File: perf0.grp

package info (click to toggle)
gap 4r8p6-2
  • links: PTS
  • area: main
  • in suites: stretch
  • size: 33,476 kB
  • ctags: 7,663
  • sloc: ansic: 108,841; xml: 47,807; sh: 3,628; perl: 2,342; makefile: 796; asm: 62; awk: 6
file content (246 lines) | stat: -rw-r--r-- 11,930 bytes parent folder | download | duplicates (3)
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
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
#############################################################################
##
#W  perf0.grp              GAP Groups Library                 Volkmar Felsch
##                                                           Alexander Hulpke
##
##
#Y  Copyright (C)  1997,  Lehrstuhl D für Mathematik,  RWTH Aachen,  Germany
##
##  All data is based on Holt/Plesken: Perfect Groups, OUP 1989
##

##  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.notAvailable
##        is a list of all sizes less than 10^6  for which the perfect groups
##        are known, but not yet in the library.  It is needed by subroutines
##        DisplayInformationPerfectGroups and NumberPerfectLibraryGroups.
##
##     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 tripel [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 := rec(length:=331);

 PERFRec.covered := [38,59,70,71,80,113,151,158,201,249,295,331];

 IsSSortedList( PERFRec.covered );

 PERFRec.notKnown := [
 61440,122880,172032,245760,344064,491520,688128,983040];

 IsSSortedList( PERFRec.notKnown );

 PERFRec.notAvailable := [86016,368640,737280];

 IsSSortedList( PERFRec.notAvailable );

 PERFRec.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)"];

 IsSSortedList( PERFRec.nameSimpleGroup );

 PERFRec.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];

 PERFRec.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]];

 IsSSortedList( PERFRec.sizeNumberSimpleGroup );

 PERFRec.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];

 IsSSortedList( PERFRec.sizes );

 PERFRec.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,
 1,1,4,1,1,37,2,1,1,4,1,1,1,4,25,3,1,1,1,3,1,1,1,2,2,2,1,2,1,3,0,1,
 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,
 2,0,1,6,4,3,2,2,1,1,1,1,1,1,18,1,3,1,12,1,0,8,1,1,1,3,1,19,1,1,2,1,
 1,1,1,1,3,1,2,1,26,3,3,1,17,5,1,1,2,0,1,1,4,3,2,7,1,1,2,1,3,2,3,1,
 3,18,1,27,1,1,0,3,1,1,1,6,1,1,3,3,46,1,1,11,1,1,2,2,1,1,4,3,1,1,1,1,
 3,1,2,1,1,3,8,1,1,25,4,3,18,1,4,17,6,1,0,1,1,1,1,1,9,1,1,1,1,19,1,1,
 7,1,1,2,3,1,4,1,12,1,2,41,1,1,1,3,2,1,0,23,3,2,1,1,1,1,2,3,2,1,1,3,
 54,1,13,2,5,3,16,2,2,1,3,2,3,3,2,1,2,1,1,3,1,7,6,4,1,23,8,2,21,3,8,1,
 2,1,12,1,20,1,1,4,0,1];

PERFGRP := [];
PERFSELECT:=BlistList([1..PERFRec.length],[]); # what have we loaded

#############################################################################
##
#E  perf0.grp . . . . . . . . . . . . . . . . . . . . . . . . . ends here
##