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Views: 418346############################################################################# ## #A imf12.grp GAP group library Volkmar Felsch ## ## #Y Copyright (C) 1995, Lehrstuhl D für Mathematik, RWTH Aachen, Germany ## ## This file contains, for each Q-class representative of the irreducible ## maximal finite integral matrix groups of dimension 12, ## ## [1] a quadratic form (as lower triangle of the Gram matrix), ## [2] a list of matrix generators. ## ############################################################################# ## ## Quadratic form and matrix generators for the Q-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 12. ## IMFList[12].matrices := [ [ # Q-class [12][01] [[1], [0,1], [0,0,1], [0,0,0,1], [0,0,0,0,1], [0,0,0,0,0,1], [0,0,0,0,0,0,1], [0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,1], [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], [0,0,1,0,0,0,0,0,0,0,0,0], [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], [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], [1,0,0,0,0,0,0,0,0,0,0,0]]]], [ # Q-class [12][02] [[2], [0,2], [-1,1,2], [-1,1,1,2], [0,0,0,0,2], [0,0,0,0,0,2], [0,0,0,0,-1,1,2], [0,0,0,0,-1,1,1,2], [0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,-1,1,2], [0,0,0,0,0,0,0,0,-1,1,1,2]], [[[0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,1,-1,0], [0,0,0,0,0,0,0,0,0,0,-1,0], [0,0,0,0,0,0,0,0,-1,1,-1,-1], [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]], [[-1,0,0,-1,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0], [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]], [[0,0,0,0,1,0,0,0,0,0,0,0], [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], [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], [0,0,0,0,0,0,0,0,1,0,0,0], [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]]]], [ # Q-class [12][03] [[2], [-1,2], [0,-1,2], [0,0,-1,2], [0,0,0,-1,2], [0,0,-1,0,0,2], [0,0,0,0,0,0,2], [0,0,0,0,0,0,-1,2], [0,0,0,0,0,0,0,-1,2], [0,0,0,0,0,0,0,0,-1,2], [0,0,0,0,0,0,0,0,0,-1,2], [0,0,0,0,0,0,0,0,-1,0,0,2]], [[[0,0,0,0,0,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0], [1,2,2,1,0,1,0,0,0,0,0,0], [0,-1,-2,-2,-1,-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]], [[-1,-2,-3,-2,-1,-1,0,0,0,0,0,0], [0,0,0,0,0,-1,0,0,0,0,0,0], [0,0,1,0,0,1,0,0,0,0,0,0], [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], [0,0,0,0,0,0,1,0,0,0,0,0], [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]], [[0,0,0,0,0,0,1,0,0,0,0,0], [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], [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]]]], [ # Q-class [12][04] [[2], [1,2], [0,0,2], [0,0,1,2], [0,0,0,0,2], [0,0,0,0,1,2], [0,0,0,0,0,0,2], [0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,1,2]], [[[0,0,0,1,0,0,0,0,0,0,0,0], [0,0,-1,1,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0], [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], [0,0,1,0,0,0,0,0,0,0,0,0], [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]], [[0,0,1,0,0,0,0,0,0,0,0,0], [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], [1,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0]]]], [ # Q-class [12][05] [[4], [0,4], [1,0,4], [-2,2,1,4], [0,1,-2,-1,4], [-2,1,-2,1,2,4], [0,-2,0,-2,0,-1,4], [1,-2,2,-1,-2,-2,2,4], [-2,0,0,2,0,2,-2,-1,4], [1,0,0,0,-2,-2,0,1,-2,4], [0,2,1,2,-1,-1,-2,0,0,2,4], [-2,0,-2,0,2,2,0,-1,2,-2,-1,4]], [[[0,0,0,0,0,0,0,0,0,0,0,1], [0,0,-1,1,0,-1,0,0,0,0,0,0], [0,0,0,0,0,0,-1,1,-1,0,0,1], [0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,-1,0,1,-1,0,-1,1,0], [-1,0,0,0,0,0,0,0,0,0,0,-1], [0,0,1,0,1,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,1,0,0,0,0], [0,0,0,0,-1,1,0,0,-1,0,0,0], [0,0,0,0,1,-1,0,0,1,1,-1,0], [0,0,-1,0,0,-1,0,0,0,0,0,0], [1,-1,0,1,-1,1,1,-1,-1,-1,1,0]], [[-2,1,0,-1,1,-1,-1,1,1,1,-1,-1], [0,1,0,0,0,0,1,0,1,0,0,0], [-1,1,0,-1,1,-1,-1,1,1,0,-1,-1], [1,1,0,0,0,0,1,0,1,0,0,0], [0,0,0,0,-1,1,0,0,-1,0,0,1], [1,0,0,0,-2,1,1,-1,-1,-1,1,1], [0,-1,0,1,0,0,-1,0,-1,0,-1,0], [-1,0,0,0,1,-1,-1,1,0,0,-1,-1], [1,0,1,-1,-1,1,1,-1,0,0,1,1], [0,0,-1,1,1,-1,0,1,1,0,0,-1], [0,1,-1,0,1,-1,1,1,2,0,0,-1], [1,-1,1,0,-1,2,1,-1,-1,0,1,1]]]], [ # Q-class [12][06] [[4], [2,4], [-1,1,4], [-1,0,0,4], [0,0,0,-1,4], [-1,0,2,1,1,4], [-1,-1,0,0,2,2,4], [1,0,0,1,1,1,0,4], [2,1,1,0,-1,0,-1,1,4], [-1,-1,0,1,0,1,0,1,0,4], [0,-1,-1,2,1,1,1,2,1,2,4], [0,0,0,-1,0,-1,0,-1,1,2,1,4]], [[[0,0,1,-1,0,-1,0,-1,0,1,1,-2], [0,0,0,0,0,0,0,-1,0,1,0,-1], [0,0,-1,0,0,1,0,0,0,0,0,0], [0,0,-1,1,1,1,0,0,1,0,-2,1], [-1,1,0,-1,-1,-1,1,0,0,0,1,-1], [0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,-1,1,0,0,0,0,0], [0,1,1,-2,-1,-1,1,-1,0,1,2,-2], [0,0,0,-1,0,0,0,0,0,1,0,-1], [-1,1,0,-1,0,0,0,0,0,0,1,0], [-1,1,0,-1,0,-1,1,0,1,1,0,-1], [-1,1,0,-1,0,-1,0,0,0,1,1,-1]], [[1,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,-1,0,-1,-1,0,1], [-1,1,0,-1,-1,-1,1,0,0,0,1,-1], [0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,-1,0,0,0,0], [0,0,0,0,0,0,0,-1,0,0,1,0], [0,0,0,0,0,-1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,-1,0,0,0], [-1,0,-1,0,1,0,0,0,1,0,-1,0], [0,0,0,0,0,-1,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0]], [[1,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0], [-1,1,0,-1,0,-1,1,-1,1,1,1,-2], [1,-1,0,2,1,0,0,0,0,0,-2,1], [0,0,1,0,0,-1,1,0,0,0,0,0], [0,0,1,0,0,-2,1,0,0,1,0,-1], [1,0,1,0,0,-1,1,-1,0,1,1,-1], [0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,-1,0,1,0,0,0,0,0], [0,0,0,0,0,-1,1,-1,1,1,0,-1], [0,0,0,0,-1,0,0,0,0,0,0,0]]]], [ # Q-class [12][07] [[3], [1,3], [0,1,3], [-1,1,1,3], [1,0,1,-1,3], [-1,-1,1,0,1,3], [0,0,0,0,0,0,3], [0,0,0,0,0,0,1,3], [0,0,0,0,0,0,0,1,3], [0,0,0,0,0,0,-1,1,1,3], [0,0,0,0,0,0,1,0,1,-1,3], [0,0,0,0,0,0,-1,-1,1,0,1,3]], [[[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,-1,1,1,0,0,0,0,0,0,0], [-1,0,0,0,1,-1,0,0,0,0,0,0], [0,1,-1,0,0,1,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,1,0,0,0], [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]], [[1,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0], [0,1,-1,0,0,1,0,0,0,0,0,0], [-1,1,0,-1,0,0,0,0,0,0,0,0], [1,0,0,0,-1,1,0,0,0,0,0,0], [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]], [[0,0,0,0,0,0,1,0,0,0,0,0], [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], [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]]]], [ # Q-class [12][08] [[2], [1,2], [1,1,2], [1,1,1,2], [0,0,0,0,2], [0,0,0,0,1,2], [0,0,0,0,1,1,2], [0,0,0,0,1,1,1,2], [0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,1,1,2], [0,0,0,0,0,0,0,0,1,1,1,2]], [[[0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,-1,1], [0,0,0,0,0,0,0,0,0,-1,0,1], [0,0,0,0,0,0,0,0,-1,0,0,1], [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]], [[-1,0,1,0,0,0,0,0,0,0,0,0], [0,0,1,-1,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0], [0,-1,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0], [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]], [[0,0,0,0,1,0,0,0,0,0,0,0], [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], [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], [0,0,0,0,0,0,0,0,1,0,0,0], [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]]]], [ # Q-class [12][09] [[4], [-2,4], [0,-1,4], [0,1,-2,4], [-2,0,-1,0,4], [0,0,0,-2,-1,4], [0,-2,1,0,1,-2,4], [2,0,1,-1,-1,0,0,4], [-1,1,0,0,2,0,0,1,4], [1,-1,2,0,0,-1,1,2,2,4], [-1,0,1,1,1,-2,2,0,1,2,4], [0,0,0,0,1,0,1,2,2,2,2,4]], [[[0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,1,-1], [0,0,1,0,0,-1,0,0,0,-1,-1,1], [0,1,-1,0,1,1,1,0,-1,2,0,-1], [-1,-1,0,1,0,1,0,1,0,0,0,-1], [0,0,0,-1,-1,-1,-1,-1,0,0,0,1], [1,1,1,1,1,1,1,0,0,0,-1,0], [0,0,1,1,0,0,0,0,0,-1,0,1], [0,0,1,1,1,1,0,0,-1,0,0,0], [0,0,1,1,1,0,0,0,-1,0,-1,1], [0,0,1,1,1,0,0,0,0,0,-1,0], [0,0,1,1,0,0,0,-1,0,0,-1,1]], [[-1,-2,0,0,-1,-1,-1,0,1,-1,0,0], [1,2,0,0,1,1,1,-1,-1,1,0,0], [-1,-1,0,1,0,1,0,2,0,-1,1,-1], [1,1,0,-1,0,-1,0,-1,0,0,0,0], [0,1,0,0,0,0,1,0,0,1,-1,0], [0,0,0,0,1,1,0,0,-1,1,0,0], [-1,-1,0,0,-1,-1,-1,1,1,-1,0,0], [-1,-1,0,0,-1,0,0,0,1,-1,0,0], [0,1,0,0,0,1,1,0,0,1,0,-1], [-1,-1,0,0,-1,0,0,1,1,-1,1,-1], [0,0,0,0,0,0,0,1,1,-1,1,-1], [0,0,1,0,0,0,0,0,1,-1,0,0]]]], [ # Q-class [12][10] [[4], [-1,4], [2,-1,4], [-1,2,-1,4], [-2,2,-1,1,4], [-1,1,1,0,1,4], [1,0,1,-1,0,1,4], [0,-1,-1,1,-1,-1,1,4], [0,0,1,2,0,1,-1,1,4], [-1,1,1,2,1,1,1,1,2,4], [-1,-1,0,-1,0,1,1,1,1,1,4], [1,0,1,1,-1,1,1,0,1,2,1,4]], [[[0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,1,-1,0,0,-1,0,0,1,-1], [-2,1,1,-1,0,-1,1,1,1,-2,-1,2], [0,0,0,0,0,0,0,0,1,-1,0,0], [1,-1,-1,2,-1,1,0,-1,-1,1,1,-2], [0,0,0,1,-1,0,1,-1,0,0,0,-1], [-2,0,1,0,0,-1,1,0,1,-1,-1,1], [-1,0,0,-1,1,-1,1,0,2,-1,-1,1], [0,0,0,0,0,0,1,0,1,-1,0,0], [-2,1,1,-1,0,-1,1,1,2,-2,-1,1], [-1,0,0,-1,0,0,1,0,1,0,-1,0], [-1,1,1,-1,0,0,0,1,1,-1,-1,1]], [[-3,1,2,-1,1,-2,1,1,2,-3,-1,2], [1,0,0,1,0,1,-1,0,-2,1,1,-1], [-2,0,1,0,0,-1,1,0,1,-1,-1,1], [1,0,0,0,0,1,-1,0,-1,1,0,-1], [1,0,0,1,-1,1,-1,0,-2,1,1,-1], [0,-1,0,1,0,1,0,0,-1,0,0,0], [-2,0,0,-1,0,-1,1,0,1,-1,-1,1], [0,0,-1,-1,0,0,0,0,1,0,-1,0], [1,-1,0,1,0,1,-1,0,-1,1,0,-1], [1,-1,-1,1,-1,1,0,-1,-1,2,0,-2], [2,-2,-2,2,-1,1,0,-2,-1,2,1,-2], [0,-1,0,1,0,0,1,-1,0,0,0,-1]]]], [ # Q-class [12][11] [[6], [2,6], [2,2,6], [-2,2,0,6], [-2,0,2,2,6], [0,-2,2,-2,2,6], [3,1,1,-1,-1,0,6], [1,3,1,1,0,-1,2,6], [1,1,3,0,1,1,2,2,6], [-1,1,0,3,1,-1,-2,2,0,6], [-1,0,1,1,3,1,-2,0,2,2,6], [0,-1,1,-1,1,3,0,-2,2,-2,2,6]], [[[0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,-1,1,0,0,-1], [0,0,0,0,0,0,0,0,0,-1,1,-1], [0,0,0,0,0,0,1,0,-1,0,1,0], [0,0,0,0,0,-1,0,0,0,0,0,1], [0,0,-1,0,0,0,0,0,1,0,0,0], [0,0,0,0,-1,0,0,0,0,0,1,0], [0,1,-1,0,0,1,0,-1,1,0,0,-1], [0,0,0,1,-1,1,0,0,0,-1,1,-1], [-1,0,1,0,-1,0,1,0,-1,0,1,0]], [[1,-1,0,1,0,0,-1,1,0,-1,0,0], [0,0,0,1,0,0,0,0,0,-1,0,0], [0,0,0,1,-1,1,0,0,0,-1,1,-1], [0,1,0,0,0,0,0,-1,0,0,0,0], [0,1,-1,0,0,1,0,-1,1,0,0,-1], [0,0,0,0,0,1,0,0,0,0,0,-1], [0,0,0,0,0,0,-1,1,0,-1,0,0], [0,0,0,0,0,0,0,0,0,-1,0,0], [0,0,0,0,0,0,0,0,0,-1,1,-1], [0,0,0,0,0,0,0,-1,0,0,0,0], [0,0,0,0,0,0,0,-1,1,0,0,-1], [0,0,0,0,0,0,0,0,0,0,0,-1]], [[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], [-1,1,0,-1,0,0,0,0,0,0,0,0], [-1,0,1,0,-1,0,0,0,0,0,0,0], [0,-1,1,0,0,-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,-1,1,0,-1,0,0], [0,0,0,0,0,0,-1,0,1,0,-1,0], [0,0,0,0,0,0,0,-1,1,0,0,-1]]]], [ # Q-class [12][12] [[8], [1,8], [2,0,8], [4,-1,-1,8], [0,2,2,-2,8], [3,-1,4,0,4,8], [-4,-3,-3,-3,-3,-4,8], [-3,3,2,-1,2,-2,-1,8], [-2,-2,3,-4,4,2,1,1,8], [-2,1,-4,-2,-2,-4,2,1,-2,8], [-3,-4,-4,1,0,-1,3,-1,1,2,8], [2,4,0,-2,4,1,-3,0,2,2,-2,8]], [[[0,0,0,0,0,0,0,0,0,0,0,1], [0,0,1,1,1,0,1,0,0,1,0,0], [1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,-1,0,0,0,0,-1,-1,1,1], [0,0,1,0,1,-1,-1,-1,0,1,0,-1], [0,0,0,0,0,0,-1,0,0,0,0,0], [0,0,-1,0,0,0,0,0,1,0,-1,-1], [0,1,1,1,1,0,1,-1,0,1,0,-1], [1,0,0,-1,0,-1,-1,0,0,0,0,-1], [-1,0,0,1,0,1,1,0,0,1,-1,0], [0,0,-1,-1,0,0,-1,0,0,0,0,-1], [0,0,1,0,0,0,0,0,0,1,0,0]], [[-1,-1,0,1,0,0,0,0,0,0,-1,1], [0,0,-1,1,0,1,0,0,1,1,-1,-1], [1,-1,-1,-1,-1,0,0,1,0,-1,0,1], [-1,0,0,1,0,0,0,0,0,0,0,1], [1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,-1,0,0,0,0,-1,0,1], [0,0,1,-1,0,0,0,0,-1,0,1,0], [1,0,-1,0,0,1,1,1,0,0,0,0], [1,0,0,-1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,-1], [0,1,1,0,0,0,0,0,0,0,1,0], [0,0,0,1,1,0,0,-1,1,1,-1,-1]], [[1,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,1,1,0,1,-1,1,1,-1,-1], [0,0,0,0,0,0,0,0,0,-1,0,0], [1,-1,0,-1,0,-1,-1,0,0,0,0,0], [-1,1,0,1,0,1,0,-1,1,1,-1,-1], [0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,-1,-1,0,0,1,-1,-1,1,1], [0,0,-1,0,0,0,0,0,1,0,-1,-1], [-1,1,0,1,-1,1,0,0,1,0,0,0], [0,0,-1,0,0,0,0,0,0,0,0,0], [0,0,0,-1,-1,0,-1,0,0,0,1,0], [-1,1,0,2,0,1,1,-1,1,1,-1,0]]]], [ # Q-class [12][13] [[2], [1,2], [1,1,2], [1,1,1,2], [1,1,1,1,2], [1,1,1,1,1,2], [0,0,0,0,0,0,2], [0,0,0,0,0,0,1,2], [0,0,0,0,0,0,1,1,2], [0,0,0,0,0,0,1,1,1,2], [0,0,0,0,0,0,1,1,1,1,2], [0,0,0,0,0,0,1,1,1,1,1,2]], [[[0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,-1,1,0,0,0,0,0,0], [0,0,0,-1,0,1,0,0,0,0,0,0], [0,0,-1,0,0,1,0,0,0,0,0,0], [0,-1,0,0,0,1,0,0,0,0,0,0], [-1,0,0,0,0,1,0,0,0,0,0,0], [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]], [[-1,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,1,-1,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,-1,1,0,0,0,0,0,0,0], [0,0,-1,0,1,0,0,0,0,0,0,0], [0,-1,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0], [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]], [[0,0,0,0,0,0,1,0,0,0,0,0], [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], [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]]]], [ # Q-class [12][14] [[4], [0,4], [2,-2,4], [2,1,1,4], [1,-1,1,2,4], [0,-1,2,1,2,4], [0,0,0,0,0,0,4], [0,0,0,0,0,0,0,4], [0,0,0,0,0,0,2,-2,4], [0,0,0,0,0,0,2,1,1,4], [0,0,0,0,0,0,1,-1,1,2,4], [0,0,0,0,0,0,0,-1,2,1,2,4]], [[[-1,0,1,0,0,-1,0,0,0,0,0,0], [0,0,0,0,1,-1,0,0,0,0,0,0], [0,0,0,0,-1,0,0,0,0,0,0,0], [0,0,1,0,0,-1,0,0,0,0,0,0], [0,-1,0,1,-1,0,0,0,0,0,0,0], [0,0,0,1,-1,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0], [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]], [[1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0], [1,0,-1,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,1,-1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0], [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]], [[0,0,0,0,0,0,1,0,0,0,0,0], [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], [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]]]], [ # Q-class [12][15] [[4], [-1,4], [-2,1,4], [0,-2,1,4], [1,2,0,-2,4], [0,-1,0,-1,0,4], [1,-1,1,2,0,-1,4], [0,0,1,0,0,1,0,4], [-1,1,0,-1,0,0,1,-1,4], [2,0,0,0,2,0,1,0,0,4], [-1,0,2,2,-1,0,2,0,1,1,4], [1,0,-1,-1,1,1,1,1,2,2,1,4]], [[[-1,0,-2,-1,0,0,1,1,0,1,1,-2], [1,-2,1,0,2,-1,-2,0,1,-1,1,0], [1,0,1,1,0,0,-1,0,1,0,-1,0], [0,1,0,0,-1,0,1,0,0,0,-1,0], [1,-2,0,0,2,-1,-2,1,1,-1,2,-1], [0,0,0,0,-1,0,0,0,0,1,0,0], [0,0,-1,0,0,0,0,1,1,0,0,-1], [0,0,0,0,0,0,0,1,1,1,0,-1], [1,-1,0,0,1,0,-1,0,1,-1,1,0], [0,-1,-1,0,1,0,0,1,1,0,1,-2], [0,0,0,1,0,0,0,0,1,0,-1,0], [0,-1,-1,0,1,0,0,1,1,0,1,-1]], [[-1,2,0,0,-2,1,2,-1,-1,1,-2,1], [0,-1,0,0,0,0,0,0,0,0,0,0], [1,-1,0,0,1,0,-1,1,1,-1,1,-1], [0,0,0,0,1,0,0,0,0,-1,0,0], [-1,1,-1,1,-1,1,1,0,0,1,-1,0], [0,0,0,0,0,0,0,1,1,1,0,-1], [0,1,-1,0,0,1,1,0,0,0,0,-1], [-1,1,0,0,-1,1,1,0,-1,1,-1,0], [1,-1,0,0,1,0,-1,0,1,0,1,-1], [-1,1,-1,0,-1,1,1,0,0,1,-1,0], [0,-1,-1,-1,1,0,0,1,1,0,1,-2], [-1,1,-1,0,-1,1,1,0,0,2,-1,-1]]]], [ # Q-class [12][16] [[8], [-2,8], [-4,4,8], [4,-2,-1,8], [-2,-3,1,-2,8], [-3,4,3,0,1,8], [1,3,3,3,-4,2,8], [3,-4,-3,0,0,-4,-3,8], [4,-1,0,0,0,-1,1,4,8], [-4,2,1,0,0,2,1,-2,-4,8], [4,-1,-4,4,-2,-1,-1,0,0,0,8], [4,-1,-4,3,-1,-2,-2,3,0,-1,4,8]], [[[0,-1,1,0,-1,0,-1,-1,1,1,0,1], [1,-1,1,-1,-1,1,0,1,-1,0,0,0], [-1,1,-1,0,1,0,2,2,-1,-1,1,-1], [0,0,0,0,0,0,0,0,0,0,1,0], [-2,2,-2,2,2,-1,1,1,0,-1,0,-1], [1,0,0,0,0,0,0,1,-1,0,0,-1], [0,0,0,-1,0,0,1,1,-1,0,1,0], [0,-1,0,0,-1,0,-1,-2,2,1,-1,1], [0,-2,1,-1,-1,0,0,-1,1,1,0,1], [0,1,-1,0,1,0,1,1,-1,-1,0,0], [2,-2,2,-1,-1,1,-1,-1,0,1,0,1], [1,-2,1,0,-2,1,-2,-2,1,1,-1,1]], [[0,-2,1,-1,-1,0,0,-1,1,1,0,1], [0,1,-1,0,1,0,1,0,0,0,0,0], [0,1,-1,1,0,0,-1,-1,1,0,-1,0], [0,-1,0,0,-1,0,-1,-1,1,1,-1,0], [-1,2,-1,2,1,-1,0,1,0,-1,0,-1], [-2,3,-2,2,2,-1,1,1,0,-1,0,-1], [-1,0,-1,0,0,0,0,-1,1,0,0,0], [0,-1,1,-1,-1,0,0,0,0,0,0,1], [-1,0,0,0,0,-1,0,-1,1,0,0,1], [0,1,-1,0,1,0,1,1,-1,-1,0,-1], [1,-1,1,-1,0,0,0,0,0,1,0,0], [1,-1,1,-1,-1,0,0,0,0,1,0,0]]]], [ # Q-class [12][17] [[4], [2,4], [2,1,4], [1,2,2,4], [2,1,2,1,4], [1,2,1,2,2,4], [2,1,2,1,2,1,4], [1,2,1,2,1,2,2,4], [2,1,2,1,2,1,2,1,4], [1,2,1,2,1,2,1,2,2,4], [2,1,2,1,2,1,2,1,2,1,4], [1,2,1,2,1,2,1,2,1,2,2,4]], [[[0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,-1,1,0,0], [0,0,0,0,0,0,0,0,0,1,0,-1], [0,0,0,0,0,0,0,0,-1,1,1,-1], [0,0,0,0,0,0,0,-1,0,1,0,0], [0,0,0,0,0,0,1,-1,-1,1,0,0], [0,0,0,0,0,-1,0,0,0,1,0,0], [0,0,0,0,1,-1,0,0,-1,1,0,0], [0,0,0,-1,0,0,0,0,0,1,0,0], [0,0,1,-1,0,0,0,0,-1,1,0,0], [0,-1,0,0,0,0,0,0,0,1,0,0], [1,-1,0,0,0,0,0,0,-1,1,0,0]], [[-1,0,0,0,0,0,0,0,0,0,1,0], [-1,1,0,0,0,0,0,0,0,0,1,-1], [0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,1,-1], [0,0,0,0,0,0,0,0,-1,0,1,0], [0,0,0,0,0,0,0,0,-1,1,1,-1], [0,0,0,0,0,0,-1,0,0,0,1,0], [0,0,0,0,0,0,-1,1,0,0,1,-1], [0,0,0,0,-1,0,0,0,0,0,1,0], [0,0,0,0,-1,1,0,0,0,0,1,-1], [0,0,-1,0,0,0,0,0,0,0,1,0], [0,0,-1,1,0,0,0,0,0,0,1,-1]], [[1,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0], [1,0,-1,0,0,0,0,0,0,0,0,0], [0,1,0,-1,0,0,0,0,0,0,0,0], [1,0,0,0,-1,0,0,0,0,0,0,0], [0,1,0,0,0,-1,0,0,0,0,0,0], [1,0,0,0,0,0,-1,0,0,0,0,0], [0,1,0,0,0,0,0,-1,0,0,0,0], [1,0,0,0,0,0,0,0,-1,0,0,0], [0,1,0,0,0,0,0,0,0,-1,0,0], [1,0,0,0,0,0,0,0,0,0,-1,0], [0,1,0,0,0,0,0,0,0,0,0,-1]]]], [ # Q-class [12][18] [[8], [4,8], [4,2,8], [2,4,4,8], [-2,-1,2,1,8], [-1,-2,1,2,4,8], [0,0,-2,-1,2,1,8], [0,0,-1,-2,1,2,4,8], [4,2,0,0,-4,-2,2,1,8], [2,4,0,0,-2,-4,1,2,4,8], [4,2,4,2,-2,-1,-4,-2,2,1,8], [2,4,2,4,-1,-2,-2,-4,1,2,4,8]], [[[0,0,0,1,0,0,0,0,0,0,0,0], [0,0,-1,1,0,0,0,0,0,0,0,0], [0,-1,0,1,0,0,0,0,0,1,0,0], [1,-1,-1,1,0,0,0,0,-1,1,0,0], [0,-1,0,0,0,0,0,1,0,0,0,1], [1,-1,0,0,0,0,-1,1,0,0,-1,1], [0,0,0,0,0,-1,0,1,0,-1,0,1], [0,0,0,0,1,-1,-1,1,1,-1,-1,1], [0,1,0,0,0,0,0,0,0,0,0,0], [-1,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,-1,0,1,0,0], [0,0,0,0,-1,1,1,-1,-1,1,0,0]], [[-1,0,0,0,0,0,0,0,0,0,1,0], [-1,1,0,0,0,0,0,0,0,0,1,-1], [0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,1,-1], [0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,1,-1,0,0], [-1,0,1,0,-1,0,1,0,0,0,0,0], [-1,1,1,-1,-1,1,1,-1,0,0,0,0], [-1,0,1,0,0,0,0,0,0,0,0,0], [-1,1,1,-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,-1,1,0,0,0,0]], [[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], [-1,0,1,0,-1,0,0,0,0,0,0,0], [0,-1,0,1,0,-1,0,0,0,0,0,0], [0,0,0,0,0,0,-1,0,1,0,-1,0], [0,0,0,0,0,0,0,-1,0,1,0,-1], [1,0,0,0,0,0,0,0,0,0,-1,0], [0,1,0,0,0,0,0,0,0,0,0,-1], [1,0,0,0,0,0,0,0,-1,0,0,0], [0,1,0,0,0,0,0,0,0,-1,0,0]]]], [ # Q-class [12][19] [[2], [1,2], [1,1,2], [1,1,1,2], [1,1,1,1,2], [1,1,1,1,1,2], [1,1,1,1,1,1,2], [1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,2]], [[[0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,-1,1], [0,0,0,0,0,0,0,0,0,-1,0,1], [0,0,0,0,0,0,0,0,-1,0,0,1], [0,0,0,0,0,0,0,-1,0,0,0,1], [0,0,0,0,0,0,-1,0,0,0,0,1], [0,0,0,0,0,-1,0,0,0,0,0,1], [0,0,0,0,-1,0,0,0,0,0,0,1], [0,0,0,-1,0,0,0,0,0,0,0,1], [0,0,-1,0,0,0,0,0,0,0,0,1], [0,-1,0,0,0,0,0,0,0,0,0,1], [-1,0,0,0,0,0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,1,-1], [0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,-1,1,0], [0,0,0,0,0,0,0,0,-1,0,1,0], [0,0,0,0,0,0,0,-1,0,0,1,0], [0,0,0,0,0,0,-1,0,0,0,1,0], [0,0,0,0,0,-1,0,0,0,0,1,0], [0,0,0,0,-1,0,0,0,0,0,1,0], [0,0,0,-1,0,0,0,0,0,0,1,0], [0,0,-1,0,0,0,0,0,0,0,1,0], [0,-1,0,0,0,0,0,0,0,0,1,0]]]] ]; MakeImmutable( IMFList[12].matrices );