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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346#############################################################################
##
#W irredsol.grp GAP group library Mark Short
#W Burkhard Höfling
##
##
#Y Copyright (C) 1993, Murdoch University, Perth, Australia
##
## This file contains the functions and data for the irreducible solvable
## matrix group library. It contains exactly one member for each of the
## 372 conjugacy classes of irreducible solvable subgroups of $GL(n,p)$
## where $1 < n$, $p$ is a prime, and $p^n < 256$.
##
## By well known theory, this data also doubles as a library of primitive
## solvable permutation groups of non-prime degree <256.
##
## This file contains the data from Mark Short's thesis, plus two groups
## missing from that list, subsequently discovered by Alexander Hulpke.
##
#############################################################################
##
#V PrimitiveIndexIrreducibleSolvableGroup
##
InstallValue(PrimitiveIndexIrreducibleSolvableGroup,
[,,,[1,2],,,,[1,2],[1,2,3,4,5,6,7],,,,,,,
[1,2,3,4,5,6,7,8,9,10],,,,,,,,,
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],,
[1,2,3,4,5,6,7,8,9],,,,,[1,2],,,,,,,,,,,,,,,,,
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29],,,,,,,,,,,,,,,
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40],,,,,,,,,,,,,,,,,
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108],
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],,,,
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22],,,[1,2],,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,
# the two missing ones (in increasing order)
74,75],
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]]);
#############################################################################
##
#V IrredSolJSGens[] . . . . . . . . . . . . . . . generators for the groups
##
## 'IrredSolJSGens[<n>][<p>][<k>]' is a generating set for the <k>-th
## JS-maximal of GL(<n>,<p>).
## This generating set is polycyclic, i.e. forms an AG-system for the group.
## A JS-maximal is a maximal irreducible solvable subgroup of GL(<n>,<p>)
## (for a few exceptional small values of n and p this group isn't maximal).
## Every group in the library is generated with reference to the generating
## set of one of these JS-maximals, called its guardian (a group may be a
## subgroup of several JS-maximals but it only has one guardian).
##
InstallValue(IrredSolJSGens,
[
[], # GL(1,*)
[ # GL(2,*)
[], # GL(2,1)
[ # GL(2,2)
[], # 1-th JS-maximal
[ # 2-th JS-maximal
[[1,0],[1,1]]*Z(2)^0,
[[0,1],[1,1]]*Z(2)^0 ]],
[ # GL(2,3)
[ # 1-th JS-maximal
[[0,1],[1,0]]*Z(3)^0,
[[2,0],[0,1]]*Z(3)^0,
[[1,0],[0,2]]*Z(3)^0 ],
[ # 2-th JS-maximal
[[1,0],[2,2]]*Z(3)^0,
[[0,1],[1,2]]*Z(3)^0 ],
[ # 3-th JS-maximal
[[1,2],[0,2]]*Z(3)^0,
[[1,2],[0,1]]*Z(3)^0,
[[0,2],[1,0]]*Z(3)^0,
[[1,1],[1,2]]*Z(3)^0,
[[2,0],[0,2]]*Z(3)^0 ]],
[], # GL(2,4)
[ # GL(2,5)
[ # 1-th JS-maximal
[[0,1],[1,0]]*Z(5)^0,
[[2,0],[0,1]]*Z(5)^0,
[[1,0],[0,2]]*Z(5)^0 ],
[ # 2-th JS-maximal
[[1,0],[4,4]]*Z(5)^0,
[[0,1],[3,4]]*Z(5)^0 ],
[], # 3-th JS-maximal
[ # 4-th JS-maximal
[[1,4],[4,4]]*Z(5)^0,
[[3,4],[3,1]]*Z(5)^0,
[[0,2],[2,0]]*Z(5)^0,
[[2,0],[0,3]]*Z(5)^0,
[[2,0],[0,2]]*Z(5)^0 ]],
[], # GL(2,6)
[ # GL(2,7)
[ # 1-th JS-maximal
[[0,1],[1,0]]*Z(7)^0,
[[3,0],[0,1]]*Z(7)^0,
[[1,0],[0,3]]*Z(7)^0 ],
[ # 2-th JS-maximal
[[1,0],[6,6]]*Z(7)^0,
[[0,1],[4,6]]*Z(7)^0 ],
[ # 3-th JS-maximal
[[4,1],[4,3]]*Z(7)^0,
[[6,2],[3,0]]*Z(7)^0,
[[0,6],[1,0]]*Z(7)^0,
[[2,3],[3,5]]*Z(7)^0,
[[3,0],[0,3]]*Z(7)^0 ]],
[], # GL(2,8)
[], # GL(2,9)
[], # GL(2,10)
[ # GL(2,11)
[ # 1-th JS-maximal
[[0,1],[1,0]]*Z(11)^0,
[[2,0],[0,1]]*Z(11)^0,
[[1,0],[0,2]]*Z(11)^0 ],
[ # 2-th JS-maximal
[[1,0],[10,10]]*Z(11)^0,
[[0,1],[4,10]]*Z(11)^0 ],
[ # 3-th JS-maximal
[[4,5],[8,7]]*Z(11)^0,
[[4,7],[8,6]]*Z(11)^0,
[[0,10],[1,0]]*Z(11)^0,
[[1,3],[3,10]]*Z(11)^0,
[[2,0],[0,2]]*Z(11)^0 ]],
[], # GL(2,12)
[ # GL(2,13)
[ # 1-th JS-maximal
[[0,1],[1,0]]*Z(13)^0,
[[2,0],[0,1]]*Z(13)^0,
[[1,0],[0,2]]*Z(13)^0 ],
[ # 2-th JS-maximal
[[1,0],[12,12]]*Z(13)^0,
[[0,1],[11,12]]*Z(13)^0 ],
[], # 3-th JS-maximal
[ # 4-th JS-maximal
[[3,10],[10,10]]*Z(13)^0,
[[2,3],[2,10]]*Z(13)^0,
[[0,5],[5,0]]*Z(13)^0,
[[5,0],[0,8]]*Z(13)^0,
[[2,0],[0,2]]*Z(13)^0 ]]],
[ # GL(3,*)
[], # GL(3,1)
[ # GL(3,2)
[], # 1-th JS-maximal
[ # 2-th JS-maximal
[[1,0,0],[0,0,1],[1,1,1]]*Z(2)^0,
[[0,1,0],[0,0,1],[1,0,1]]*Z(2)^0 ]],
[ # GL(3,3)
[ # 1-th JS-maximal
[[0,1,0],[1,0,0],[0,0,1]]*Z(3)^0,
[[0,1,0],[0,0,1],[1,0,0]]*Z(3)^0,
[[2,0,0],[0,1,0],[0,0,1]]*Z(3)^0,
[[1,0,0],[0,2,0],[0,0,1]]*Z(3)^0,
[[1,0,0],[0,1,0],[0,0,2]]*Z(3)^0 ],
[ # 2-th JS-maximal
[[1,0,0],[2,0,1],[0,2,2]]*Z(3)^0,
[[0,1,0],[0,0,1],[2,0,1]]*Z(3)^0 ]],
[], # GL(3,4)
[ # GL(3,5)
[ # 1-th JS-maximal
[[0,1,0],[1,0,0],[0,0,1]]*Z(5)^0,
[[0,1,0],[0,0,1],[1,0,0]]*Z(5)^0,
[[2,0,0],[0,1,0],[0,0,1]]*Z(5)^0,
[[1,0,0],[0,2,0],[0,0,1]]*Z(5)^0,
[[1,0,0],[0,1,0],[0,0,2]]*Z(5)^0 ],
[ # 2-th JS-maximal
[[1,0,0],[3,2,2],[1,4,2]]*Z(5)^0,
[[0,1,0],[0,0,1],[3,0,4]]*Z(5)^0 ]]],
[ # GL(4,*)
[], # GL(4,1)
[ # GL(4,2)
[], # 1-th JS-maximal
[ # 2-th JS-maximal
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]*Z(2)^0,
[[1,0,0,0],[1,1,0,0],[0,0,1,0],[0,0,0,1]]*Z(2)^0,
[[0,1,0,0],[1,1,0,0],[0,0,1,0],[0,0,0,1]]*Z(2)^0,
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,1,1]]*Z(2)^0,
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,1]]*Z(2)^0 ],
[], # 3-th JS-maximal
[], # 4-th JS-maximal
[ # 5-th JS-maximal
[[1,0,0,0],[0,0,1,0],[1,0,0,1],[1,1,1,1]]*Z(2)^0,
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,1]]*Z(2)^0 ]],
[ # GL(4,3)
[ # 1-th JS-maximal
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]*Z(3)^0,
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]*Z(3)^0,
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]*Z(3)^0,
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]*Z(3)^0,
[[2,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]*Z(3)^0,
[[1,0,0,0],[0,2,0,0],[0,0,1,0],[0,0,0,1]]*Z(3)^0,
[[1,0,0,0],[0,1,0,0],[0,0,2,0],[0,0,0,1]]*Z(3)^0,
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,2]]*Z(3)^0 ],
[ # 2-th JS-maximal
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]*Z(3)^0,
[[1,0,0,0],[2,2,0,0],[0,0,1,0],[0,0,0,1]]*Z(3)^0,
[[0,1,0,0],[1,2,0,0],[0,0,1,0],[0,0,0,1]]*Z(3)^0,
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,2,2]]*Z(3)^0,
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,2]]*Z(3)^0 ],
[ # 3-th JS-maximal
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]*Z(3)^0,
[[1,2,0,0],[0,2,0,0],[0,0,1,0],[0,0,0,1]]*Z(3)^0,
[[1,2,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]*Z(3)^0,
[[0,2,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]*Z(3)^0,
[[1,1,0,0],[1,2,0,0],[0,0,1,0],[0,0,0,1]]*Z(3)^0,
[[1,0,0,0],[0,1,0,0],[0,0,1,2],[0,0,0,2]]*Z(3)^0,
[[1,0,0,0],[0,1,0,0],[0,0,1,2],[0,0,0,1]]*Z(3)^0,
[[1,0,0,0],[0,1,0,0],[0,0,0,2],[0,0,1,0]]*Z(3)^0,
[[1,0,0,0],[0,1,0,0],[0,0,1,1],[0,0,1,2]]*Z(3)^0 ],
[], # 4-th JS-maximal
[ # 5-th JS-maximal
[[1,0,0,0],[0,0,0,1],[1,2,1,2],[0,2,2,1]]*Z(3)^0,
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,2]]*Z(3)^0 ],
[ # 6-th JS-maximal
[[1,0,0,0],[0,1,0,0],[2,0,2,0],[0,2,0,2]]*Z(3)^0,
[[0,0,1,0],[0,0,0,1],[1,0,2,0],[0,1,0,2]]*Z(3)^0,
[[1,2,0,0],[0,2,0,0],[0,0,1,2],[0,0,0,2]]*Z(3)^0,
[[1,2,0,0],[0,1,0,0],[0,0,1,2],[0,0,0,1]]*Z(3)^0,
[[0,2,0,0],[1,0,0,0],[0,0,0,2],[0,0,1,0]]*Z(3)^0,
[[1,1,0,0],[1,2,0,0],[0,0,1,1],[0,0,1,2]]*Z(3)^0 ],
[ # 7-th JS-maximal
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]*Z(3)^0,
[[1,0,2,0],[0,1,0,2],[0,0,2,0],[0,0,0,2]]*Z(3)^0,
[[1,0,2,0],[0,1,0,2],[0,0,1,0],[0,0,0,1]]*Z(3)^0,
[[0,0,2,0],[0,0,0,2],[1,0,0,0],[0,1,0,0]]*Z(3)^0,
[[1,0,1,0],[0,1,0,1],[1,0,2,0],[0,1,0,2]]*Z(3)^0,
[[1,2,0,0],[0,2,0,0],[0,0,1,2],[0,0,0,2]]*Z(3)^0,
[[1,2,0,0],[0,1,0,0],[0,0,1,2],[0,0,0,1]]*Z(3)^0,
[[0,2,0,0],[1,0,0,0],[0,0,0,2],[0,0,1,0]]*Z(3)^0,
[[1,1,0,0],[1,2,0,0],[0,0,1,1],[0,0,1,2]]*Z(3)^0 ],
[ # 8-th JS-maximal
[[1,0,0,1],[1,1,2,1],[2,0,0,1],[2,2,2,1]]*Z(3)^0,
[[2,0,2,0],[0,1,0,1],[2,2,1,1],[1,2,2,1]]*Z(3)^0,
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]*Z(3)^0,
[[1,0,0,0],[0,1,0,0],[0,0,2,0],[0,0,0,2]]*Z(3)^0,
[[0,2,0,0],[1,0,0,0],[0,0,0,2],[0,0,1,0]]*Z(3)^0,
[[1,1,0,0],[1,2,0,0],[0,0,1,1],[0,0,1,2]]*Z(3)^0,
[[2,0,0,0],[0,2,0,0],[0,0,2,0],[0,0,0,2]]*Z(3)^0 ]]],
[ # GL(5,*)
[], # GL(5,1)
[ # GL(5,2)
[], # 1-th JS-maximal
[ # 2-th JS-maximal
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,1],[0,1,0,1,1]]*Z(2)^0,
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,1,0]]*Z(2)^0 ]],
[ # GL(5,3)
[ # 1-th JS-maximal
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]*Z(3)^0,
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0]]*Z(3)^0,
[[2,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]*Z(3)^0,
[[1,0,0,0,0],[0,2,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]*Z(3)^0,
[[1,0,0,0,0],[0,1,0,0,0],[0,0,2,0,0],[0,0,0,1,0],[0,0,0,0,1]]*Z(3)^0,
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,2,0],[0,0,0,0,1]]*Z(3)^0,
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,2]]*Z(3)^0 ],
[ # 2-th JS-maximal
[[1,0,0,0,0],[0,0,0,1,0],[1,2,1,2,1],[0,2,2,0,1],[0,1,2,1,1]]*Z(3)^0,
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[2,0,2,0,2]]*Z(3)^0 ]]],
[ # GL(6,*)
[], # GL(6,1)
[ # GL(6,2)
[], # 1-th JS-maximal
[], # 2-th JS-maximal
[ # 3-th JS-maximal
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],
[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]*Z(2)^0,
[[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],
[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0]]*Z(2)^0,
[[1,0,0,0,0,0],[1,1,0,0,0,0],[0,0,1,0,0,0],
[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]*Z(2)^0,
[[0,1,0,0,0,0],[1,1,0,0,0,0],[0,0,1,0,0,0],
[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]*Z(2)^0,
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],
[0,0,1,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]*Z(2)^0,
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],
[0,0,1,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]*Z(2)^0,
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],
[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,1,1]]*Z(2)^0,
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],
[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,1]]*Z(2)^0 ],
[], # 4-th JS-maximal
[], # 5-th JS-maximal
[ # 6-th JS-maximal
[[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],
[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]]*Z(2)^0,
[[1,0,0,0,0,0],[0,0,1,0,0,0],[1,1,1,0,0,0],
[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]*Z(2)^0,
[[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,1,0,0,0],
[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]*Z(2)^0,
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],
[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,1,1,1]]*Z(2)^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],[0,0,0,0,0,1],[0,0,0,1,0,1]]*Z(2)^0 ],
[], # 7-th JS-maximal
[ # 8-th JS-maximal
[[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],
[1,0,0,0,0,1],[1,1,1,0,0,1],[1,1,1,1,1,1]]*Z(2)^0,
[[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],
[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,1]]*Z(2)^0 ],
[], # 9-th JS-maximal
[], # 10-th JS-maximal
[ # 11-th JS-maximal
[[1,0,0,0,0,0],[1,1,0,0,0,0],[0,0,1,0,0,0],
[0,0,1,1,0,0],[0,0,0,0,1,0],[0,0,0,0,1,1]]*Z(2)^0,
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],
[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,1]]*Z(2)^0,
[[0,1,1,1,0,1],[1,1,1,0,1,1],[1,1,0,1,0,1],
[1,0,1,1,1,1],[1,1,1,1,1,0],[1,0,1,0,0,1]]*Z(2)^0,
[[0,1,1,1,1,1],[1,1,1,0,1,0],[1,1,0,1,1,1],
[1,0,1,1,1,0],[0,1,0,1,1,0],[1,1,1,1,0,1]]*Z(2)^0,
[[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],
[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0]]*Z(2)^0,
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],
[0,0,1,1,0,0],[0,0,0,0,1,1],[0,0,0,0,1,0]]*Z(2)^0,
[[0,1,0,0,0,0],[1,1,0,0,0,0],[0,0,0,1,0,0],
[0,0,1,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,1]]*Z(2)^0 ]]],
[ # GL(7,*)
[], # GL(7,1)
[ # GL(7,2)
[], # 1-th JS-maximal
[ # 2-th JS-maximal
[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],
[0,1,1,0,0,0,0],[0,0,0,1,1,0,0],[0,0,0,0,0,1,1]]*Z(2)^0,
[[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],
[0,0,0,0,0,1,0],[0,0,0,0,0,0,1],[1,1,0,0,0,0,0]]*Z(2)^0 ]]]]);
#############################################################################
##
#V IrredSolGroupList[] . . . . . . . . . . . . . . description of the groups
##
## 'IrredSolGroupList[<n>][<p>][<i>] is a list containing the information
## about the <i>-th group from GL(<n>,<p>).
## The groups are ordered with respect to the following criteria:
## 1. Increasing size
## 2. Increasing guardian number
## If two groups have the same size and guardian, they are in no particular
## order.
##
## The list 'IrredSolGroupList[<n>][<p>][<i>] contains the following info:
## Position: [1]: the size of the group
## [2]: 0 if group is linearly primitive,
## otherwise its minimal block size
## [3]: the number of the group's guardian,
## i.e. its position in 'IrredSolJSGens[<n>][<p>]',
## [4..]: the group's generators in normal form
## (with respect to its guardian's AG-system)
##
InstallValue (IrredSolGroupList,
[
[], # GL(1,*)
[ # GL(2,*)
[], # GL(2,1)
[ # GL(2,2)
[ 3, 0, 2, 0,1 ],
[ 6, 0, 2, 1,0, 0,1 ]], # guardian
[ # GL(2,3)
[ 4, 1, 2, 0,2 ],
[ 8, 1, 1, 1,0,0, 0,1,0, 0,0,1 ], # guardian, not max.
[ 8, 0, 2, 1,1, 0,2 ],
[ 8, 0, 2, 0,1 ],
[ 16, 0, 2, 1,0, 0,1 ], # guardian, not max.
[ 24, 0, 3, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ],
[ 48, 0, 3, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ]], # guardian
[], # GL(2,4)
[ # GL(2,5)
[ 3, 0, 2, 0,8 ],
[ 6, 0, 2, 1,0, 0,8 ],
[ 6, 0, 2, 0,4 ],
[ 8, 1, 1, 1,2,0, 0,1,-1 ],
[ 8, 1, 1, 1,0,0, 0,1,-1 ],
[ 8, 1, 2, 0,3 ],
[ 12, 0, 2, 1,0, 0,4 ],
[ 12, 0, 2, 1,2, 0,4 ],
[ 12, 0, 2, 0,2 ],
[ 16, 1, 1, 1,1,0, 0,1,-1, 0,1,1 ],
[ 16, 1, 1, 1,0,0, 0,1,-1, 0,1,1 ],
[ 24, 0, 2, 1,1, 0,2 ],
[ 24, 0, 2, 1,0, 0,2 ],
[ 24, 0, 2, 0,1 ],
[ 24, 0, 4, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ],
[ 32, 1, 1, 1,0,0, 0,1,0, 0,0,1 ], # guardian, not max.
[ 48, 0, 2, 1,0, 0,1 ], # guardian
[ 48, 0, 4, 2,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ],
[ 96, 0, 4, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ]], # guardian
[], # GL(2,6)
[ # GL(2,7)
[ 4, 1, 2, 0,12 ],
[ 6, 1, 1, 1,0,0, 0,2,-2 ],
[ 8, 1, 1, 1,0,0, 0,3,0, 0,0,3 ],
[ 8, 0, 2, 1,3, 0,12 ],
[ 8, 0, 2, 0,6 ],
[ 12, 1, 1, 1,3,0, 0,3,3, 0,2,-2 ],
[ 12, 1, 1, 1,0,0, 0,3,3, 0,2,-2 ],
[ 12, 1, 2, 0,4 ],
[ 16, 0, 2, 1,0, 0,6 ],
[ 16, 0, 2, 0,3 ],
[ 16, 0, 2, 1,3, 0,6 ],
[ 18, 1, 1, 1,0,0, 0,2,-2, 0,2,2 ],
[ 24, 1, 1, 1,0,0, 0,3,0, 0,0,3, 0,2,-2 ],
[ 24, 1, 1, 1,0,0, 0,3,0, 0,0,3, 0,2,2 ],
[ 24, 0, 2, 0,2 ],
[ 24, 0, 2, 1,3, 0,4 ],
[ 24, 0, 3, 0,1,0,0,2, 0,0,1,0,0, 0,0,0,1,0 ],
[ 24, 0, 3, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ],
[ 32, 0, 2, 1,0, 0,3 ],
[ 36, 1, 1, 1,3,0, 0,3,3, 0,2,-2, 0,2,2 ],
[ 36, 1, 1, 1,0,0, 0,3,3, 0,2,-2, 0,2,2 ],
[ 48, 0, 2, 1,3, 0,2 ],
[ 48, 0, 2, 0,1 ],
[ 48, 0, 2, 1,0, 0,2 ],
[ 48, 0, 3, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ],
[ 72, 1, 1, 1,0,0, 0,3,0, 0,0,3, 0,2,-2, 0,2,2 ], # guardian
[ 72, 0, 3, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,2 ],
[ 96, 0, 2, 1,0, 0,1 ], # guardian
[ 144, 0, 3, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,2]
# guardian
],
[], # GL(2,8)
[], # GL(2,9)
[], # GL(2,10)
[ # GL(2,11)
[ 3, 0, 2, 0,40 ],
[ 4, 1, 2, 0,30 ],
[ 6, 0, 2, 0,20 ],
[ 6, 0, 2, 1,0, 0,40 ],
[ 8, 1, 1, 1,0,0, 0,5,0, 0,0,5 ],
[ 8, 0, 2, 0,15 ],
[ 8, 0, 2, 1,5, 0,30 ],
[ 10, 1, 1, 1,0,0, 0,2,-2 ],
[ 12, 0, 2, 0,10 ],
[ 12, 0, 2, 1,5, 0,20 ],
[ 12, 0, 2, 1,0, 0,20 ],
[ 15, 0, 2, 0,8 ],
[ 16, 0, 2, 1,0, 0,15 ],
[ 20, 1, 1, 1,0,0, 0,5,5, 0,2,-2 ],
[ 20, 1, 1, 1,5,0, 0,5,5, 0,2,-2 ],
[ 20, 1, 2, 0,6 ],
[ 24, 0, 2, 1,0, 0,10 ],
[ 24, 0, 2, 0,5 ],
[ 24, 0, 2, 1,5, 0,10 ],
[ 24, 0, 3, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ],
[ 30, 0, 2, 0,4 ],
[ 30, 0, 2, 1,0, 0,8 ],
[ 40, 1, 1, 1,0,0, 0,5,0, 0,0,5, 0,2,2 ],
[ 40, 1, 1, 1,0,0, 0,5,0, 0,0,5, 0,2,-2 ],
[ 40, 0, 2, 1,5, 0,6 ],
[ 40, 0, 2, 0,3 ],
[ 48, 0, 2, 1,0, 0,5 ],
[ 48, 0, 3, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ],
[ 50, 1, 1, 1,0,0, 0,2,-2, 0,2,2 ],
[ 60, 0, 2, 1,0, 0,4 ],
[ 60, 0, 2, 1,5, 0,4 ],
[ 60, 0, 2, 0,2 ],
[ 80, 0, 2, 1,0, 0,3 ],
[ 100, 1, 1, 1,0,0, 0,5,5, 0,2,-2, 0,2,2 ],
[ 100, 1, 1, 1,5,0, 0,5,5, 0,2,-2, 0,2,2 ],
[ 120, 0, 2, 1,0, 0,2 ],
[ 120, 0, 2, 0,1 ],
[ 120, 0, 2, 1,5, 0,2 ],
[ 120, 0, 3, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,2 ],
[ 200, 1, 1, 1,0,0, 0,5,0, 0,0,5, 0,2,-2, 0,2,2 ],# guardian
[ 240, 0, 2, 1,0, 0,1 ],# guardian
[ 240, 0, 3, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,2 ]],# guardian
[], # GL(2,12)
[ # GL(2,13)
[ 6, 1, 1, 1,0,0, 0,4,-4 ],
[ 7, 0, 2, 0,24 ],
[ 8, 1, 1, 1,0,0, 0,3,-3 ],
[ 8, 1, 1, 1,6,0, 0,3,-3 ],
[ 8, 1, 2, 0,21 ],
[ 12, 1, 1, 1,0,0, 0,6,6, 0,4,-4 ],
[ 12, 1, 1, 1,6,0, 0,6,6, 0,4,-4 ],
[ 14, 0, 2, 0,12 ],
[ 14, 0, 2, 1,0, 0,24 ],
[ 16, 1, 1, 1,0,0, 0,3,-3, 0,3,3 ],
[ 16, 1, 1, 1,3,0, 0,3,-3, 0,3,3 ],
[ 18, 1, 1, 1,0,0, 0,4,-4, 0,4,4 ],
[ 21, 0, 2, 0,8 ],
[ 24, 1, 1, 1,6,0, 0,3,-3, 0,4,4 ],
[ 24, 1, 1, 1,0,0, 0,3,-3, 0,4,-4 ],
[ 24, 1, 1, 1,6,0, 0,3,-3, 0,4,-4 ],
[ 24, 1, 1, 1,0,0, 0,3,-3, 0,4,4 ],
[ 24, 1, 1, 1,0,0, 0,3,3, 0,4,-4 ],
[ 24, 1, 1, 1,3,0, 0,3,3, 0,4,-4 ],
[ 24, 1, 2, 0,7 ],
[ 24, 0, 4, 0,1,0,0,4, 0,0,1,0,0, 0,0,0,1,0 ],
[ 24, 0, 4, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ],
[ 28, 0, 2, 0,6 ],
[ 28, 0, 2, 1,6, 0,12 ],
[ 28, 0, 2, 1,0, 0,12 ],
[ 32, 1, 1, 1,0,0, 0,3,0, 0,0,3 ],
[ 36, 1, 1, 1,0,0, 0,6,6, 0,4,-4, 0,4,4 ],
[ 36, 1, 1, 1,6,0, 0,6,6, 0,4,-4, 0,4,4 ],
[ 42, 0, 2, 0,4 ],
[ 42, 0, 2, 1,0, 0,8 ],
[ 48, 1, 1, 1,0,0, 0,3,-3, 0,3,3, 0,4,-4 ],
[ 48, 1, 1, 1,3,0, 0,3,-3, 0,3,3, 0,4,-4 ],
[ 48, 1, 1, 1,3,0, 0,3,-3, 0,3,3, 0,4,4 ],
[ 48, 1, 1, 1,0,0, 0,3,-3, 0,3,3, 0,4,4 ],
[ 48, 0, 4, 2,0,0,0,0, 0,1,0,0,4, 0,0,1,0,0, 0,0,0,1,0 ],
[ 48, 0, 4, 2,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ],
[ 56, 0, 2, 0,3 ],
[ 56, 0, 2, 1,0, 0,6 ],
[ 56, 0, 2, 1,3, 0,6 ],
[ 72, 1, 1, 1,0,0, 0,3,3, 0,4,-4, 0,4,4 ],
[ 72, 1, 1, 1,3,0, 0,3,3, 0,4,-4, 0,4,4 ],
[ 72, 1, 1, 1,6,0, 0,3,-3, 0,4,-4, 0,4,4 ],
[ 72, 1, 1, 1,0,0, 0,3,-3, 0,4,-4, 0,4,4 ],
[ 72, 0, 4, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,4 ],
[ 84, 0, 2, 1,6, 0,4 ],
[ 84, 0, 2, 1,0, 0,4 ],
[ 84, 0, 2, 0,2 ],
[ 96, 1, 1, 1,0,0, 0,3,0, 0,0,3, 0,4,-4 ],
[ 96, 1, 1, 1,0,0, 0,3,0, 0,0,3, 0,4,4 ],
[ 96, 0, 4, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0 ],
[ 112, 0, 2, 1,0, 0,3 ],
[ 144, 1, 1, 1,3,0, 0,3,-3, 0,3,3, 0,4,-4, 0,4,4 ],
[ 144, 1, 1, 1,0,0, 0,3,-3, 0,3,3, 0,4,-4, 0,4,4 ],
[ 144, 0, 4, 2,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,4 ],
[ 168, 0, 2, 0,1 ],
[ 168, 0, 2, 1,0, 0,2 ],
[ 168, 0, 2, 1,3, 0,2 ],
[ 288, 1, 1, 1,0,0, 0,3,0, 0,0,3, 0,4,-4, 0,4,4 ],# guardian
[ 288, 0, 4, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,4 ],# guardian
[ 336, 0, 2, 1,0, 0,1 ],# guardian
[ 24, 1, 1, 1,0,0, 0,4,-4, 0,6,0, 0,0,6], # BH: new group
[ 72, 1, 1, 1,0,0, 0,2,0, 0,0,2] # BH: new group
]],
[ # GL(3,*)
[], # GL(3,1)
[ # GL(3,2)
[ 7, 0, 2, 0,1 ],
[ 21, 0, 2, 1,0, 0,1 ]],# guardian
[ # GL(3,3)
[ 12, 1, 1, 0,1,0,0,0, 0,0,1,0,1, 0,0,0,1,1 ],
[ 13, 0, 2, 0,2 ],
[ 24, 1, 1, 1,0,1,1,1, 0,1,0,0,0, 0,0,1,0,1, 0,0,0,1,1 ],
[ 24, 1, 1, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,1 ],
[ 24, 1, 1, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,1, 0,0,0,1,1 ],
[ 26, 0, 2, 0,1 ],
[ 39, 0, 2, 1,0, 0,2 ],
[ 48, 1, 1, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,1 ],# guardian
[ 78, 0, 2, 1,0, 0,1 ]],# guardian
[], # GL(3,4)
[ # GL(3,5)
[ 12, 1, 1, 0,1,0,0,0, 0,0,2,0,-2, 0,0,0,2,-2 ],
[ 24, 1, 1, 1,0,0,0,0, 0,1,0,0,0, 0,0,2,0,-2, 0,0,0,2,-2 ],
[ 24, 1, 1, 1,0,2,2,2, 0,1,0,0,0, 0,0,2,0,-2, 0,0,0,2,-2 ],
[ 24, 1, 1, 0,1,0,0,0, 0,0,2,0,-2, 0,0,0,2,-2, 0,0,2,2,2 ],
[ 31, 0, 2, 0,4 ],
[ 48, 1, 1, 0,1,0,0,0, 0,0,2,0,-2, 0,0,0,2,-2, 0,0,1,1,1 ],
[ 48, 1, 1, 1,0,3,3,3, 0,1,0,0,0, 0,0,2,0,-2, 0,0,0,2,-2 ],
[ 48, 1, 1, 0,1,0,0,0, 0,0,1,0,-1, 0,0,0,1,-1 ],
[ 48, 1, 1, 1,0,2,2,2, 0,1,0,0,0, 0,0,2,0,-2, 0,0,0,2,-2, 0,0,2,2,2 ],
[ 62, 0, 2, 0,2 ],
[ 93, 0, 2, 1,0, 0,4 ],
[ 96, 1, 1, 1,0,2,2,2, 0,1,0,0,0, 0,0,2,0,-2, 0,0,0,2,-2, 0,0,1,1,1 ],
[ 96, 1, 1, 0,1,0,0,0, 0,0,1,0,-1, 0,0,0,1,-1, 0,0,2,2,2 ],
[ 96, 1, 1, 1,0,2,2,2, 0,1,0,0,0, 0,0,1,0,-1, 0,0,0,1,-1 ],
[ 96, 1, 1, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,-1, 0,0,0,1,-1 ],
[ 124, 0, 2, 0,1 ],
[ 186, 0, 2, 1,0, 0,2 ],
[ 192, 1, 1, 1,0,3,3,3, 0,1,0,0,0, 0,0,1,0,-1, 0,0,0,1,-1 ],
[ 192, 1, 1, 0,1,0,0,0, 0,0,1,0,-1, 0,0,0,1,-1, 0,0,1,1,1 ],
[ 192, 1, 1, 1,0,2,2,2, 0,1,0,0,0, 0,0,1,0,-1, 0,0,0,1,-1, 0,0,2,2,2 ],
[ 372, 0, 2, 1,0, 0,1 ],# guardian
[ 384, 1, 1, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,1 ]]],# guardian
[ # GL(4,*)
[], # GL(4,1)
[ # GL(4,2)
[ 5, 0, 5, 0,3 ],
[ 10, 0, 5, 2,0, 0,3 ],
[ 15, 0, 5, 0,1 ],
[ 18, 2, 2, 1,0,0,0,0, 0,0,1,0,0, 0,0,0,0,1 ],
[ 20, 0, 5, 1,0, 0,3 ],
[ 30, 0, 5, 2,0, 0,1 ],
[ 36, 2, 2, 1,0,0,0,0, 0,1,0,1,0, 0,0,1,0,0, 0,0,0,0,1 ],
[ 36, 2, 2, 1,1,0,0,0, 0,0,1,0,0, 0,0,0,0,1 ],
[ 60, 0, 5, 1,0, 0,1 ],# guardian
[ 72, 2, 2, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,1 ]],# guardian
[ # GL(4,3)
[ 5, 0, 5, 0,64 ],
[ 10, 0, 5, 0,64, 2,16 ],
[ 10, 0, 5, 0,64, 0,40 ],
[ 16, 1, 1, 1,2,1,1,1,0,0,0, 1,2,1,0,1,0,1,1 ],
[ 16, 1, 1, 1,1,1,0,1,1,1,0, 1,1,1,0,0,1,0,0 ],
[ 16, 1, 1, 0,0,0,1,1,0,1,0, 0,0,1,1,0,1,1,0, 0,0,1,1,1,1,0,0 ],
[ 16, 2, 2, 1,1,0,1,3 ],
[ 16, 2, 2, 1,0,0,1,1, 0,1,7,0,6 ],
[ 20, 0, 5, 0,64, 2,16, 2,40 ],
[ 20, 0, 5, 2,76, 2,12 ],
[ 20, 0, 5, 0,60, 0,64 ],
[ 20, 0, 5, 3,44, 3,76 ],
[ 32, 1, 1, 1,0,1,1,1,1,0,1, 1,0,1,0,0,0,1,0 ],
[ 32, 1, 1, 1,1,1,0,0,1,0,1, 1,1,1,0,1,1,1,1, 1,1,0,0,0,0,1,1 ],
[ 32, 1, 1, 1,0,1,1,1,1,0,1, 1,0,1,0,1,0,0,0, 1,0,0,1,1,1,0,1 ],
[ 32, 1, 1, 0,0,0,1,1,0,1,0, 0,0,1,0,0,1,0,1, 0,0,1,1,0,1,1,0,
0,0,0,1,0,1,1,0 ],
[ 32, 1, 1, 1,0,1,1,1,1,0,1, 1,0,1,0,1,0,0,0, 0,0,1,1,0,1,1,0 ],
[ 32, 2, 2, 1,1,3,0,6, 1,0,6,1,7, 1,0,0,1,1 ],
[ 32, 2, 2, 1,0,5,0,1, 0,0,5,0,1, 1,1,6,1,2 ],
[ 32, 2, 2, 1,0,5,0,1, 1,0,7,0,7, 1,0,0,0,6 ],
[ 32, 2, 2, 1,1,5,1,7, 0,0,3,0,1, 1,0,6,0,6 ],
[ 32, 2, 2, 1,0,6,0,6, 1,1,7,1,7, 1,1,5,1,5, 1,0,4,0,0 ],
[ 32, 2, 2, 1,0,5,0,1, 1,0,7,0,7, 0,0,5,0,1 ],
[ 32, 2, 2, 1,1,0,1,3, 1,1,3,1,0 ],
[ 40, 0, 5, 0,70, 0,64 ],
[ 40, 0, 5, 3,44, 3,52 ],
[ 40, 0, 5, 2,66, 2,62 ],
[ 40, 0, 5, 2,76, 2,12, 0,60 ],
[ 40, 0, 5, 3,39, 3,7 ],
[ 48, 2, 3, 1,1,0,1,3,1,0,0,0, 1,1,2,0,3,1,2,0,3 ],
[ 48, 2, 3, 1,1,2,1,3,1,2,0,1, 0,0,0,0,3,0,0,1,3, 0,0,0,1,3,0,0,0,1,
0,0,2,0,3,0,1,0,1 ],
[ 64, 1, 1, 1,1,1,0,1,1,1,0, 1,1,1,0,0,1,0,0, 1,1,0,1,0,1,0,0,
1,1,0,0,0,0,1,1 ],
[ 64, 1, 1, 1,1,1,0,0,1,0,1, 1,1,1,0,1,1,1,1, 1,1,1,0,1,0,0,1,
0,0,0,1,0,1,1,1 ],
[ 64, 1, 1, 1,0,1,1,1,1,0,1, 1,0,1,0,0,0,1,0, 1,0,0,1,1,1,0,1 ],
[ 64, 1, 1, 1,0,1,0,0,0,1,1, 1,0,1,0,1,1,0,0, 1,0,1,0,1,1,1,1,
1,0,1,0,1,0,0,1, 1,0,0,1,1,0,0,1 ],
[ 64, 2, 2, 1,1,0,1,3, 1,1,0,1,1 ],
[ 64, 2, 2, 1,1,7,0,0, 1,0,2,1,5, 1,1,5,1,7 ],
[ 64, 2, 2, 1,0,7,0,2, 1,0,1,0,0, 0,1,4,1,3 ],
[ 64, 2, 2, 1,0,5,0,1, 1,0,7,0,7, 1,0,0,0,6, 0,0,5,0,1 ],
[ 64, 2, 2, 1,1,5,1,7, 1,1,3,1,5, 1,0,5,0,1, 1,1,6,1,0 ],
[ 64, 2, 2, 1,1,0,1,3, 1,1,3,1,0, 1,0,5,0,1 ],
[ 64, 2, 2, 1,0,5,0,1, 1,0,7,0,7, 0,0,5,0,1, 1,1,6,1,2 ],
[ 64, 2, 2, 1,1,3,0,6, 1,0,6,1,7, 1,0,0,1,1, 0,1,7,0,6 ],
[ 80, 0, 5, 2,27, 2,75 ],
[ 80, 0, 5, 2,66, 2,62, 0,70 ],
[ 80, 0, 5, 3,44, 3,52, 3,48 ],
[ 80, 0, 5, 0,75, 0,64 ],
[ 80, 0, 5, 3,39, 3,35 ],
[ 96, 1, 1, 0,0,0,1,1,0,1,0, 0,0,1,0,0,1,0,1, 0,0,1,1,0,1,1,0,
0,0,0,1,0,1,1,0, 0,1,1,0,1,0,0,1 ],
[ 96, 2, 3, 1,0,1,0,3,0,2,1,3, 1,0,2,0,1,0,1,0,0, 0,1,2,1,3,1,2,1,1 ],
[ 96, 2, 3, 1,1,0,1,0,1,0,1,0, 1,1,0,0,3,1,0,0,1, 1,1,2,0,3,1,2,0,3 ],
[ 96, 2, 3, 1,1,1,1,3,1,1,1,0, 1,1,1,0,3,1,1,0,1, 1,1,1,1,2,1,1,1,1,
1,1,1,0,2,1,1,0,0, 0,0,2,1,2,0,1,0,1 ],
[ 96, 2, 3, 1,0,1,1,0,0,2,1,2, 1,0,2,0,3,0,1,0,0, 0,1,0,1,0,1,1,1,2 ],
[ 96, 0, 6, 0,3,0,0,1,1, 0,3,0,0,0,1, 0,3,0,0,1,2, 0,0,0,2,1,2 ],
[ 96, 0, 6, 0,0,0,0,1,1, 0,0,0,0,1,2, 1,3,0,0,0,0,
1,1,0,0,0,0, 0,0,0,2,1,2 ],
[ 96, 0, 6, 1,3,1,1,1,2, 1,1,1,1,1,2, 1,3,1,2,0,1 ],
[ 96, 0, 6, 0,3,1,1,0,3, 0,3,1,2,1,0, 0,3,1,1,0,2 ],
[ 128, 1, 1, 1,1,1,0,1,1,1,0, 1,1,1,0,0,1,0,0, 1,1,0,1,0,1,0,0,
1,1,1,0,0,1,0,1, 1,1,0,0,0,0,1,1 ],
[ 128, 2, 2, 1,1,5,1,7, 1,1,3,1,5, 1,0,5,0,1, 1,1,6,1,0, 1,0,0,0,6 ],
[ 128, 2, 2, 0,0,5,0,1, 0,0,7,0,1, 1,1,6,0,4 ],
[ 128, 2, 2, 1,1,7,0,0, 1,0,2,1,5, 1,1,3,0,6, 1,0,7,1,2 ],
[ 128, 2, 2, 1,0,7,0,2, 1,1,0,1,3 ],
[ 128, 2, 2, 1,0,7,1,2, 1,1,0,0,3, 1,0,1,1,6, 1,1,5,1,7 ],
[ 128, 2, 2, 1,1,6,1,0, 1,1,2,1,0, 1,0,0,0,6, 0,1,1,0,5 ],
[ 128, 2, 2, 1,1,0,1,3, 1,1,0,1,1, 1,0,5,0,1 ],
[ 128, 2, 2, 1,1,7,0,0, 1,0,2,1,5, 1,1,3,0,6, 1,1,5,1,7 ],
[ 128, 2, 2, 1,1,0,1,3, 1,1,0,1,1, 1,1,5,1,7 ],
[ 160, 0, 5, 2,66, 2,62, 0,70, 3,50 ],
[ 160, 0, 5, 3,39, 3,35, 3,21 ],
[ 160, 0, 5, 2,27, 2,75, 0,75 ],
[ 160, 0, 8, 0,0,0,0,1,0,1, 0,0,0,1,1,0,0, 0,0,1,0,1,1,1,
0,0,0,0,1,1,0, 0,4,0,0,0,1,0 ],
[ 192, 1, 1, 0,0,0,1,0,1,1,1, 0,0,1,1,0,1,1,1, 0,0,1,0,1,1,0,1,
0,1,1,0,1,0,0,1 ],
[ 192, 1, 1, 1,0,1,1,1,1,0,1, 1,0,1,0,0,0,1,0, 1,2,1,1,1,0,0,0 ],
[ 192, 1, 1, 1,1,1,0,0,1,0,1, 1,1,1,0,1,1,1,1, 1,2,1,1,1,1,1,1 ],
[ 192, 2, 3, 1,0,2,1,1,0,1,0,1, 1,0,2,1,1,0,1,0,3, 1,0,1,1,0,0,2,1,2,
0,1,0,1,0,1,1,1,0 ],
[ 192, 0, 6, 1,2,1,1,1,2, 1,0,1,1,1,0, 1,2,1,2,0,1, 0,3,1,1,0,3 ],
[ 192, 0, 6, 1,3,1,1,1,2, 1,1,1,1,1,2, 1,3,1,2,0,1, 0,3,1,1,0,3 ],
[ 192, 0, 6, 1,3,1,1,1,2, 1,1,1,1,1,2, 1,3,1,2,0,1, 1,2,1,1,1,2 ],
[ 192, 0, 6, 0,3,0,0,1,1, 0,3,0,0,0,1, 0,3,0,0,1,2,
1,2,0,0,1,1, 0,0,0,2,1,2 ],
[ 192, 0, 6, 0,3,1,1,0,3, 0,3,1,2,1,0, 0,3,1,1,0,2, 0,2,1,1,1,2 ],
[ 192, 0, 6, 1,3,1,1,1,2, 1,1,1,1,1,2, 1,3,1,2,0,1, 0,2,1,1,1,2 ],
[ 256, 2, 2, 1,1,7,0,0, 1,0,2,1,5, 1,1,3,0,6, 1,0,7,1,2, 1,1,5,1,7 ],
[ 256, 2, 2, 1,1,5,1,7, 1,1,3,1,5, 1,0,5,0,1,
1,1,6,1,0, 1,0,0,0,6, 0,1,1,0,5 ],
[ 256, 2, 2, 1,0,7,0,2, 1,1,0,1,3, 0,1,4,0,7 ],
[ 256, 2, 2, 1,1,7,0,0, 1,0,2,1,5, 1,1,3,0,6, 1,0,7,1,2, 0,0,2,0,7 ],
[ 256, 2, 2, 1,0,7,0,2, 1,1,0,1,3, 1,1,5,1,7 ],
[ 256, 2, 2, 1,0,7,0,2, 1,1,0,1,3, 1,1,7,0,0 ],
[ 288, 0, 7, 0,0,0,0,0,0,0,1,3, 0,0,0,1,1,0,0,0,2, 0,0,0,0,0,0,0,0,3,
0,0,0,0,1,0,0,0,2, 0,0,2,1,0,0,1,0,3, 0,0,1,0,1,0,1,0,1 ],
[ 320, 0, 5, 1,0, 0,1 ],# guardian
[ 320, 0, 8, 2,1,1,0,1,1,1, 2,3,0,1,1,0,1 ],
[ 384, 1, 1, 1,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,
0,0,0,1,0,0,0,0, 0,0,0,0,1,0,0,0, 0,0,0,0,0,1,0,0,
0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,1 ],# guardian, not max.
[ 384, 2, 3, 1,1,1,1,3,1,1,0,1, 1,1,1,1,1,1,1,0,1, 1,1,1,1,3,1,1,1,1,
1,1,1,1,0,1,1,0,1, 0,0,2,1,2,0,1,0,1 ],
[ 384, 2, 3, 1,0,0,1,0,0,0,0,3, 1,0,0,0,3,0,0,1,2, 1,0,0,1,1,0,0,0,0,
1,0,2,1,1,0,1,0,1 ],
[ 384, 0, 6, 1,0,0,0,0,0, 0,1,0,0,0,0, 0,0,1,0,0,0,
0,0,0,1,0,0, 0,0,0,0,1,0, 0,0,0,0,0,1 ],# guardian, not max.
[ 512, 2, 2, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,1 ],# guardian, not maximal
[ 576, 0, 7, 0,1,1,0,1,1,1,1,2, 0,1,1,1,0,1,1,0,3, 0,1,2,1,0,1,1,1,0,
0,1,1,0,1,1,2,0,1 ],
[ 576, 0, 7, 1,0,0,1,0,0,0,0,3, 1,0,0,0,1,0,0,1,0, 1,0,0,1,1,0,0,0,0,
1,0,2,1,1,0,1,0,1, 0,0,1,0,1,0,1,0,1 ],
[ 576, 0, 7, 0,1,1,1,0,0,0,1,3, 0,1,2,0,1,0,0,1,1, 0,1,1,1,0,0,0,0,3,
0,1,1,1,0,0,0,1,0, 0,0,2,1,0,0,1,0,3 ],
[ 640, 0, 8, 1,0,0,0,0,0,0, 0,1,0,0,0,0,0, 0,0,1,0,0,0,0,
0,0,0,1,0,0,0, 0,0,0,0,1,0,0, 0,0,0,0,0,1,0,
0,0,0,0,0,0,1 ],# guardian
[ 768, 2, 3, 1,1,0,1,0,1,0,1,0, 1,0,0,1,0,0,0,0,3, 1,0,0,1,1,0,0,0,0,
1,1,0,1,1,1,0,0,0, 1,1,2,1,3,1,2,1,0 ],
[1152, 2, 3, 1,0,0,1,0,0,0,0,3, 1,0,0,0,3,0,0,1,2, 1,0,0,1,1,0,0,0,0,
1,0,2,1,1,0,1,0,1, 0,0,1,0,1,0,1,0,1 ],
[1152, 0, 7, 0,1,1,0,1,1,1,1,2, 0,1,1,1,0,1,1,0,3, 0,1,2,1,0,1,1,1,0,
0,1,1,0,1,1,2,0,1, 0,1,1,1,0,0,0,1,3 ],
[1152, 0, 7, 0,1,1,0,1,1,1,1,2, 0,1,1,1,0,1,1,0,3, 0,1,2,1,0,1,1,1,0,
0,1,1,0,1,1,2,0,1, 1,1,0,1,0,1,0,1,0 ],
[1152, 0, 7, 0,1,1,0,1,1,1,1,2, 0,1,1,1,0,1,1,0,3, 0,1,2,1,0,1,1,1,0,
0,1,1,0,1,1,2,0,1, 1,0,0,0,0,1,1,1,1 ],
[2304, 2, 3, 1,0,0,0,0,1,1,1,1, 1,1,1,0,0,0,0,1,2, 1,1,0,1,3,0,1,0,3 ],
[2304, 2, 3, 1,1,0,1,0,1,0,1,0, 1,0,0,1,0,0,0,0,3, 1,0,0,1,1,0,0,0,0,
1,1,0,1,1,1,0,0,0, 1,1,2,1,3,1,2,1,0, 1,0,2,1,1,0,1,0,1 ],
[2304, 0, 7, 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,
0,0,0,1,0,0,0,0,0, 0,0,0,0,1,0,0,0,0, 0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,1 ],# guardian
[4608, 2, 3, 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,
0,0,0,1,0,0,0,0,0, 0,0,0,0,1,0,0,0,0, 0,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,1 ]]],# guardian
[ # GL(5,*)
[], # GL(5,1)
[ # GL(5,2)
[ 31, 0, 2, 0,1 ],
[ 155, 0, 2, 1,0, 0,1 ]],# guardian
[ # GL(5,3)
[ 11, 0, 2, 0,22 ],
[ 22, 0, 2, 0,11 ],
[ 55, 0, 2, 1,0, 0,22 ],
[ 80, 1, 1, 0,1,0,0,0,0,0, 0,0,1,1,0,0,0, 0,0,0,1,1,0,0,
0,0,0,0,1,1,0, 0,0,0,0,0,1,1 ],
[ 110, 0, 2, 1,0, 0,11 ],
[ 121, 0, 2, 0,2 ],
[ 160, 1, 1, 0,1,0,0,0,0,0, 0,0,1,1,0,0,0, 0,0,0,1,1,0,0,
0,0,0,0,1,1,0, 0,0,0,0,0,1,1, 0,0,1,1,1,1,1 ],
[ 160, 1, 1, 2,0,0,0,0,0,0, 0,1,0,0,0,0,0, 0,0,1,1,0,0,0,
0,0,0,1,1,0,0, 0,0,0,0,1,1,0, 0,0,0,0,0,1,1 ],
[ 160, 1, 1, 2,0,1,1,1,1,1, 0,1,0,0,0,0,0, 0,0,1,1,0,0,0,
0,0,0,1,1,0,0, 0,0,0,0,1,1,0, 0,0,0,0,0,1,1 ],
[ 242, 0, 2, 0,1 ],
[ 320, 1, 1, 1,0,0,0,0,0,0, 0,1,0,0,0,0,0, 0,0,1,1,0,0,0,
0,0,0,1,1,0,0, 0,0,0,0,1,1,0, 0,0,0,0,0,1,1 ],
[ 320, 1, 1, 2,0,0,0,0,0,0, 0,1,0,0,0,0,0, 0,0,1,1,0,0,0,
0,0,0,1,1,0,0, 0,0,0,0,1,1,0, 0,0,0,0,0,1,1,
0,0,1,1,1,1,1 ],
[ 320, 1, 1, 1,0,1,1,1,1,1, 0,1,0,0,0,0,0, 0,0,1,1,0,0,0,
0,0,0,1,1,0,0, 0,0,0,0,1,1,0, 0,0,0,0,0,1,1 ],
[ 605, 0, 2, 1,0, 0,2 ],
[ 640, 1, 1, 1,0,0,0,0,0,0, 0,1,0,0,0,0,0, 0,0,1,0,0,0,0,
0,0,0,1,0,0,0, 0,0,0,0,1,0,0, 0,0,0,0,0,1,0,
0,0,0,0,0,0,1 ],# guardian
[1210, 0, 2, 1,0, 0,1 ]]],# guardian
[ # GL(6,*)
[], # GL(6,1)
[ # GL(6,2)
[ 9, 2, 3, 0,1,1,1,0,0,1,0 ],
[ 14, 3, 6, 0,0,6,0,2, 1,2,5,1,4 ],
[ 18, 2, 3, 0,1,1,1,0,0,1,0, 1,1,0,1,1,1,0,2 ],
[ 21, 0, 8, 0,54, 0,42 ],
[ 27, 2, 3, 0,2,0,0,0,0,0,1, 0,2,0,0,0,1,0,0 ],
[ 27, 2, 3, 0,2,0,2,1,2,1,1, 0,2,0,1,1,1,1,2, 0,2,0,2,1,0,1,2 ],
[ 42, 3, 6, 0,0,6,0,2, 0,1,1,1,1, 1,2,5,1,4 ],
[ 42, 0, 8, 0,54, 0,42, 3,14 ],
[ 54, 2, 3, 0,2,0,2,1,2,1,1, 0,2,0,1,1,1,1,2, 0,2,0,2,1,0,1,2,
1,2,0,0,1,2,1,2 ],
[ 54, 2, 3, 0,2,0,2,1,2,1,1, 0,2,0,1,1,1,1,2, 0,2,0,2,1,0,1,2,
1,1,0,2,1,1,0,1 ],
[ 54, 2, 3, 0,1,1,1,0,0,1,0, 0,1,1,0,0,0,1,2, 1,1,0,1,1,1,0,2 ],
[ 63, 0, 8, 0,56, 0,54 ],
[ 63, 0, 8, 0,54, 4,30, 4,27 ],
[ 63, 0, 8, 4,38, 4,11 ],
[ 81, 2, 3, 0,1,1,1,0,0,1,0, 0,1,1,0,0,0,1,2, 0,2,0,1,1,1,1,1 ],
[ 98, 3, 6, 0,0,6,0,2, 0,0,5,0,1, 1,2,5,1,4 ],
[ 108, 2, 3, 0,2,0,2,1,2,1,1, 0,2,0,1,1,1,1,2, 0,2,0,2,1,0,1,2,
1,1,0,1,1,1,0,2, 0,0,1,1,1,1,1,2 ],
[ 108, 0,11, 0,0,1,3,1,0,2, 0,0,1,3,2,1,0 ],
[ 126, 0, 8, 0,54, 4,30, 4,27, 3,14 ],
[ 126, 0, 8, 0,56, 0,54, 3,14 ],
[ 162, 2, 3, 0,1,1,1,0,0,1,0, 0,1,1,0,0,0,1,2, 0,2,0,1,1,1,1,1,
1,2,0,0,1,2,1,2 ],
[ 162, 2, 3, 0,1,1,1,0,0,1,0, 0,1,1,0,0,0,1,2, 0,2,0,1,1,1,1,1,
0,0,1,1,1,1,1,1 ],
[ 162, 2, 3, 0,2,0,0,0,0,0,1, 0,1,0,1,0,0,0,0, 1,1,1,2,1,1,1,2 ],
[ 189, 0, 8, 4,38, 4,11, 4,19 ],
[ 216, 0,11, 0,0,1,3,1,0,2, 0,0,1,3,2,1,0, 0,0,1,2,0,2,1 ],
[ 216, 0,11, 1,0,0,3,1,2,2, 1,0,1,0,1,0,0 ],
[ 216, 0,11, 0,0,1,2,0,2,1, 0,0,1,0,1,1,2, 1,2,0,2,1,2,0 ],
[ 294, 3, 6, 0,0,6,0,2, 0,0,5,0,1, 0,1,1,1,1,
1,2,5,1,4 ],
[ 294, 3, 6, 0,0,6,0,2, 0,0,5,0,1, 0,2,3,1,1,
1,2,5,1,4 ],
[ 324, 2, 3, 0,1,1,1,0,0,1,0, 0,1,1,0,0,0,1,2, 0,2,0,1,1,1,1,1,
1,1,0,2,1,1,0,1, 0,0,1,1,1,1,1,1 ],
[ 324, 2, 3, 0,1,1,1,0,0,1,0, 0,1,0,1,1,0,1,0 ],
[ 378, 0, 8, 1,0, 0,1 ],# guardian
[ 432, 0,11, 1,2,0,1,1,0,0, 1,2,0,1,1,2,0, 0,0,1,3,1,0,2 ],
[ 648, 2, 3, 0,1,1,1,0,0,1,0, 0,1,0,1,1,0,1,0, 0,0,1,1,1,1,1,1 ],
[ 648, 2, 3, 0,1,1,1,0,0,1,0, 0,1,0,1,1,0,1,0, 1,1,1,1,0,0,0,0 ],
[ 648, 2, 3, 0,1,1,1,0,0,1,0, 0,1,0,1,1,0,1,0, 1,0,0,0,1,1,1,1 ],
[ 648, 0,11, 0,2,1,2,1,1,0, 0,1,1,1,2,0,1 ],
[ 882, 3, 6, 1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0, 0,0,0,1,0, 0,0,0,0,1 ],# guardian
[1296, 2, 3, 1,0,0,0,0,0,0,0, 0,1,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,
0,0,0,1,0,0,0,0, 0,0,0,0,1,0,0,0, 0,0,0,0,0,1,0,0,
0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,1 ],# guardian
[1296, 0,11, 1,0,0,0,0,0,0, 0,1,0,0,0,0,0, 0,0,1,0,0,0,0,
0,0,0,1,0,0,0, 0,0,0,0,1,0,0, 0,0,0,0,0,1,0,
0,0,0,0,0,0,1 ]]],# guardian
[ # GL(7,*)
[], # GL(7,1)
[ # GL(7,2)
[ 127, 0, 2, 0,1 ],
[ 889, 0, 2, 1,0, 0,1 ]]]]);# guardian
#############################################################################
##
#E
##