File: imf27.grp

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#############################################################################
##
#A  imf27.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 27,
##
##  [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 27.
##
IMFList[27].matrices := [

[ # Q-class [27][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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]],
 [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
  [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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
  [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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
  [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],
  [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [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],
  [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [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,-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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
  [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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
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  [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],
  [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [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],
  [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [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],
  [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]]],

[ # Q-class [27][02]
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  [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],
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  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2]],
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  [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,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
 [[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],
  [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [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],
  [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
  [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,-1,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1],
  [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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1],
  [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,-1,1,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]],
 [[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [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],
  [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
  [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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
  [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,-1,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1],
  [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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1]]]],

[ # Q-class [27][03]
 [[4],
  [2,4],
  [0,1,4],
  [1,2,2,4],
  [2,1,0,1,4],
  [2,1,1,2,2,4],
  [0,0,1,0,0,1,4],
  [0,1,2,1,0,0,1,4],
  [2,1,0,1,2,2,0,1,4],
  [1,1,0,1,2,1,0,0,1,4],
  [1,1,0,1,1,1,0,0,2,1,4],
  [1,1,0,2,2,1,0,0,1,2,1,4],
  [0,0,1,0,0,0,1,1,0,-1,0,0,4],
  [1,2,0,1,2,1,0,0,1,2,1,2,0,4],
  [0,1,2,1,0,0,2,2,0,0,0,0,1,0,4],
  [0,0,1,0,0,0,1,2,2,0,1,0,1,0,1,4],
  [0,0,1,0,0,0,1,1,0,1,0,0,2,0,1,1,4],
  [2,1,0,2,1,1,0,0,1,1,1,2,0,1,0,0,0,4],
  [1,2,2,1,0,0,1,2,0,0,0,0,1,0,2,1,1,0,4],
  [1,2,1,2,1,1,0,2,2,1,1,1,0,1,1,1,0,1,1,4],
  [1,1,0,2,1,1,0,0,2,1,2,2,0,1,0,1,0,2,0,1,4],
  [1,2,0,1,1,1,0,0,2,1,2,1,0,2,0,1,0,1,0,1,2,4],
  [2,1,0,1,1,1,0,0,1,1,2,1,0,2,0,0,0,2,0,1,1,1,4],
  [1,0,1,0,0,0,2,1,0,0,0,0,1,0,2,1,1,1,1,0,0,0,1,4],
  [0,0,1,0,1,0,2,1,0,2,0,1,1,1,2,1,2,0,1,0,0,0,0,2,4],
  [1,1,0,1,1,1,0,0,1,2,2,1,1,1,0,0,2,1,0,1,1,1,2,0,1,4],
  [0,0,1,0,0,0,2,1,1,0,1,0,1,0,2,2,1,0,1,0,1,1,0,2,2,0,4]],
 [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
  [1,-1,0,0,0,0,0,1,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,-1,1,1],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
  [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],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,1,-1,1,0],
  [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],
  [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
  [-1,1,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,1,0,0,-1,0],
  [-1,1,-1,0,0,1,0,0,0,1,0,0,1,-1,0,0,0,0,0,0,0,0,1,0,0,-1,0],
  [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [1,-1,0,1,0,-1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,-1,1,0],
  [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0],
  [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0],
  [1,-1,0,0,0,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,1,0,0,-1,0,-1,1,1],
  [0,-1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,-1,1,-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,-1,0],
  [1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
  [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],
  [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,1,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]],
 [[-1,0,-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],
  [-1,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
  [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,-1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,1,0,0,0,-1,0,0,1,0],
  [-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
  [-1,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
  [0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,1,0],
  [-1,0,0,0,0,0,0,-1,1,0,-1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0],
  [1,-1,0,0,-1,0,0,0,0,0,0,0,0,1,0,0,-1,0,1,0,0,0,-1,0,0,1,0],
  [0,0,0,0,0,0,0,0,0,-1,0,0,-1,1,0,0,0,0,0,0,0,0,-1,1,0,1,0],
  [0,-1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,-1,1,1,0,0,0,-1,0,0,1,0],
  [0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
  [-1,1,0,0,0,0,0,-1,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0,1,-1,0],
  [0,0,0,0,0,0,0,0,0,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,1,1,0],
  [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],
  [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0],
  [0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
  [-1,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,1,1,0,-1,0,0,0,0,0,0],
  [0,-1,-1,1,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0],
  [0,0,-1,1,0,0,0,0,0,-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,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,1,0],
  [0,-1,0,0,0,0,0,0,0,-1,0,0,-1,1,0,0,0,0,1,0,0,0,0,0,0,1,0],
  [0,0,0,0,0,0,0,-1,0,-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0]]]],

[ # Q-class [27][04]
 [[6],
  [3,6],
  [1,1,6],
  [2,2,2,6],
  [3,2,0,1,6],
  [2,1,3,1,0,6],
  [1,1,3,3,0,2,6],
  [1,3,2,1,0,2,2,6],
  [1,2,2,1,0,2,3,3,6],
  [2,3,1,3,1,1,1,2,2,6],
  [2,1,2,1,0,3,2,3,2,1,6],
  [1,1,0,1,3,0,0,0,0,1,0,6],
  [2,3,1,2,1,1,1,2,3,3,1,2,6],
  [3,2,1,3,1,2,1,1,1,3,3,1,2,6],
  [3,3,3,3,2,1,2,1,1,2,1,1,2,2,6],
  [2,2,0,1,3,0,0,0,0,1,0,2,1,1,3,6],
  [2,3,0,1,3,0,0,0,0,1,0,2,1,1,2,3,6],
  [1,1,3,2,0,2,3,3,2,1,3,0,1,1,2,0,0,6],
  [0,0,1,0,3,1,2,1,2,0,1,2,0,0,0,1,1,1,6],
  [1,1,0,2,3,0,0,0,0,3,0,3,1,2,1,2,2,0,2,6],
  [0,0,1,0,2,1,1,2,1,0,2,3,0,0,0,1,1,3,3,2,6],
  [1,1,0,1,2,0,0,0,0,1,0,3,2,1,1,2,3,0,1,2,1,6],
  [1,1,0,2,2,0,0,0,0,2,0,2,1,3,1,3,2,0,1,3,1,2,6],
  [1,1,0,1,2,0,0,0,0,1,0,3,3,1,1,3,2,0,1,2,1,3,3,6],
  [3,2,1,2,1,3,1,1,1,2,2,2,3,3,2,1,1,1,0,1,0,3,1,2,6],
  [0,0,2,0,2,2,1,1,1,0,1,2,0,0,0,1,1,1,3,3,3,1,1,1,0,6],
  [0,0,1,0,1,1,3,1,2,0,1,1,0,0,0,1,2,1,3,1,2,2,1,1,0,2,6]],
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[ # Q-class [27][05]
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];

MakeImmutable( IMFList[27].matrices );