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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Volkmar Felsch, Alexander Hulpke.
##
## 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
##
## Data is based on Holt/Plesken: Perfect Groups, OUP 1989 and
## Hulpke: The perfect groups of order up to 10^6
##
## The 1097 nontrivial
## perfect groups of the library have been ordered by increasing
## size, and each library group G is charcterized by the pair [size, n],
## where size is the group size of G and n is its number within the list of
## library groups of that size. We denote this pair as the 'size number' of
## G. Another number associated with G is the Holt-Plesken number which
## consists of a triple [k,i,j] which means that, in the Holt-Plesken book,
## G occurs under the number (i,j) in class k. As G may occur in more than
## one of these classes it may have more than one such Holt-Plesken numbers.
##
## 489 of the library groups are given by explixit presentations on file.
## The essential information about each ot these group is available in form
## of a function which allows to construct the group as a finitely presented
## group. The list of all these functions has been broken into 12 parts
## which are provided in 12 separate secondary files. Whenever a group is
## needed and the associated function is not available, the corresponding
## part of the list will be loaded into the list PERFFun.
##
## The record PERFRec provides certain reference lists and some additional
## information. It contains the following components:
##
## The following components of PERFRec are general lists of different
## lengths.
##
## PERFRec.covered
## is a list which in its n-th entry provides the number of perfect
## group sizes covered by the first n function files. It is needed by
## subroutine PERFLoad.
##
## PERFRec.notKnown
## is a list of all sizes less than 10^6 for which the perfect groups
## have not yet been determined. It is needed by subroutine
## NumberPerfectGroups.
##
## PERFRec.sizeNumberSimpleGroup
## is an ordered list of the 'size numbers' of all nonabelian simple
## groups which occur as composition factor of any library group.
##
## PERFRec.nameSimpleGroup
## is a list which contains one or two names (as text strings) for
## each simple group in the preceding list.
##
## PERFRec.numberSimpleGroup
## is a list which, for each simple group name in the preceding list,
## contains the number of the respective group with respect to the
## list PERFRec.sizeNumberSimpleGroup.
##
## PERFRec.sizes
## is an ordered list of all occurring group sizes.
##
## The remaining lists are all parallel to the preceding
## list of all occurring group sizes. We assume in the following that
## PERFRec.sizes[i] = s(i).
##
## PERFRec.number[i]
## is the number of perfect groups of size s(i).
##
## PERFGRP is the actual storage of groups. It is a list whose i-th entry
## is a list of all perfect groups of size s(i). (The list might be longer
## than number[i], then this group is just used as intermediate storage.)
## Each group is represented either by 'fail' if no information is
## available or by a list l giving information about this group.
## We list the entries of 'l':
##
## l[1] (source) information on how to construct the group. It is of one of
## the following forms:
## [1,namesgens,wordfunc,subgrpindices] where namesgens is a list of
## characters giving names for the generators,
## wordfunc is a function that gets |namesgens| free generators as
## arguments and returns a list [relators,subgrpgens], where relators
## are defining relators and subgrpgens is a list whose entries are
## lists of subgroup generators. (It is a function to allow storage
## of *terms* in unexpanded form.)
## subgrpindices is a list that gives the indices of the subgroups
## defined in wordfunc.
## A further component 'auxiliaryGens' might be added.
##
## [2,<size1>,<n1>,<size2>,<n2>], if G is given as a direct product,
##
## [3,<size1>,<n1>,<size2>,<n2>,<string1>,<string2>...], if G is given
## as a central product,
##
## [4,<size1>,<n1>,<size2>,<n2>,<size0>] or
##
## [4,<size1>,<n1>,<size2>,<n2>,<size0>,<n1'>,<n2'>], if G is given as
## a subdirect product.
##
## The entries 2.. might be missing if the group is not actually a library
## group but only used as part of some construction.
##
## l[2] (description)
## is a descriptive name as given in the Holt-Plesken book.
##
## l[3] (hpNumber)
## is either a class
## number k or a list [k,i,j] or [k,i,j,k2,...,kn]. The triple [k,i,j]
## means that the respective group is listed in the k-th class of the
## Holt-Plesken book under the number (i,j). If the group also occurs
## in some additional classes, then their numbers are given as
## k2, ..., kn.
##
## l[4] (centre)
## gives the size of the groups centre, a negative index indicating the
## group is simple or quasisimple
##
## l[5] (simpleFactors)
## is the 'size number'
## (if there is only one) or a list of the 'size numbers' (if there is
## more than one) of its nonabelian composition factors.
##
## l[6] (orbitSize)
## is a list of
## the orbit sizes of the faithful permutation representation of G
## which is offered by the library or, if that representation is
## transitive, i. e., if there is only one orbit, just the size of
## that orbit.
##
PERFRec := MakeImmutable(rec(
length:=453,
covered:=[38,59,70,71,80,113,151,158,201,249,295,331,331,331,331,331,
331,331,331,331,331,331,331,354,370,380,381,395,420,434,435,450,451,453],
notKnown := [],
nameSimpleGroup := [
"A(5)","A(6)","A(7)","A(8)","A(9)","A5","A6","A7","A8","A9","J(1)",
"J(2)","J1","J2","L(2,101)","L(2,103)","L(2,107)","L(2,109)",
"L(2,11)","L(2,113)","L(2,121)","L(2,125)","L(2,13)","L(2,16)",
"L(2,17)","L(2,19)","L(2,23)","L(2,25)","L(2,27)","L(2,29)",
"L(2,31)","L(2,32)","L(2,37)","L(2,4)","L(2,41)","L(2,43)",
"L(2,47)","L(2,49)","L(2,5)","L(2,53)","L(2,59)","L(2,61)",
"L(2,64)","L(2,67)","L(2,7)","L(2,71)","L(2,73)","L(2,79)",
"L(2,8)","L(2,81)","L(2,83)","L(2,89)","L(2,9)","L(2,97)","L(3,2)",
"L(3,3)","L(3,4)","L(3,5)","L2(101)","L2(103)","L2(107)","L2(109)",
"L2(11)","L2(113)","L2(121)","L2(125)","L2(13)","L2(16)","L2(17)",
"L2(19)","L2(23)","L2(25)","L2(27)","L2(29)","L2(31)","L2(32)",
"L2(37)","L2(4)","L2(41)","L2(43)","L2(47)","L2(49)","L2(5)",
"L2(53)","L2(59)","L2(61)","L2(64)","L2(67)","L2(7)","L2(71)",
"L2(73)","L2(79)","L2(8)","L2(81)","L2(83)","L2(89)","L2(9)",
"L2(97)","L3(2)","L3(3)","L3(4)","L3(5)","M(11)","M(12)","M(22)",
"M11","M12","M22","S(4,4)","Sp4(4)","Sz(8)","U(3,3)","U(3,4)",
"U(3,5)","U(4,2)","U3(3)","U3(4)","U3(5)","U4(2)",
"PSL(2,127)", "PSL(2,131)", "PSL(2,137)", "PSL(2,139)", "PSp(6,2)",
"PSL(2,149)", "PSL(2,151)", "A10", "PSL(3,7)", "PSL(2,157)"],
numberSimpleGroup := [
1,3,8,19,38,1,3,8,19,38,36,50,36,50,48,49,51,52,5,53,54,55,6,10,7,9,
13,14,16,17,18,24,21,1,25,26,27,28,1,30,32,33,41,35,2,37,39,40,4,42,
43,44,3,47,2,11,20,45,48,49,51,52,5,53,54,55,6,10,7,9,13,14,16,17,18,
24,21,1,25,26,27,28,1,30,32,33,41,35,2,37,39,40,4,42,43,44,3,47,2,11,
20,45,15,31,46,15,31,46,56,56,23,12,29,34,22,12,29,34,22,
57, 58, 59, 60, 61, 62, 63, 64, 65, 66],
sizeNumberSimpleGroup := [
[60,1],[168,1],[360,1],[504,1],[660,1],[1092,1],[2448,1],[2520,1],
[3420,1],[4080,1],[5616,1],[6048,1],[6072,1],[7800,1],[7920,1],
[9828,1],[12180,1],[14880,1],[20160,4],[20160,5],[25308,1],[25920,1],
[29120,1],[32736,1],[34440,1],[39732,1],[51888,1],[58800,1],[62400,1],
[74412,1],[95040,1],[102660,1],[113460,1],[126000,1],[150348,1],
[175560,1],[178920,1],[181440,1],[194472,1],[246480,1],[262080,1],
[265680,1],[285852,1],[352440,1],[372000,1],[443520,1],[456288,1],
[515100,1],[546312,1],[604800,1],[612468,1],[647460,1],[721392,1],
[885720,1],[976500,1],[979200,1],
[ 1024128, 1 ], [ 1123980, 1 ], [ 1285608, 1 ], [ 1342740, 1 ],
[ 1451520, 1 ], [ 1653900, 1 ], [ 1721400, 1 ], [ 1814400, 1 ],
[ 1876896, 1 ], [ 1934868, 1 ]],
sizes := [
1,60,120,168,336,360,504,660,720,960,1080,1092,1320,1344,1920,2160,
2184,2448,2520,2688,3000,3420,3600,3840,4080,4860,4896,5040,5376,
5616,5760,6048,6072,6840,7200,7500,7560,7680,7800,7920,9720,9828,
10080,10752,11520,12144,12180,14400,14520,14580,14880,15000,15120,
15360,15600,16464,17280,19656,20160,21504,21600,23040,24360,25308,
25920,28224,29120,29160,29760,30240,30720,32256,32736,34440,34560,
37500,39600,39732,40320,43008,43200,43320,43740,46080,48000,50616,
51840,51888,56448,57600,57624,58240,58320,58800,60480,61440,62400,
64512,64800,65520,68880,69120,74412,75000,77760,79200,79464,79860,
80640,84672,86016,86400,87480,92160,95040,96000,100920,102660,103776,
110880,112896,113460,115200,115248,115320,116480,117600,120000,120960,
122472,122880,126000,129024,129600,131040,131712,138240,144060,146880,
148824,150348,151200,151632,155520,158400,159720,160380,161280,169344,
172032,174960,175560,178920,180000,181440,183456,184320,187500,190080,
192000,194472,201720,205200,205320,216000,221760,223608,225792,226920,
230400,232320,233280,237600,240000,241920,243000,244800,244944,245760,
246480,254016,258048,259200,262080,262440,263424,265680,276480,285852,
288120,291600,293760,300696,302400,311040,320760,322560,332640,336960,
344064,345600,352440,357840,360000,362880,363000,364320,366912,367416,
368640,369096,372000,375000,378000,384000,387072,388800,388944,393120,
393660,410400,411264,411540,417720,423360,432000,435600,443520,446520,
447216,450000,451584,453600,456288,460800,460992,464640,466560,468000,
475200,480000,483840,489600,491520,492960,504000,515100,516096,518400,
524880,531360,544320,546312,550368,552960,571704,574560,583200,587520,
589680,600000,604800,604920,607500,612468,622080,626688,633600,645120,
647460,665280,673920,675840,677376,685440,688128,691200,693120,699840,
704880,712800,720720,721392,725760,728640,729000,730800,733824,734832,
737280,748920,768000,774144,777600,786240,787320,806736,816480,820800,
822528,823080,846720,864000,871200,874800,878460,881280,885720,887040,
892800,900000,903168,907200,912576,921600,921984,929280,933120,936000,
937500,943488,950400,950520,960000,962280,967680,976500,979200,979776,
983040,987840,
1008000, 1008420, 1016064, 1020096, 1024128, 1030200, 1036800, 1044480,
1048320, 1053696, 1080000, 1083000, 1088640, 1092624, 1100736, 1102248,
1105920, 1123980, 1125000, 1149120, 1166400, 1176120, 1179360, 1180980,
1192464, 1200000, 1209600, 1215000, 1224120, 1224936, 1231200, 1233792,
1244160, 1253376, 1260000, 1267200, 1270080, 1277760, 1285608, 1290240,
1294920, 1296000, 1310400, 1330560, 1342740, 1350000, 1351680, 1354752,
1370880, 1376256, 1382400, 1386240, 1399680, 1414944, 1425600, 1425720,
1441440, 1442784, 1451520, 1457280, 1461600, 1463340, 1467648, 1468800,
1474560, 1512000, 1518480, 1536000, 1548288, 1555200, 1572480,
1574640, 1592136, 1614720, 1615680, 1632960, 1645056, 1651104, 1653900,
1658880, 1663200, 1693440, 1713660, 1721400, 1723680, 1728000, 1728720,
1742400, 1747200, 1749600, 1756920, 1762560, 1771440, 1774080, 1785600,
1787460, 1788864, 1800000, 1806336, 1814400, 1815000, 1822500, 1837080,
1843200, 1843968, 1845120, 1858560, 1866240, 1872000, 1875000, 1876896,
1886976, 1920000, 1924560, 1934868, 1935360, 1953000, 1959552, 1964160,
1966080, 1975680, 1980000 ],
newlyAdded:=[61440,86016,122880,172032,245760,344064,368640,491520,
688128,737280,983040],
number:=[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 7, 1, 1, 1, 1, 3, 1, 1,
1, 7, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 5, 1, 1, 3, 1, 1, 9, 4, 1, 1,
1, 1, 1, 1, 3, 1, 7, 1, 1, 1, 1, 5, 22, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 37,
2, 1, 1, 4, 1, 1, 1, 4, 25, 3, 1, 1, 1, 3, 1, 1, 1, 2, 2, 2, 1, 2, 1, 3,
98, 1, 4, 1, 1, 1, 4, 1, 4, 4, 3, 1, 1, 6, 1, 52, 1, 8, 2, 1, 3, 1, 1, 1,
1, 1, 1, 15, 3, 1, 1, 1, 4, 5, 2, 258, 1, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1,
18, 1, 3, 1, 12, 1, 154, 8, 1, 1, 1, 3, 1, 19, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1,
2, 1, 26, 3, 3, 1, 17, 5, 3, 1, 2, 582, 1, 1, 4, 3, 2, 7, 1, 1, 2, 1, 3, 2,
3, 1, 3, 18, 1, 27, 1, 1, 291, 3, 1, 1, 1, 6, 1, 1, 3, 3, 46, 1, 1, 11, 1, 1,
2, 2, 1, 1, 4, 3, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 8, 1, 1, 25, 4, 3, 18, 1,
4, 17, 6, 1, 1004, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 19, 1, 1, 7, 1, 1, 2, 3, 1,
4, 1, 12, 1, 2, 41, 1, 1, 1, 3, 2, 1, 508, 23, 3, 2, 1, 1, 1, 1, 2, 3, 3, 1,
1, 3, 54, 1, 13, 2, 5, 3, 16, 2, 2, 1, 3, 2, 3, 3, 3, 1, 3, 1, 1, 3, 1, 7,
6, 4, 1, 23, 8, 2, 21, 3, 8, 1, 2, 1, 12, 1, 20, 1, 1, 4, 1880, 1,
1, 1, 1, 1, 1, 1, 3, 4, 2, 9, 1, 1, 1, 1, 1, 3, 49, 1, 1, 3, 4, 3, 4, 14,
1, 17, 8, 9, 1, 1, 1, 1, 15, 4, 2, 15, 2, 2, 1, 88, 1, 1, 1, 2, 1, 1, 8, 3,
1, 1639, 38, 3, 21, 1, 3, 1, 3, 1, 3, 1, 3, 1, 2, 1, 26, 1, 1, 33, 1, 3,
1, 4, 1, 3, 1, 7, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 8, 8, 3, 1, 9, 3,
1, 4, 3, 13, 6, 3, 2, 1, 113, 3, 3, 1, 13, 1, 22, 1, 1, 15, 2, 1, 26, 1, 6,
1, 7344, 1, 1],
));
IsSSortedList( PERFRec.covered );
IsSSortedList( PERFRec.notKnown );
IsSSortedList( PERFRec.nameSimpleGroup );
IsSSortedList( PERFRec.sizeNumberSimpleGroup );
IsSSortedList( PERFRec.sizes );
[ Konzepte0.15Was zu einem Entwurf gehört
Wie die Entwicklung von Software durchgeführt wird
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