#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Volkmar Felsch.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains, for each Q-class representative of the irreducible
## maximal finite integral matrix groups of dimension 24,
##
## [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 24.
##
IMFList[24 ].matrices := [
[ # Q-class [24][01]
[[1 ],
[0 ,1 ],
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[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 ],
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[0 ,0 ,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 ],
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[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 ]]]],
[ # Q-class [24][02]
[[2 ],
[-1 ,2 ],
[0 ,-1 ,2 ],
[0 ,0 ,-1 ,2 ],
[0 ,0 ,0 ,-1 ,2 ],
[0 ,0 ,0 ,0 ,-1 ,2 ],
[0 ,0 ,0 ,0 ,0 ,-1 ,2 ],
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[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 ,0 ,-1 ,2 ],
[0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,-1 ,0 ,0 ,0 ,0 ,2 ]],
[[[0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,1 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ],
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[0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,2 ,3 ,4 ,3 ,2 ,1 ,1 ,2 ,0 ,0 ,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 ,0 ,0 ,0 ,0 ,0 ,1 ]]]],
[ # Q-class [24][03]
[[4 ],
[-2 ,4 ],
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[2 ,0 ,0 ,4 ],
[2 ,-2 ,0 ,0 ,4 ],
[2 ,0 ,-2 ,0 ,0 ,4 ],
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[-2 ,2 ,2 ,0 ,-1 ,-1 ,0 ,2 ,0 ,0 ,4 ],
[2 ,-1 ,0 ,2 ,1 ,1 ,-2 ,-1 ,2 ,1 ,0 ,4 ],
[-2 ,1 ,0 ,-2 ,-1 ,-1 ,2 ,1 ,-2 ,-2 ,1 ,-2 ,4 ],
[1 ,1 ,-2 ,1 ,0 ,1 ,0 ,0 ,1 ,0 ,-1 ,0 ,0 ,4 ],
[-1 ,-1 ,1 ,0 ,0 ,-1 ,0 ,-1 ,0 ,-1 ,0 ,1 ,-1 ,-1 ,4 ],
[1 ,1 ,-1 ,2 ,-1 ,1 ,0 ,1 ,1 ,1 ,1 ,0 ,0 ,1 ,-1 ,4 ],
[1 ,-2 ,-1 ,-1 ,0 ,1 ,2 ,-1 ,-1 ,-1 ,-1 ,0 ,1 ,0 ,-1 ,0 ,4 ],
[2 ,-2 ,-1 ,0 ,2 ,0 ,-1 ,-1 ,0 ,1 ,-2 ,1 ,-1 ,-1 ,0 ,-1 ,1 ,4 ],
[0 ,-1 ,1 ,-1 ,0 ,1 ,0 ,-1 ,-1 ,0 ,0 ,0 ,-1 ,-2 ,0 ,-1 ,1 ,1 ,4 ],
[-1 ,1 ,-1 ,0 ,-2 ,0 ,0 ,-1 ,-2 ,-1 ,0 ,-1 ,1 ,0 ,0 ,0 ,0 ,-1 ,0 ,4 ],
[0 ,1 ,-1 ,1 ,-2 ,1 ,-1 ,-1 ,0 ,-1 ,0 ,1 ,0 ,0 ,0 ,1 ,0 ,-1 ,0 ,2 ,4 ],
[-2 ,2 ,1 ,-1 ,-1 ,0 ,1 ,1 ,-1 ,-1 ,2 ,-2 ,2 ,0 ,-1 ,1 ,0 ,-2 ,0 ,0 ,0 ,4 ],
[-2 ,1 ,0 ,-1 ,-2 ,-1 ,2 ,1 ,-1 ,-1 ,1 ,-2 ,2 ,0 ,0 ,0 ,0 ,-2 ,-1 ,2 ,1 ,1 ,4 ],
[2 ,-2 ,-1 ,0 ,2 ,1 ,-1 ,-1 ,0 ,1 ,-2 ,1 ,-2 ,0 ,0 ,-1 ,0 ,2 ,1 ,-1 ,-1 ,-2 ,-2 ,4 ]],
[[[-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 ,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 ],
[-2 ,-1 ,-1 ,1 ,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 ,1 ,0 ,0 ,0 ,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 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ],
[0 ,-1 ,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 ],
[-2 ,-1 ,-1 ,0 ,0 ,0 ,0 ,0 ,1 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ],
[-2 ,-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 ,0 ,0 ,0 ,0 ,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 ,-1 ,1 ,0 ,1 ,-1 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ],
[2 ,1 ,1 ,0 ,0 ,0 ,0 ,1 ,-1 ,-1 ,0 ,0 ,-1 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ],
[-2 ,0 ,-1 ,2 ,1 ,1 ,0 ,1 ,0 ,-1 ,-1 ,0 ,0 ,-1 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ],
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];
MakeImmutable( IMFList[24 ].matrices );
Messung V0.5 in Prozent C=97 H=99 G=97