# Character: X3 # Comment: exterior square of 10-dim rep of 2.M22 # Ind: 0 # Ring: C # Sparsity: 82% # Checker result: pass # Conjugacy class representative result: pass 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 := "M22 as 45 x 45 matrices\n"; result.generators := [ [[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0], [29/14*b+B,0,0,0,0,0,0,0,0,-2/7*b-1/7*B,13/7*b,-1,-1/14*b-2/7*B,-20/7*b-8/7*B, -5/7*b-6/7*B,3/7*b+4/7*B,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0], [11/28*b-3/2*B,0,0,0,0,0,0,0,0,-4/7*b-2/7*B,17/14*b-B,-1/2*b-B,-39/28*b-15/14*B, 2/7*b+19/7*B,1/14*b+2/7*B,-9/14*b-6/7*B,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,-1,1,1,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0], [39/14*b+9/7*B,0,0,0,0,0,0,0,0,-4/7*b-6/7*B,-17/7,b,-9/14*b-12/7*B, -20/7*b-8/7*B,-3/7*b+6/7*B,3/7*b-3/7*B,1,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0], [13/7*b+4/7*B,-2/7*b-1/7*B,13/7*b,-1,-1/14*b-2/7*B,-20/7*b-8/7*B,-5/7*b-6/7*B, 3/7*b+4/7*B,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0], [5/7*b-6/7*B,-4/7*b-2/7*B,17/14*b-B,-1/2*b-B,-39/28*b-15/14*B,2/7*b+19/7*B, 1/14*b+2/7*B,-9/14*b-6/7*B,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [1,-1,1,1,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0], [15/7*b+9/7*B,-4/7*b-6/7*B,-17/7,b,-9/14*b-12/7*B,-20/7*b-8/7*B,-3/7*b+6/7*B, 3/7*b-3/7*B,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,29/14*b+B,0,0,0,0,0,0,0,-13/7*b-4/7*B,0,0,0,0,0,0,2/7*b+1/7*B, 0,0,0,0,0,-13/7*b,0,0,0,0,0,-1/14*b-2/7*B,-20/7*b-8/7*B,-5/7*b-6/7*B, 3/7*b+4/7*B,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0], 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