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Project: cocalc-sagemath-dev-slelievre
Views: 418346############################################################################# ## #A imf25.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 25, ## ## [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 25. ## IMFList[25].matrices := [ [ # Q-class [25][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], [0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]], [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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]]]], [ # Q-class [25][02] [[2], [1,2], [1,1,2], [1,1,1,2], [1,1,1,1,2], [0,0,0,0,0,2], [0,0,0,0,0,1,2], [0,0,0,0,0,1,1,2], [0,0,0,0,0,1,1,1,2], [0,0,0,0,0,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,1,1,2], [0,0,0,0,0,0,0,0,0,0,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2]], [[[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,-1,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1], [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,-1,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0], [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,-1,1,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [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,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]], [[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], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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,-1,0,0,0,0,0,0,0,0,0,0], [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,-1,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1], [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,-1,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]], [[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1], [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,-1,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0], [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,-1,1,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0]]]], [ # Q-class [25][03] [[4], [2,4], [1,1,4], [2,2,2,4], [2,1,2,1,4], [1,2,0,1,0,4], [2,1,1,1,2,0,4], [1,1,1,1,1,-1,1,4], [1,1,1,1,1,0,2,2,4], [2,1,1,1,2,0,2,1,1,4], [1,1,2,2,1,0,2,1,2,1,4], [1,1,2,1,2,0,1,2,2,1,1,4], [1,1,1,1,1,0,2,1,2,1,2,1,4], [2,2,1,2,1,1,1,2,2,1,1,2,1,4], [2,1,1,1,2,-1,2,2,1,2,1,1,1,1,4], [1,2,1,1,1,0,2,1,2,1,2,1,2,1,1,4], [1,1,2,2,1,-1,1,2,1,1,2,1,1,1,2,1,4], [2,2,1,2,1,1,1,1,1,1,1,1,2,2,1,1,1,4], [1,1,1,1,1,0,1,2,2,2,1,2,1,2,1,1,1,1,4], [1,1,2,2,1,0,1,1,1,2,2,1,1,1,1,1,2,1,2,4], [1,1,1,1,1,0,1,1,1,2,1,1,2,1,1,1,1,2,2,2,4], [1,1,1,1,1,-1,1,2,1,1,1,1,2,1,2,1,2,2,1,1,2,4], [1,1,2,1,2,0,1,1,1,1,1,2,2,1,1,1,1,2,1,1,2,2,4], [1,2,2,1,2,0,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,1,2,4], [1,2,1,1,1,0,1,1,1,2,1,1,1,1,1,2,1,1,2,2,2,1,1,2,4]], [[[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,-1,1], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,-1,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,1], [0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,1], [0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,0,0,1], [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], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,-1,0,0,0,-1,0,0,0,0,1], [0,-1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1], [0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,1], [0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,-1,1], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,0,0,-1,0,0,0,1], [0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,-1,0,0,0,1,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0,-1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1], [1,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,0,1], [0,-1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,-1,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,0,-1,1], [0,0,0,0,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1]], [[-1,0,0,0,0,0,0,-1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,-1,0,0], [0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,-1,0,0,0,1,0,0,0], [0,0,0,0,-1,0,0,-1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,-1,0,0,0,0,0,0], [0,0,0,0,0,0,-1,-1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,-1,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,-1], [0,1,0,0,0,-1,0,-1,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,-1,1,0,0,0,-1,0,0,0,0,0,0,0,0,1,0,0,0], [0,1,0,0,0,-1,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,-1,0], [0,0,0,0,0,0,0,-1,1,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,-1,0,-1,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,-1,1,0,0,0], [0,0,0,-1,0,0,0,-1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0], [0,1,0,0,0,-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,-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,-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,-1,0,0,0,0,0,0,0,0,1,0,1,-1,0,0,0,0,0], [0,0,-1,0,0,0,0,-1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [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]], [[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], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0], [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], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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]]]], [ # Q-class [25][04] [[6], [3,6], [2,2,6], [2,2,2,6], [2,2,2,0,6], [2,2,3,2,2,6], [2,2,3,2,2,0,6], [3,3,1,1,1,0,1,6], [1,1,1,3,0,1,1,2,6], [2,3,2,1,1,1,1,3,2,6], [1,2,1,0,3,2,0,2,1,1,6], [3,0,2,2,2,2,2,1,1,0,0,6], [2,1,3,1,2,0,2,2,1,2,1,1,6], [2,2,1,2,0,1,0,2,1,2,2,2,2,6], [1,2,3,1,1,1,2,2,2,2,3,0,3,2,6], [2,2,2,2,0,0,2,2,2,2,0,1,3,2,3,6], [2,1,2,2,1,1,0,2,2,2,1,2,2,2,1,2,6], [0,1,2,0,3,1,1,1,1,3,3,1,2,2,1,1,2,6], [0,2,0,2,2,0,1,2,2,2,2,0,2,2,2,2,1,2,6], [2,2,2,0,2,2,0,1,0,2,2,1,2,2,2,2,2,2,0,6], [2,1,1,2,1,2,-1,2,2,1,2,2,1,2,1,1,0,1,1,1,6], [2,1,2,1,1,0,3,1,2,2,0,1,3,1,3,2,2,1,0,2,-1,6], [1,0,2,2,2,2,0,2,1,2,2,1,2,1,2,2,2,2,2,2,2,0,6], [2,1,3,1,1,0,3,2,2,2,0,1,2,0,2,3,1,2,0,2,1,3,2,6], [2,2,2,3,3,2,2,2,3,1,3,2,1,2,1,1,2,3,2,0,2,1,2,2,6]], [[[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,-1,0,0,0,0,0,0,1], [-1,-2,-1,2,2,1,-1,0,-1,2,2,0,1,1,0,1,0,-2,-1,-1,-1,-1,-2,2,0], [0,0,2,0,1,-1,-1,0,1,0,2,0,-1,1,-2,1,-1,-1,0,-1,-1,1,1,0,-1], [-2,-2,-2,3,3,2,-1,1,-1,2,2,0,1,1,0,1,0,-2,-1,-1,-1,-1,-3,3,-1], [-2,-3,-2,3,4,2,0,1,-1,3,2,-1,1,2,0,1,1,-3,-2,-1,-1,-2,-3,3,-1], [0,1,1,-1,-1,-1,-1,-1,0,0,1,1,0,0,-1,0,-1,-1,1,0,0,1,1,0,1], [2,2,1,-2,-2,-1,0,-1,1,-2,-2,0,-1,-1,1,-1,0,2,1,0,1,1,2,-2,1], [1,-1,1,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,1,0,0,0,0,0,0], [2,0,-1,0,-1,0,0,0,0,-1,-3,-1,0,-1,3,-1,0,2,0,1,0,-1,0,-1,2], [-1,-2,-2,2,3,2,0,1,-1,1,0,-1,0,1,1,1,1,-1,-1,-1,0,-1,-2,2,-1], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,-1,0,0,0,1,0,0,0,-1,1,-1,0,0,-1,0,1,0,0,0], [1,1,0,-1,-1,0,0,0,0,-1,-1,0,0,-1,1,0,0,1,0,0,0,0,1,-1,1], [0,-1,0,1,1,0,-1,0,-1,1,1,0,0,0,0,1,0,-1,0,-1,0,0,-1,1,0], [2,2,3,-3,-3,-2,0,-1,1,-2,0,0,-1,-1,-2,0,-1,1,2,0,1,3,3,-3,1], [2,1,2,-1,-2,-1,-1,0,1,-2,0,0,-1,-1,-1,0,-1,2,1,0,0,2,2,-2,0], [1,0,-1,0,0,1,0,0,0,-1,-1,-1,0,0,1,0,0,1,0,0,0,0,0,0,0], [1,2,2,-1,-1,-1,-1,0,1,-2,0,0,-1,0,-1,0,-1,1,1,-1,0,2,2,-1,-1], [0,-2,-3,1,1,2,1,1,-1,1,-1,-1,1,0,2,0,1,0,-1,0,0,-2,-2,1,1], [-1,-1,-1,1,2,1,1,0,0,1,1,-1,0,1,0,1,1,-1,-1,-1,0,-1,-1,1,-1], [1,1,1,-1,-2,-1,-1,-1,0,0,1,1,0,-1,-1,0,-1,0,1,0,0,1,1,0,1], [0,-2,-1,2,3,1,-1,1,0,1,0,-1,0,1,1,1,0,0,-1,-1,-1,-1,-2,1,-1], [1,0,0,-1,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1], [-1,-1,0,1,2,1,-1,0,0,1,2,0,0,1,-1,1,0,-2,0,-1,-1,0,-1,2,-1]], [[-2,-3,-2,2,2,2,0,1,-2,3,1,0,1,0,1,1,1,-2,-1,0,-1,-2,-3,2,1], [0,-2,0,1,1,1,0,1,-1,1,0,-1,-1,0,0,1,0,0,0,0,0,0,-1,0,0], [0,-2,0,2,1,1,-1,1,-1,1,0,0,0,0,1,0,0,0,0,0,-1,-1,-2,1,0], [1,1,0,-1,-2,0,0,0,0,-1,-2,0,0,-1,1,-1,0,2,1,1,0,0,1,-1,1], [1,0,0,0,-1,0,0,0,-1,0,-1,0,0,-1,1,0,0,1,0,0,0,0,0,-1,1], [1,1,0,0,-1,0,0,0,0,-1,-1,0,0,-1,1,-1,0,2,0,0,0,0,1,-1,0], [1,0,1,-1,-1,0,0,0,0,-1,-1,0,-1,0,0,0,0,1,1,0,0,1,1,-1,0], [-2,-2,0,2,2,1,-1,1,-1,2,3,0,0,1,-2,2,0,-2,-1,-1,-1,0,-2,2,-1], [1,3,3,-2,-3,-2,-1,-1,1,-2,1,1,-1,-1,-3,0,-1,1,2,0,0,3,3,-2,0], [-1,-1,1,1,1,0,-1,1,-1,1,1,0,-1,0,-1,1,0,-1,0,0,0,1,-1,0,0], [1,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,-1,0], [1,2,1,-2,-3,-1,0,-1,0,-1,0,1,0,-1,0,-1,0,1,1,0,0,1,2,-1,1], [-2,-3,-2,3,3,2,-1,1,-2,3,1,0,1,1,1,1,1,-2,-1,-1,-1,-2,-4,3,0], [0,-2,-1,1,1,1,0,1,-1,1,0,-1,0,0,1,0,1,0,0,0,0,-1,-2,1,0], [0,-2,-1,2,1,1,-1,1,-1,1,0,0,0,0,1,0,0,0,0,0,-1,-1,-2,1,0], [-2,-2,0,2,2,1,-1,1,-1,2,2,0,0,1,-1,1,0,-2,0,-1,-1,0,-2,2,-1], [0,1,2,-1,-2,-1,-1,0,0,0,1,1,0,-1,-2,0,-1,0,1,0,0,2,1,-1,1], [1,1,2,-1,-2,-1,0,0,0,-1,0,0,-1,-1,-1,0,0,1,1,0,1,2,1,-2,0], [1,0,0,0,0,0,0,1,0,-1,-2,-1,-1,0,1,0,0,2,0,0,0,0,0,-1,0], [0,-1,0,1,0,0,-1,0,-1,1,0,0,0,-1,1,0,0,0,0,0,0,0,-1,0,1], [-1,-1,-2,2,1,1,0,0,-1,2,1,0,1,0,1,0,1,-1,-1,0,-1,-2,-2,2,0], [0,0,0,0,-1,0,-1,0,-1,0,0,1,0,-1,0,0,0,0,1,0,0,1,0,0,1], [-1,-1,-1,2,1,1,-1,1,-1,1,0,0,1,0,1,0,0,0,-1,0,-1,-1,-2,1,0], [-1,-2,0,2,1,1,-1,1,-1,1,1,0,0,0,0,1,0,-1,0,0,-1,0,-2,1,0], [1,1,1,-1,-2,0,0,0,0,-1,0,0,0,-1,-1,0,0,1,1,0,0,1,1,-1,0]]]], [ # Q-class [25][05] [[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], [1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]], [[[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,-1,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1], [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], [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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1], [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], [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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]]]] ]; MakeImmutable( IMFList[25].matrices );