J2Database:= [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, 4, 4, 0, 4, 0, 8, 12, 12, 36 ], [ 0, 0, 0, 4, 0, 4, 4, 8, 8, 16, 8, 28 ], [ 0, 0, 0, 0, 4, 4, 4, 6, 8, 16, 12, 26 ], [ 0, 1, 0, 1, 4, 5, 5, 6, 4, 12, 20, 22 ], [ 0, 0, 2, 2, 3, 3, 2, 9, 7, 13, 11, 28 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 128 ], [ 0, 0, 0, 0, 0, 32, 0, 32, 0, 32, 32, 32 ], [ 0, 0, 0, 0, 8, 0, 16, 0, 16, 24, 48, 48 ], [ 0, 0, 0, 5, 0, 0, 10, 15, 10, 30, 30, 60 ], [ 0, 0, 8, 0, 0, 0, 0, 8, 24, 32, 32, 56 ], [ 0, 0, 0, 8, 8, 0, 8, 0, 16, 24, 24, 72 ], [ 1, 0, 4, 0, 6, 4, 0, 16, 21, 28, 40, 40 ], [ 0, 1, 0, 4, 4, 12, 8, 21, 4, 30, 24, 52 ], [ 0, 0, 2, 3, 6, 8, 6, 14, 15, 24, 26, 56 ], [ 0, 0, 2, 6, 6, 8, 6, 20, 12, 26, 18, 56 ], [ 0, 1, 1, 3, 6, 7, 9, 10, 13, 28, 28, 54 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 128 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 32, 32, 64, 32 ], [ 0, 0, 0, 0, 8, 16, 16, 16, 0, 24, 32, 48 ], [ 0, 0, 0, 5, 10, 10, 0, 10, 15, 20, 30, 60 ], [ 0, 0, 0, 8, 8, 16, 8, 24, 8, 24, 8, 56 ], [ 0, 0, 0, 8, 0, 8, 8, 16, 16, 32, 16, 56 ], [ 0, 1, 0, 4, 4, 12, 8, 21, 4, 30, 24, 52 ], [ 1, 0, 4, 0, 6, 4, 8, 4, 17, 28, 32, 56 ], [ 0, 0, 2, 3, 4, 6, 8, 15, 14, 26, 26, 56 ], [ 0, 0, 4, 4, 6, 2, 4, 12, 16, 26, 26, 60 ], [ 0, 1, 1, 3, 6, 7, 7, 13, 14, 28, 30, 50 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 320, 0, 0 ], [ 0, 0, 0, 0, 64, 0, 0, 0, 0, 256, 0, 0 ], [ 0, 0, 0, 0, 32, 0, 0, 32, 32, 128, 0, 96 ], [ 0, 0, 0, 0, 24, 0, 0, 24, 24, 136, 0, 112 ], [ 0, 5, 10, 15, 0, 10, 20, 30, 20, 40, 70, 100 ], [ 0, 0, 0, 0, 8, 8, 16, 32, 24, 72, 56, 104 ], [ 0, 0, 0, 0, 16, 16, 16, 24, 32, 64, 48, 104 ], [ 0, 0, 4, 6, 12, 16, 12, 28, 30, 48, 52, 112 ], [ 0, 0, 4, 6, 8, 12, 16, 30, 28, 52, 52, 112 ], [ 1, 4, 8, 17, 8, 18, 16, 24, 26, 32, 66, 100 ], [ 0, 0, 0, 0, 14, 14, 12, 26, 26, 66, 54, 108 ], [ 0, 0, 3, 7, 10, 13, 13, 28, 28, 50, 54, 114 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 320, 0 ], [ 0, 0, 0, 0, 0, 64, 64, 0, 0, 0, 192, 0 ], [ 0, 0, 16, 16, 0, 0, 0, 32, 64, 0, 32, 160 ], [ 0, 0, 8, 24, 0, 8, 8, 48, 32, 0, 16, 176 ], [ 0, 0, 0, 0, 10, 10, 20, 30, 30, 70, 50, 100 ], [ 0, 4, 0, 4, 8, 28, 20, 32, 8, 56, 72, 88 ], [ 0, 4, 0, 4, 16, 20, 20, 24, 16, 48, 80, 88 ], [ 0, 0, 4, 12, 12, 16, 12, 40, 24, 52, 36, 112 ], [ 0, 0, 8, 8, 12, 4, 8, 24, 32, 52, 52, 120 ], [ 0, 0, 0, 0, 14, 14, 12, 26, 26, 66, 54, 108 ], [ 1, 3, 2, 2, 10, 18, 20, 18, 26, 54, 82, 84 ], [ 0, 0, 5, 11, 10, 11, 11, 28, 30, 54, 42, 118 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 640 ], [ 0, 0, 0, 0, 0, 0, 0, 128, 128, 0, 0, 384 ], [ 0, 0, 0, 0, 32, 32, 64, 32, 32, 96, 160, 192 ], [ 0, 0, 0, 0, 16, 48, 32, 48, 48, 112, 176, 160 ], [ 0, 0, 10, 10, 20, 30, 30, 60, 60, 100, 100, 220 ], [ 0, 0, 8, 24, 24, 16, 24, 56, 56, 104, 88, 240 ], [ 0, 0, 16, 16, 24, 24, 16, 72, 56, 104, 88, 224 ], [ 0, 4, 4, 12, 24, 28, 36, 40, 52, 112, 112, 216 ], [ 0, 4, 4, 12, 24, 28, 28, 52, 56, 112, 120, 200 ], [ 0, 0, 6, 14, 20, 26, 26, 56, 56, 100, 108, 228 ], [ 0, 0, 10, 22, 20, 22, 22, 56, 60, 108, 84, 236 ], [ 1, 3, 6, 10, 22, 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, 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, 1, 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, 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, 24, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 24, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 6, 0, 0, 16, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 24 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 24 ], [ 0, 0, 2, 0, 0, 6, 6, 6, 4 ], [ 0, 0, 0, 0, 0, 6, 6, 6, 6 ], [ 0, 0, 0, 0, 0, 6, 6, 6, 6 ], [ 0, 0, 0, 2, 2, 2, 3, 3, 12 ] ], [ [ 0, 0, 0, 32, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 32, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 32 ], [ 1, 0, 0, 3, 4, 12, 0, 12, 0 ], [ 0, 1, 0, 4, 3, 12, 12, 0, 0 ], [ 0, 0, 0, 2, 2, 4, 6, 6, 12 ], [ 0, 0, 0, 0, 2, 6, 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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, 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, 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, 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, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 3, 0, 0, 0, 0, 8, 0, 0, 0, 0 ], [ 0, 1, 0, 3, 0, 0, 8, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 3, 0, 2, 6, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 2, 6 ], [ 0, 0, 0, 0, 0, 2, 1, 0, 6, 3, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 3, 0, 3, 6, 0, 0 ], [ 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 6, 3 ], [ 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 6 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0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0 ], [ 0, 1, 0, 0, 0, 7, 12, 0, 0, 12, 0, 0 ], [ 1, 0, 0, 0, 7, 0, 0, 12, 0, 0, 0, 12 ], [ 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 12, 12 ], [ 0, 0, 0, 0, 0, 4, 4, 0, 12, 12, 0, 0 ], [ 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 12, 12 ], [ 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 12, 12 ], [ 0, 0, 0, 2, 0, 0, 6, 0, 12, 12, 0, 0 ], [ 0, 0, 0, 0, 0, 2, 6, 0, 12, 12, 0, 0 ] ], [ [ 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0 ], [ 0, 0, 0, 8, 0, 0, 24, 0, 16, 48, 0, 0 ], [ 0, 0, 8, 0, 0, 0, 0, 24, 0, 0, 16, 48 ], [ 0, 0, 0, 0, 0, 12, 12, 0, 36, 36, 0, 0 ], [ 0, 0, 0, 0, 12, 0, 0, 12, 0, 0, 36, 36 ], [ 1, 0, 3, 0, 4, 0, 0, 16, 0, 0, 30, 42 ], [ 0, 1, 0, 3, 0, 4, 16, 0, 30, 42, 0, 0 ], [ 0, 0, 1, 0, 6, 0, 0, 15, 0, 0, 41, 33 ], [ 0, 0, 3, 0, 6, 0, 0, 21, 0, 0, 33, 33 ], [ 0, 0, 0, 1, 0, 6, 15, 0, 41, 33, 0, 0 ], [ 0, 0, 0, 3, 0, 6, 21, 0, 33, 33, 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 ], [ 0, 0, 8, 0, 0, 0, 0, 24, 0, 0, 16, 48 ], [ 0, 0, 0, 8, 0, 0, 24, 0, 16, 48, 0, 0 ], [ 0, 0, 0, 0, 12, 0, 0, 12, 0, 0, 36, 36 ], [ 0, 0, 0, 0, 0, 12, 12, 0, 36, 36, 0, 0 ], [ 0, 1, 0, 3, 0, 4, 16, 0, 30, 42, 0, 0 ], [ 1, 0, 3, 0, 4, 0, 0, 16, 0, 0, 30, 42 ], [ 0, 0, 0, 1, 0, 6, 15, 0, 41, 33, 0, 0 ], [ 0, 0, 0, 3, 0, 6, 21, 0, 33, 33, 0, 0 ], [ 0, 0, 1, 0, 6, 0, 0, 15, 0, 0, 41, 33 ], [ 0, 0, 3, 0, 6, 0, 0, 21, 0, 0, 33, 33 ] ], [ [ 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, 32, 16, 0, 96, 48, 0, 0 ], [ 0, 0, 0, 0, 32, 0, 0, 16, 0, 0, 96, 48 ], [ 0, 0, 0, 12, 0, 0, 36, 0, 72, 72, 0, 0 ], [ 0, 0, 12, 0, 0, 0, 0, 36, 0, 0, 72, 72 ], [ 0, 0, 2, 0, 12, 0, 0, 30, 0, 0, 82, 66 ], [ 0, 0, 0, 2, 0, 12, 30, 0, 82, 66, 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, 1, 0, 6, 0, 12, 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^{+-} + 22\ 5a^{+-}", 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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0, 96, 0 ], [ 0, 0, 0, 0, 16, 0, 0, 0, 48, 0, 0, 80, 0, 96 ], [ 0, 0, 0, 12, 12, 0, 0, 0, 72, 0, 0, 72, 0, 72 ], [ 0, 0, 12, 0, 0, 12, 0, 0, 0, 72, 72, 0, 72, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 60, 0, 120 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 60, 0, 120, 0 ], [ 0, 0, 0, 4, 8, 0, 8, 0, 52, 0, 0, 64, 0, 104 ], [ 0, 0, 4, 0, 0, 8, 0, 8, 0, 52, 64, 0, 104, 0 ], [ 0, 1, 5, 0, 0, 6, 0, 6, 0, 48, 72, 0, 102, 0 ], [ 1, 0, 0, 5, 6, 0, 6, 0, 48, 0, 0, 72, 0, 102 ], [ 0, 0, 4, 0, 0, 4, 0, 8, 0, 52, 68, 0, 104, 0 ], [ 0, 0, 0, 4, 4, 0, 8, 0, 52, 0, 0, 68, 0, 104 ] ], [ [ 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, 0, 0, 360 ], [ 0, 0, 0, 0, 0, 0, 24, 0, 96, 0, 0, 96, 0, 144 ], [ 0, 0, 0, 0, 0, 0, 0, 24, 0, 96, 96, 0, 144, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 18, 0, 72, 72, 0, 198, 0 ], [ 0, 0, 0, 0, 0, 0, 18, 0, 72, 0, 0, 72, 0, 198 ], [ 0, 0, 15, 0, 0, 15, 0, 15, 0, 60, 120, 0, 135, 0 ], [ 0, 0, 0, 15, 15, 0, 15, 0, 60, 0, 0, 120, 0, 135 ], [ 0, 0, 8, 0, 0, 8, 0, 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 ], [ 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, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 4, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 12, 0 ], [ 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 4, 8 ], [ 0, 0, 0, 0, 3, 0, 0, 3, 3, 6, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 2, 0, 0, 4, 0, 8 ], [ 0, 1, 0, 0, 0, 2, 4, 0, 0, 4, 0, 4 ], [ 0, 0, 0, 0, 2, 0, 0, 0, 3, 2, 4, 4 ], [ 0, 0, 0, 0, 2, 0, 0, 3, 0, 2, 4, 4 ], [ 0, 0, 0, 0, 2, 2, 2, 1, 1, 3, 0, 4 ], [ 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 5, 4 ], [ 0, 0, 0, 1, 0, 2, 1, 1, 1, 2, 2, 5 ] ], [ [ 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 20, 0 ], [ 1, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0 ], [ 0, 1, 4, 0, 4, 8, 0, 0, 0, 0, 0, 8 ], [ 0, 0, 0, 3, 4, 0, 0, 0, 0, 9, 3, 6 ], [ 0, 0, 0, 4, 0, 0, 1, 0, 4, 8, 4, 4 ], [ 0, 0, 0, 0, 0, 1, 0, 4, 4, 0, 4, 12 ], [ 0, 0, 0, 0, 0, 0, 4, 2, 5, 4, 2, 8 ], [ 0, 0, 0, 0, 0, 4, 4, 5, 4, 2, 2, 4 ], [ 0, 0, 1, 0, 3, 4, 0, 2, 1, 3, 3, 8 ], [ 0, 1, 0, 0, 1, 2, 2, 1, 1, 3, 4, 10 ], [ 0, 0, 0, 1, 1, 1, 3, 2, 1, 4, 5, 7 ] ], [ [ 0, 0, 0, 75, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 5, 0, 0, 10, 0, 0, 0, 0, 20, 40 ], [ 0, 3, 12, 0, 12, 24, 0, 0, 0, 0, 0, 24 ], [ 1, 0, 0, 12, 0, 0, 2, 0, 4, 32, 16, 8 ], [ 0, 0, 3, 0, 6, 12, 0, 3, 0, 18, 9, 24 ], [ 0, 1, 4, 0, 8, 10, 4, 8, 4, 4, 8, 24 ], [ 0, 0, 0, 1, 0, 4, 6, 8, 8, 12, 16, 20 ], [ 0, 0, 0, 0, 2, 8, 8, 7, 8, 8, 10, 24 ], [ 0, 0, 0, 2, 0, 4, 8, 8, 9, 12, 8, 24 ], [ 0, 0, 0, 8, 6, 2, 6, 4, 6, 13, 10, 20 ], [ 0, 1, 0, 4, 3, 4, 8, 5, 4, 10, 12, 24 ], [ 0, 1, 1, 1, 4, 6, 5, 6, 6, 10, 12, 23 ] ], [ [ 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 20, 0, 0, 20, 20, 40, 0, 0 ], [ 0, 0, 0, 12, 16, 0, 0, 0, 0, 36, 12, 24 ], [ 0, 0, 4, 0, 8, 16, 0, 4, 0, 24, 12, 32 ], [ 1, 3, 4, 6, 2, 6, 6, 6, 9, 15, 24, 18 ], [ 0, 0, 0, 8, 4, 8, 8, 4, 4, 16, 16, 32 ], [ 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0, 6, 12, 12, 12, 12, 24, 24, 48 ], [ 0, 2, 1, 4, 8, 15, 16, 12, 12, 20, 20, 40 ], [ 1, 4, 0, 6, 8, 16, 11, 8, 8, 28, 8, 52 ], [ 0, 0, 4, 8, 8, 12, 8, 14, 8, 24, 24, 40 ], [ 0, 0, 4, 8, 8, 12, 8, 8, 14, 24, 24, 40 ], [ 0, 2, 0, 6, 8, 10, 14, 12, 12, 22, 16, 48 ], [ 0, 0, 2, 8, 8, 10, 4, 12, 12, 16, 30, 48 ], [ 0, 1, 3, 5, 8, 10, 13, 10, 10, 24, 24, 42 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 150, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 20, 0, 0, 0, 30, 20, 40, 40 ], [ 0, 0, 0, 0, 0, 0, 24, 12, 30, 24, 12, 48 ], [ 0, 0, 0, 0, 4, 16, 16, 14, 16, 16, 20, 48 ], [ 0, 3, 0, 3, 6, 6, 12, 18, 9, 21, 30, 42 ], [ 0, 0, 0, 8, 4, 16, 12, 16, 10, 20, 24, 40 ], [ 0, 0, 4, 8, 8, 12, 8, 14, 8, 24, 24, 40 ], [ 1, 0, 2, 7, 12, 16, 14, 8, 12, 18, 24, 36 ], [ 0, 3, 5, 8, 6, 10, 8, 12, 16, 28, 14, 40 ], [ 0, 1, 2, 4, 7, 10, 12, 9, 14, 18, 25, 48 ], [ 0, 2, 1, 5, 10, 12, 12, 12, 7, 25, 22, 42 ], [ 0, 1, 2, 6, 7, 10, 10, 9, 10, 24, 21, 50 ] ], [ [ 0, 0, 0, 0, 0, 0, 0, 0, 150, 0, 0, 0 ], [ 0, 0, 0, 0, 20, 0, 0, 30, 0, 20, 40, 40 ], 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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, 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