 0, 3968055, 0, 0, 0 ], [ 1, 46134, 0, 2097152, 1824768 ], [ 0, 0, 69615, 0, 3898440 ], [ 0, 3510, 0, 837135, 3127410 ], [ 0, 648, 8064, 663552, 3295791 ] ], [ [ 0, 0, 23113728, 0, 0 ], [ 0, 0, 405504, 0, 22708224 ], [ 1, 69615, 0, 6336512, 16707600 ], [ 0, 0, 61776, 3592512, 19459440 ], [ 0, 8064, 34560, 4128768, 18942336 ] ], [ [ 0, 0, 0, 2370830336, 0 ], [ 0, 2097152, 0, 500170752, 1868562432 ], [ 0, 0, 6336512, 368492544, 1996001280 ], [ 1, 837135, 3592512, 423236608, 1943164080 ], [ 0, 663552, 4128768, 412286976, 1953751040 ] ], [ [ 0, 0, 0, 0, 11174042880 ], [ 0, 1824768, 22708224, 1868562432, 9280947456 ], [ 0, 3898440, 16707600, 1996001280, 9157435560 ], [ 0, 3127410, 19459440, 1943164080, 9208291950 ], [ 1, 3295791, 18942336, 1953751040, 9198053712 ] ] ] ), rec( name := "M", sbgname := "2.BM", degree := 97239461142009186000, rank := 9, permchar := "1a + 196883a + 842609326a + 18538750076a + 36173193327999a + 1109944460516150a + 251098487132187500a + 47377503606648784400a + 49609712911192813665a", charnmbs := [ 1, 2, 4, 5, 9, 14, 21, 34, 35 ], ctbl := [ [ 1, 27143910000, 11707448673375, 2031941058560000, 91569524834304000, 1102935324621312000, 1254793905192960000, 30434513446055706624, 64353605265653760000 ], [ 1, 2887650000, -249094652625, 62147133440000, -487071940608000, 11733354517248000, -6674435665920000, 80942854909722624, -85576602746880000 ], [ 1, 468855000, 43747806375, 3348961280000, -19026247680000, 202389851664000, 283334578560000, -369446834405376, -100644526080000 ], [ 1, 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