# Character: X4 # 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], [b+29/14*B,0,0,0,0,0,0,0,0,-1/7*b-2/7*B,13/7*B,-1,-2/7*b-1/14*B,-8/7*b-20/7*B, -6/7*b-5/7*B,4/7*b+3/7*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], [-3/2*b+11/28*B,0,0,0,0,0,0,0,0,-2/7*b-4/7*B,-b+17/14*B,-b-1/2*B,-15/14*b-39/28*B, 19/7*b+2/7*B,2/7*b+1/14*B,-6/7*b-9/14*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], [9/7*b+39/14*B,0,0,0,0,0,0,0,0,-6/7*b-4/7*B,-17/7,B,-12/7*b-9/14*B, -8/7*b-20/7*B,6/7*b-3/7*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], [4/7*b+13/7*B,-1/7*b-2/7*B,13/7*B,-1,-2/7*b-1/14*B,-8/7*b-20/7*B,-6/7*b-5/7*B, 4/7*b+3/7*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], [-6/7*b+5/7*B,-2/7*b-4/7*B,-b+17/14*B,-b-1/2*B,-15/14*b-39/28*B,19/7*b+2/7*B, 2/7*b+1/14*B,-6/7*b-9/14*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], [9/7*b+15/7*B,-6/7*b-4/7*B,-17/7,B,-12/7*b-9/14*B,-8/7*b-20/7*B,6/7*b-3/7*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,b+29/14*B,0,0,0,0,0,0,0,-4/7*b-13/7*B,0,0,0,0,0,0,1/7*b+2/7*B, 0,0,0,0,0,-13/7*B,0,0,0,0,0,-2/7*b-1/14*B,-8/7*b-20/7*B,-6/7*b-5/7*B, 4/7*b+3/7*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], [0,0,0,-3/2*b+11/28*B,0,0,0,0,0,0,0,6/7*b-5/7*B,0,0,0,0,0,0,2/7*b+4/7*B, 0,0,0,0,0,b-17/14*B,0,0,0,0,0,-15/14*b-39/28*B,19/7*b+2/7*B,2/7*b+1/14*B, -6/7*b-9/14*B,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,-1,0,0,0,0,0,0,-1, 0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,9/7*b+39/14*B,0,0,0,0,0,0,0,-9/7*b-15/7*B,0,0,0,0,0,0,6/7*b+4/7*B, 0,0,0,0,0,17/7,0,0,0,0,0,-12/7*b-9/14*B,-8/7*b-20/7*B,6/7*b-3/7*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,-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,b+29/14*B,0,0,0,0,0,0,0,-4/7*b-13/7*B,0,0,0,0,0,0,1/7*b+2/7*B, 0,0,0,0,0,-13/7*B,0,0,0,0,1,0,0,0,2/7*b+1/14*B,0,0,0,-6/7*b-5/7*B, 4/7*b+3/7*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,-1,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,-3/2*b+11/28*B,0,0,0,0,0,0,0,6/7*b-5/7*B,0,0,0,0,0,0,2/7*b+4/7*B, 0,0,0,0,0,b-17/14*B,0,0,0,0,b+1/2*B,0,0,0,15/14*b+39/28*B,0,0,0, 2/7*b+1/14*B,-6/7*b-9/14*B,0,0,0,0], 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