# Character: X21+X22 # Comment: found 2.U4(2) inside 2.O8+(2) by hunting for standard generators 2A,5,9 # Ind: 0 # Irred-dim: 4 # Ring: Z # Sparsity: 58% # Maximum absolute entry: 1 local b, B, w, W, i, result, delta, idmat; result := rec(); w := E(3); W := E(3)^2; b := E(7)+E(7)^2+E(7)^4; B := -1-b; # b7, b7** i := E(4); result.comment := "2U42 as 8 x 8 matrices\n"; result.generators := [ [[1,0,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0], [1,0,0,0,1,0,0,-1], [-1,0,1,-1,1,0,0,-1], [-1,-1,1,-1,1,0,0,0], [1,0,1,0,1,-1,0,-1], [0,1,0,-1,1,0,1,-1], [0,-1,0,-1,1,0,0,0]] , [[-1,0,-1,0,-1,1,1,1], [1,0,-1,1,0,0,0,0], [0,1,-1,0,-1,0,1,0], [1,0,0,0,0,0,0,-1], [1,0,0,1,0,0,0,-1], [0,0,-1,0,0,0,1,0], [0,0,0,0,-1,0,0,0], [0,0,-1,1,-1,1,0,0]]]; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ ]; result.centralizeralgebra := [ ]; return result;