M12Database:= [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, 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, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0 ], [ 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6 ], [ 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 6 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 6 ], [ 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 0, 2 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0 ] ], [ [ 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 6, 0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18 ], [ 0, 0, 0, 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0, 3, 3, 6, 0, 0, 14, 12, 0, 0, 0, 33 ], [ 0, 0, 0, 4, 4, 4, 0, 0, 11, 11, 0, 0, 0, 38 ], [ 0, 0, 2, 0, 0, 0, 5, 5, 0, 0, 11, 11, 38, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 0, 0, 0, 54 ], [ 0, 0, 0, 0, 0, 0, 9, 9, 0, 0, 9, 9, 36, 0 ], [ 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 16, 32, 0 ], [ 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 16, 8, 32, 0 ], [ 0, 0, 0, 6, 6, 6, 0, 0, 6, 18, 0, 0, 0, 30 ], [ 0, 0, 0, 6, 6, 6, 0, 0, 18, 6, 0, 0, 0, 30 ], [ 0, 0, 1, 0, 0, 0, 3, 9, 0, 0, 14, 12, 33, 0 ], [ 0, 0, 1, 0, 0, 0, 9, 3, 0, 0, 12, 14, 33, 0 ], [ 0, 1, 0, 3, 3, 6, 0, 0, 14, 12, 0, 0, 0, 33 ], [ 1, 0, 0, 3, 6, 3, 0, 0, 12, 14, 0, 0, 0, 33 ], [ 0, 0, 0, 4, 4, 4, 0, 0, 11, 11, 0, 0, 0, 38 ], [ 0, 0, 2, 0, 0, 0, 5, 5, 0, 0, 11, 11, 38, 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, 27, 27, 0, 0, 54, 54, 0, 0, 0, 54 ], [ 0, 0, 0, 0, 0, 0, 9, 9, 0, 0, 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^+ + 1\ 76a^-", 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, 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[ 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, 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, 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, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 2, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0 ], [ 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 3 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 3 ], [ 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 4, 0, 4 ], [ 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 4, 0, 4 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2 ], [ 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2 ], [ 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2 ] ], [ [ 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0 ], [ 1, 0, 0, 1, 0, 0, 8, 0, 6, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 0, 0, 8, 0, 6, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8 ], [ 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 6, 6, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 6, 6 ], [ 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 4, 4, 4 ], [ 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 4, 4, 4 ], [ 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 4, 2, 2 ], [ 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4, 2 ], [ 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 4 ] ], [ [ 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0 ], [ 0, 1, 0, 0, 1, 0, 0, 8, 0, 6, 0, 0, 0 ], [ 1, 0, 0, 1, 0, 0, 8, 0, 6, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8 ], [ 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 6, 6 ], [ 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 6, 6, 0 ], [ 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 4, 4, 4 ], [ 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 4, 4, 4 ], [ 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 4 ], [ 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4, 2 ], [ 0, 0, 0, 0, 0, 2, 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, 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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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