J1Database:= [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 ], 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