1#setup: extraspecial group r^(1+2n) in GL(r^n,q), r prime, r|q-1
2#
3#the functions in this file:
4#
5#    extraspecial(r,n,q)
6#    output: the extraspecial group r^(1+2n)
7#    (in the case r=2, the output is + type)
8#
9#    minusextraspecial(r,n,q)
10#    output: the group 2^(1+2n), of - type
11#
12#    c6(r,n,q)
13#    output: the normalizer of r^(1+2n) in GL(r^n,q)
14#    (in the case r=2, the extraspecial is + type
15#
16#    minusc6(r,n,q)
17#    output: the normalizer of 2^(1+2n) of - type in GL(r^n,q)
18#
19#the groups in this file: maximal subgroups of Sp(4,p) for p=5,11,13
20#as 4-dimensional groups, in lists maximals5, maximals11, maximals13
21
22
23#constructs r^(1+2n) in GL(r^n,q)
24#when r=2, the group is + type (central product of dihedrals)
25extraspecial:=function(r,n,q)
26local a,b,rho,i,perm,id,id2,gens;
27
28a:=NullMat(r,r,GF(q));
29rho:=Z(q)^((q-1)/r);
30for i in [1..r] do
31   a[i][i]:=rho^(i-1);
32od;
33perm:=Concatenation([2..r],[1]);
34perm:=PermList(perm);
35b:=PermutationMat(perm,r,GF(q));
36id:=a^0;
37gens:=[a,b];
38for i in [1..n-1] do
39   id2:=gens[1]^0;
40   gens:=List(gens,x->KroneckerProduct(x,id));
41   Add(gens,KroneckerProduct(id2,a));
42   Add(gens,KroneckerProduct(id2,b));
43od;
44return Group(gens);
45end;
46
47#constructs the group 2^(1+2n) of minus type
48minusextraspecial:=function(r,n,q)
49local a,b,c,d,mark,x,y,diff,elmts,i,j,id,id2,gens;
50
51c:=[ [0*Z(q),-Z(q)^0], [Z(q)^0, 0*Z(q)] ];
52
53#this is really inefficient
54diff:=Difference(Elements(GF(q)),[0*Z(q)]);
55elmts:=Elements(GF(q));
56mark:=false;
57j:=0;
58repeat
59  j:=j+1;
60  x:=diff[j];
61  i:=0;
62  repeat
63    i:=i+1;
64    y:=elmts[i];
65    if x^2+y^2=-Z(q)^0
66       then mark:=true;
67    fi;
68  until mark or i=q;
69until j=q-1 or mark;
70d:=[ [x,y], [y,-x] ];
71
72if n=1 then
73  return Group(c,d);
74else
75  a:=[ [Z(q)^0, 0*Z(q)], [0*Z(q),-Z(q)^0] ];
76  b:=[ [0*Z(q), Z(q)^0], [Z(q)^0, 0*Z(q)] ];
77  id:=a^0;
78
79  gens:=[a,b];
80  for i in [1..n-2] do
81    id2:=gens[1]^0;
82    gens:=List(gens,x->KroneckerProduct(x,id));
83    Add(gens,KroneckerProduct(id2,a));
84    Add(gens,KroneckerProduct(id2,b));
85  od;
86  id2:=gens[1]^0;
87  gens:=List(gens,x->KroneckerProduct(x,id));
88  Add(gens,KroneckerProduct(id2,c));
89  Add(gens,KroneckerProduct(id2,d));
90  return Group(gens);
91fi;
92
93end;
94
95#constructs the normalizer of r^(1+2n) in GL(r^n,q)
96#when r=2, the top group is O^+(2n,2)
97c6:=function(r,n,q)
98local g,gens,i,j,rho,a,b,c,id,id2,id3,gens2;
99
100g:=extraspecial(r,n,q);
101gens:=[];
102for i in [1..2*n] do
103  gens[i]:=GeneratorsOfGroup(g)[i];
104od;
105
106a:=NullMat(r,r,GF(q));
107rho:=Z(q)^((q-1)/r);
108for i in [1..r] do
109   a[i][i]:=rho^(i*(i-1)/2);
110od;
111
112b:=List([1..r],x->[]);
113for i in [1..r] do
114  for j in [1..r] do
115    b[i][j]:=rho^((i-1)*(j-1));
116  od;
117od;
118
119c:=NullMat(r^2,r^2,GF(q));
120for i in [0..r^2-1] do
121  c[i+1][((i+( (i-1) mod r )*r) mod r^2)+1]:=Z(q)^0;
122od;
123
124id:=IdentityMat(r,GF(q));
125gens2:=[a,b];
126for i in [1..n-1] do
127   gens2:=List(gens2,x->KroneckerProduct(x,id));
128   id2:=IdentityMat(r^i,GF(q));
129   Add(gens2,KroneckerProduct(id2,a));
130   Add(gens2,KroneckerProduct(id2,b));
131   id3:=IdentityMat(r^(i-1),GF(q));
132   Add(gens2,KroneckerProduct(id3,c));
133od;
134
135return Group(Concatenation(gens,gens2));
136end;
137
138#constructs the normalizer of 2^(1+2n) of - type in GL(2^n,q)
139minusc6:=function(r,n,q)
140local diff,elmts,mark,x,y,g,gens,c,d,e,u,v,w,i,j,id,id2,id3;
141
142c:=[ [0*Z(q),-Z(q)^0], [Z(q)^0, 0*Z(q)] ];
143
144#this is really inefficient
145diff:=Difference(Elements(GF(q)),[0*Z(q)]);
146elmts:=Elements(GF(q));
147mark:=false;
148j:=0;
149repeat
150  j:=j+1;
151  x:=diff[j];
152  i:=0;
153  repeat
154    i:=i+1;
155    y:=elmts[i];
156    if x^2+y^2=-Z(q)^0
157       then mark:=true;
158    fi;
159  until mark or i=q;
160until j=q-1 or mark;
161d:=[ [x,y], [y,-x] ];
162
163e:=Z(q)^0;
164u:=[ [e,e], [-e,e] ];
165v:=[ [ e+x+y, e-x+y ], [ -e-x+y, e-x-y ] ];
166
167if n=1 then return Group(c,d,u,v); fi;
168
169w:=[ [e,0*e,e,0*e], [0*e,e,0*e,e], [0*e,e,0*e,-e], [-e,0*e,e,0*e] ];
170g:=c6(r,n-1,q);
171id:=IdentityMat(r,GF(q));
172id2:=IdentityMat(r^(n-1),GF(q));
173id3:=IdentityMat(r^(n-2),GF(q));
174gens:=List(GeneratorsOfGroup(g),z->KroneckerProduct(z,id));
175Add(gens,KroneckerProduct(id2,c));
176Add(gens,KroneckerProduct(id2,d));
177Add(gens,KroneckerProduct(id2,u));
178Add(gens,KroneckerProduct(id2,v));
179Add(gens,KroneckerProduct(id3,w));
180
181return(Group(gens));
182
183end;
184
185
186
187
188	f := GF(5);
189
190maximals5 := [
191    Group([ [
192        [3,4,3,1],
193        [0,2,3,3],
194        [2,0,1,1],
195        [3,2,0,0] ]*One(f), [
196
197        [0,3,3,2],
198        [1,3,2,3],
199        [1,0,4,2],
200        [4,1,4,2] ]*One(f), [
201
202        [0,2,2,4],
203        [3,0,1,3],
204        [3,4,0,3],
205        [1,3,3,2] ]*One(f), [
206
207        [0,0,4,4],
208        [1,4,1,3],
209        [0,0,4,0],
210        [1,0,3,1] ]*One(f), [
211
212        [1,1,3,2],
213        [3,3,2,3],
214        [4,2,0,4],
215        [3,4,2,2] ]*One(f), [
216
217        [4,0,0,0],
218        [0,4,0,0],
219        [0,0,4,0],
220        [0,0,0,4] ]*One(f), [
221
222        [0,0,1,1],
223        [4,1,3,0],
224        [0,0,1,0],
225        [4,0,0,0] ]*One(f) ] ),
226
227    Group([ [
228        [3,4,3,1],
229        [0,2,3,3],
230        [2,0,1,1],
231        [3,2,0,0] ]*One(f), [
232
233        [0,2,2,4],
234        [3,0,1,3],
235        [3,4,0,3],
236        [1,3,3,2] ]*One(f), [
237
238        [1,1,3,2],
239        [3,3,2,3],
240        [4,2,0,4],
241        [3,4,2,2] ]*One(f), [
242
243        [4,0,0,0],
244        [0,4,0,0],
245        [0,0,4,0],
246        [0,0,0,4] ]*One(f), [
247
248        [3,0,4,2],
249        [3,4,3,4],
250        [0,0,4,0],
251        [2,0,2,0] ]*One(f), [
252
253        [1,4,4,1],
254        [2,1,3,4],
255        [2,1,0,1],
256        [3,2,3,0] ]*One(f), [
257
258        [0,0,1,1],
259        [4,1,3,0],
260        [0,0,1,0],
261        [4,0,0,0] ]*One(f) ]),
262
263    Group([ [
264        [0,1,1,1],
265        [3,1,4,2],
266        [4,4,3,4],
267        [3,1,0,0] ]*One(f), [
268
269        [0,1,2,0],
270        [3,0,0,3],
271        [4,0,0,1],
272        [0,1,3,0] ]*One(f), [
273
274        [1,1,3,1],
275        [3,1,4,2],
276        [3,4,1,4],
277        [0,1,4,0] ]*One(f), [
278
279        [4,0,0,0],
280        [0,4,0,0],
281        [0,0,4,0],
282        [0,0,0,4] ]*One(f) ] ),
283
284    Group([ [
285        [0,2,2,4],
286        [3,0,1,3],
287        [3,4,0,3],
288        [1,3,3,2] ]*One(f), [
289
290        [4,2,2,3],
291        [4,1,3,2],
292        [0,0,4,3],
293        [0,0,1,1] ]*One(f), [
294
295        [4,0,0,0],
296        [0,4,0,0],
297        [0,0,4,0],
298        [0,0,0,4] ]*One(f), [
299
300        [1,4,4,1],
301        [2,1,3,4],
302        [2,1,0,1],
303        [3,2,3,0] ]*One(f) ] ),
304
305    Group([ [
306        [1,1,1,4],
307        [3,0,1,1],
308        [3,3,1,4],
309        [2,3,2,0] ]*One(f), [
310
311        [3,4,1,0],
312        [0,2,0,4],
313        [2,0,2,4],
314        [0,3,0,3] ]*One(f), [
315
316        [4,0,0,0],
317        [0,4,0,0],
318        [0,0,4,0],
319        [0,0,0,4] ]*One(f), [
320
321        [0,3,2,1],
322        [3,3,3,2],
323        [2,3,1,2],
324        [1,2,2,4] ]*One(f) ] ),
325
326    Group([ [
327        [1,1,1,4],
328        [1,1,4,1],
329        [1,4,4,4],
330        [4,1,4,4] ]*One(f), [
331
332        [4,3,2,1],
333        [3,3,2,2],
334        [2,0,3,2],
335        [4,2,2,2] ]*One(f), [
336
337        [4,0,0,0],
338        [0,4,0,0],
339        [0,0,4,0],
340        [0,0,0,4] ]*One(f), [
341
342        [0,1,2,3],
343        [3,1,1,3],
344        [4,2,1,3],
345        [2,3,3,2] ]*One(f)  ]),
346
347    Group([ [
348        [2,1,4,4],
349        [0,4,3,4],
350        [3,4,0,4],
351        [4,3,0,2] ]*One(f), [
352
353        [3,2,3,4],
354        [4,0,3,0],
355        [4,4,1,2],
356        [4,4,0,3] ]*One(f), [
357
358        [2,3,3,2],
359        [2,1,0,1],
360        [3,3,3,3],
361        [3,3,4,2] ]*One(f), [
362
363        [2,3,4,3],
364        [2,3,0,4],
365        [3,1,3,2],
366        [3,3,3,4] ]*One(f), [
367
368        [0,4,3,0],
369        [4,0,0,2],
370        [0,0,0,4],
371        [0,0,4,0] ]*One(f), [
372
373        [4,0,0,0],
374        [0,4,0,0],
375        [0,0,4,0],
376        [0,0,0,4] ]*One(f), [
377
378        [4,2,4,2],
379        [3,3,1,4],
380        [0,4,2,3],
381        [1,0,2,1] ]*One(f), [
382
383        [4,1,4,2],
384        [0,3,1,4],
385        [3,3,2,4],
386        [3,3,0,1] ]*One(f), [
387
388        [0,0,4,3],
389        [4,2,2,4],
390        [3,4,3,0],
391        [4,3,1,0] ]*One(f) ] ),
392
393    Group([ [
394        [2,3,1,1],
395        [1,4,1,1],
396        [4,4,0,4],
397        [4,2,4,0] ]*One(f), [
398
399        [3,2,3,3],
400        [0,0,2,2],
401        [3,4,3,0],
402        [4,1,1,3] ]*One(f), [
403
404        [4,0,0,0],
405        [0,4,0,0],
406        [0,0,4,0],
407        [0,0,0,4] ]*One(f) ] )
408];
409
410magmasp45:=Group(
411 [ [2, 0, 0, 0],
412    [0, 1, 0, 0],
413    [0, 0, 1, 0],
414    [0, 0, 0, 3]] *One(f),
415
416  [  [1, 0, 1, 0],
417    [1, 0, 0, 0],
418    [0, 1, 0, 1],
419    [0, 4, 0, 0] ]*One(f));
420
421  f := GF(7);
422maximals7 := [
423  Group([[
424    [4,3,1,0],
425    [2,6,0,5],
426    [1,0,6,6],
427    [2,3,1,2]
428]*One(f),
429[
430    [1,0,1,5],
431    [3,3,4,4],
432    [2,2,3,5],
433    [2,0,1,4]
434]*One(f),
435[
436    [6,0,0,0],
437    [0,6,0,0],
438    [0,0,6,0],
439    [0,0,0,6]
440]*One(f),
441[
442    [4,4,2,2],
443    [5,6,0,2],
444    [4,0,6,3],
445    [5,4,2,1]
446]*One(f),
447[
448    [2,3,5,6],
449    [2,0,3,5],
450    [3,2,2,4],
451    [1,3,5,0]
452]*One(f),
453[
454    [2,2,3,0],
455    [6,3,5,3],
456    [5,5,6,5],
457    [2,5,1,0]
458]*One(f),
459[
460    [5,3,1,1],
461    [0,0,2,3],
462    [0,3,2,5],
463    [4,1,5,1]
464]*One(f)]),
465  Group([[
466    [4,3,1,0],
467    [2,6,0,5],
468    [1,0,6,6],
469    [2,3,1,2]
470]*One(f),
471[
472    [1,0,1,5],
473    [3,3,4,4],
474    [2,2,3,5],
475    [2,0,1,4]
476]*One(f),
477[
478    [6,0,0,0],
479    [0,6,0,0],
480    [0,0,6,0],
481    [0,0,0,6]
482]*One(f),
483[
484    [6,0,0,0],
485    [3,5,2,0],
486    [5,3,0,0],
487    [6,5,4,6]
488]*One(f),
489[
490    [2,3,5,6],
491    [2,0,3,5],
492    [3,2,2,4],
493    [1,3,5,0]
494]*One(f),
495[
496    [2,2,3,0],
497    [6,3,5,3],
498    [5,5,6,5],
499    [2,5,1,0]
500]*One(f),
501[
502    [2,4,0,4],
503    [1,0,1,0],
504    [6,2,1,3],
505    [0,6,6,6]
506]*One(f)]) ,
507  Group([[
508    [0,0,2,0],
509    [2,0,0,5],
510    [4,0,0,0],
511    [0,3,2,0]
512]*One(f),
513[
514    [6,0,0,0],
515    [0,6,0,0],
516    [0,0,6,0],
517    [0,0,0,6]
518]*One(f),
519[
520    [0,4,6,1],
521    [3,6,1,2],
522    [6,0,5,6],
523    [5,3,6,4]
524]*One(f),
525[
526    [4,1,5,2],
527    [5,4,0,4],
528    [4,2,5,5],
529    [0,5,6,5]
530]*One(f)]),
531  Group([[
532    [4,0,3,2],
533    [2,5,2,3],
534    [4,2,2,0],
535    [3,4,5,3]
536]*One(f),
537[
538    [1,0,1,5],
539    [3,3,4,4],
540    [2,2,3,5],
541    [2,0,1,4]
542]*One(f),
543[
544    [6,0,0,0],
545    [0,6,0,0],
546    [0,0,6,0],
547    [0,0,0,6]
548]*One(f),
549[
550    [2,4,0,4],
551    [1,0,1,0],
552    [6,2,1,3],
553    [0,6,6,6]
554]*One(f)]),
555  Group([[
556    [2,2,3,5],
557    [3,2,4,3],
558    [0,4,1,5],
559    [6,0,4,1]
560]*One(f),
561[
562    [6,0,0,0],
563    [0,6,0,0],
564    [0,0,6,0],
565    [0,0,0,6]
566]*One(f),
567[
568    [0,2,2,3],
569    [4,3,2,2],
570    [6,1,3,5],
571    [0,6,3,6]
572]*One(f),
573[
574    [6,2,4,0],
575    [4,1,0,3],
576    [5,0,1,2],
577    [0,2,4,6]
578]*One(f)]),
579  Group([[
580    [4,1,0,5],
581    [2,6,3,0],
582    [5,1,1,6],
583    [6,5,5,3]
584]*One(f),
585[
586    [6,0,0,0],
587    [0,6,0,0],
588    [0,0,6,0],
589    [0,0,0,6]
590]*One(f),
591[
592    [1,2,4,6],
593    [6,1,6,0],
594    [6,2,5,6],
595    [6,6,2,1]
596]*One(f),
597[
598    [3,2,4,3],
599    [4,4,1,4],
600    [2,6,4,5],
601    [4,2,3,5]
602]*One(f)]),
603  Group([[
604    [5,3,3,0],
605    [5,2,0,4],
606    [1,0,2,3],
607    [0,6,5,5]
608]*One(f),
609[
610    [2,2,6,4],
611    [1,6,3,3],
612    [2,2,2,1],
613    [3,1,4,2]
614]*One(f),
615[
616    [5,2,4,1],
617    [2,4,6,4],
618    [5,1,6,5],
619    [0,5,5,5]
620]*One(f),
621[
622    [0,1,2,4],
623    [1,3,3,2],
624    [6,4,4,6],
625    [0,6,6,0]
626]*One(f),
627[
628    [3,2,5,5],
629    [0,3,0,5],
630    [5,1,4,5],
631    [0,5,0,4]
632]*One(f),
633[
634    [4,0,2,2],
635    [5,5,2,5],
636    [5,3,1,4],
637    [2,6,4,6]
638]*One(f),
639[
640    [6,0,0,0],
641    [0,6,0,0],
642    [0,0,6,0],
643    [0,0,0,6]
644]*One(f),
645[
646    [5,5,2,0],
647    [2,2,0,5],
648    [4,0,2,5],
649    [0,3,2,5]
650]*One(f),
651[
652    [3,5,2,6],
653    [6,5,4,4],
654    [4,4,2,5],
655    [4,3,4,6]
656]*One(f),
657[
658    [5,5,3,6],
659    [5,6,1,3],
660    [2,6,4,2],
661    [0,2,2,5]
662]*One(f),
663[
664    [0,6,2,2],
665    [5,2,0,2],
666    [1,3,6,1],
667    [1,1,2,1]
668]*One(f),
669[
670    [4,3,6,4],
671    [3,4,4,6],
672    [4,5,3,4],
673    [5,4,4,3]
674]*One(f),
675[
676    [1,3,5,0],
677    [3,6,0,2],
678    [1,0,6,3],
679    [0,6,3,1]
680]*One(f)]),
681  Group([[
682    [6,1,6,4],
683    [0,4,2,6],
684    [2,5,4,1],
685    [6,0,2,5]
686]*One(f),
687[
688    [6,0,0,0],
689    [0,6,0,0],
690    [0,0,6,0],
691    [0,0,0,6]
692]*One(f),
693[
694    [4,2,0,1],
695    [2,0,1,0],
696    [0,2,4,5],
697    [2,0,5,0]
698]*One(f),
699[
700    [1,6,4,6],
701    [3,0,0,4],
702    [4,3,0,1],
703    [1,4,4,6]
704]*One(f),
705[
706    [5,6,3,2],
707    [2,1,1,3],
708    [6,1,0,3],
709    [5,4,0,6]
710]*One(f),
711[
712    [6,2,1,0],
713    [2,1,0,6],
714    [3,0,1,2],
715    [0,4,2,6]
716]*One(f),
717[
718    [2,5,0,0],
719    [5,5,0,0],
720    [5,0,5,5],
721    [0,2,5,2]
722]*One(f),
723[
724    [2,0,0,3],
725    [4,6,6,6],
726    [6,4,3,2],
727    [3,3,5,5]
728]*One(f),
729[
730    [6,6,5,0],
731    [6,1,0,2],
732    [4,0,1,6],
733    [0,3,6,6]
734]*One(f),
735[
736    [0,4,1,5],
737    [5,3,0,1],
738    [1,1,5,3],
739    [4,1,2,1]
740]*One(f),
741[
742    [1,1,0,4],
743    [1,6,4,0],
744    [0,1,1,6],
745    [1,0,6,6]
746]*One(f),
747[
748    [1,1,6,6],
749    [0,4,4,6],
750    [6,6,3,6],
751    [3,6,0,6]
752]*One(f),
753[
754    [0,5,0,6],
755    [5,4,6,0],
756    [0,5,0,2],
757    [5,0,2,4]
758]*One(f)]),
759  Group([[
760    [2,1,4,6],
761    [5,0,0,1],
762    [5,2,2,4],
763    [3,0,1,2]
764]*One(f),
765[
766    [6,0,0,0],
767    [0,6,0,0],
768    [0,0,6,0],
769    [0,0,0,6]
770]*One(f),
771[
772    [3,1,5,0],
773    [4,6,0,3],
774    [2,0,6,5],
775    [5,1,5,5]
776]*One(f)]),
777  Group([[
778    [6,0,0,0],
779    [0,6,0,0],
780    [0,0,6,0],
781    [0,0,0,6]
782]*One(f),
783[
784    [4,0,6,3],
785    [1,4,0,5],
786    [2,3,3,6],
787    [6,3,3,4]
788]*One(f),
789[
790    [1,3,4,5],
791    [6,2,3,1],
792    [3,1,1,2],
793    [1,3,0,4]
794]*One(f)]),
795  Group([[
796    [2,0,0,2],
797    [6,1,2,6],
798    [1,4,2,1],
799    [4,6,2,1]
800]*One(f),
801[
802    [6,0,0,0],
803    [0,6,0,0],
804    [0,0,6,0],
805    [0,0,0,6]
806]*One(f),
807[
808    [5,0,0,0],
809    [0,5,0,0],
810    [0,5,3,0],
811    [2,0,0,3]
812]*One(f)])];
813
814  f := GF(11);
815maximals11 := [
816Group([[
817    [10,0,0,0],
818    [0,10,0,0],
819    [0,0,10,0],
820    [0,0,0,10]
821]*One(f),
822[
823    [7,8,3,7],
824    [4,5,3,9],
825    [1,5,7,3],
826    [7,9,1,2]
827]*One(f),
828[
829    [6,9,9,1],
830    [1,5,4,9],
831    [10,7,8,2],
832    [8,10,10,7]
833]*One(f),
834[
835    [9,9,2,8],
836    [6,8,4,8],
837    [8,5,5,2],
838    [0,5,10,1]
839]*One(f),
840[
841    [7,3,7,1],
842    [7,8,1,7],
843    [2,5,1,8],
844    [0,2,4,2]
845]*One(f),
846[
847    [9,8,1,1],
848    [4,0,7,4],
849    [2,2,4,3],
850    [5,6,4,10]
851]*One(f),
852[
853    [10,9,1,3],
854    [6,2,6,1],
855    [9,4,0,2],
856    [7,9,5,3]
857]*One(f)]),
858  Group([[
859    [10,0,0,0],
860    [0,10,0,0],
861    [0,0,10,0],
862    [0,0,0,10]
863]*One(f),
864[
865    [7,8,3,7],
866    [4,5,3,9],
867    [1,5,7,3],
868    [7,9,1,2]
869]*One(f),
870[
871    [6,9,9,1],
872    [1,5,4,9],
873    [10,7,8,2],
874    [8,10,10,7]
875]*One(f),
876[
877    [9,9,2,8],
878    [6,8,4,8],
879    [8,5,5,2],
880    [0,5,10,1]
881]*One(f),
882[
883    [7,3,7,1],
884    [7,8,1,7],
885    [2,5,1,8],
886    [0,2,4,2]
887]*One(f),
888[
889    [1,2,4,3],
890    [0,0,9,4],
891    [0,6,2,9],
892    [0,0,0,1]
893]*One(f),
894[
895    [2,5,3,3],
896    [7,2,2,3],
897    [5,1,10,6],
898    [8,5,4,10]
899]*One(f)]),
900  Group([[
901    [10,0,0,0],
902    [0,10,0,0],
903    [0,0,10,0],
904    [0,0,0,10]
905]*One(f),
906[
907    [6,0,3,8],
908    [3,0,4,4],
909    [7,4,5,4],
910    [0,9,4,1]
911]*One(f),
912[
913    [9,6,8,7],
914    [0,8,4,2],
915    [7,5,3,3],
916    [7,6,2,1]
917]*One(f),
918[
919    [10,4,6,0],
920    [8,1,0,5],
921    [2,0,1,4],
922    [0,9,8,10]
923]*One(f)]),
924  Group([[
925    [10,0,0,0],
926    [0,10,0,0],
927    [0,0,10,0],
928    [0,0,0,10]
929]*One(f),
930[
931    [7,8,3,7],
932    [4,5,3,9],
933    [1,5,7,3],
934    [7,9,1,2]
935]*One(f),
936[
937    [2,5,3,3],
938    [7,2,2,3],
939    [5,1,10,6],
940    [8,5,4,10]
941]*One(f),
942[
943    [9,5,10,9],
944    [6,7,9,10],
945    [1,1,4,6],
946    [6,1,5,2]
947]*One(f)]),
948  Group([[
949    [10,0,0,0],
950    [0,10,0,0],
951    [0,0,10,0],
952    [0,0,0,10]
953]*One(f),
954[
955    [5,1,1,0],
956    [3,3,9,1],
957    [1,9,3,10],
958    [7,1,8,1]
959]*One(f),
960[
961    [1,10,10,0],
962    [1,10,0,1],
963    [10,0,10,10],
964    [0,1,1,1]
965]*One(f),
966[
967    [8,2,4,2],
968    [10,10,3,4],
969    [3,0,0,9],
970    [8,3,1,2]
971]*One(f)]),
972  Group([[
973    [10,0,0,0],
974    [0,10,0,0],
975    [0,0,10,0],
976    [0,0,0,10]
977]*One(f),
978[
979    [9,5,10,8],
980    [2,3,3,1],
981    [8,2,0,2],
982    [8,3,3,4]
983]*One(f),
984[
985    [10,5,6,5],
986    [3,2,0,6],
987    [8,8,10,6],
988    [0,8,8,2]
989]*One(f),
990[
991    [9,6,9,7],
992    [8,2,8,9],
993    [6,10,9,5],
994    [2,6,3,2]
995]*One(f)]),
996  Group([[
997    [6,1,8,8],
998    [7,9,5,4],
999    [5,1,6,7],
1000    [3,5,3,3]
1001]*One(f),
1002[
1003    [7,9,3,3],
1004    [2,10,9,3],
1005    [2,2,1,2],
1006    [1,2,9,4]
1007]*One(f),
1008[
1009    [9,9,8,7],
1010    [1,8,3,0],
1011    [4,5,4,6],
1012    [3,6,6,3]
1013]*One(f),
1014[
1015    [0,7,3,0],
1016    [4,0,0,8],
1017    [2,0,0,7],
1018    [0,9,4,0]
1019]*One(f),
1020[
1021    [10,0,0,0],
1022    [0,10,0,0],
1023    [0,0,10,0],
1024    [0,0,0,10]
1025]*One(f),
1026[
1027    [7,5,7,0],
1028    [2,1,7,7],
1029    [3,3,9,6],
1030    [7,3,9,3]
1031]*One(f),
1032[
1033    [8,8,4,0],
1034    [10,3,0,7],
1035    [0,0,3,8],
1036    [0,0,10,8]
1037]*One(f),
1038[
1039    [2,4,9,7],
1040    [9,7,9,1],
1041    [5,2,5,0],
1042    [2,7,9,10]
1043]*One(f),
1044[
1045    [10,9,6,9],
1046    [8,1,2,6],
1047    [1,4,10,2],
1048    [7,1,3,1]
1049]*One(f)]),
1050  Group([[
1051    [10,0,0,0],
1052    [0,10,0,0],
1053    [0,0,10,0],
1054    [0,0,0,10]
1055]*One(f),
1056[
1057    [4,9,9,1],
1058    [1,3,6,10],
1059    [6,7,8,2],
1060    [6,8,4,8]
1061]*One(f),
1062[
1063    [3,0,1,4],
1064    [5,4,9,8],
1065    [5,2,1,0],
1066    [1,7,10,4]
1067]*One(f)]),
1068  Group([[
1069    [10,0,0,0],
1070    [0,10,0,0],
1071    [0,0,10,0],
1072    [0,0,0,10]
1073]*One(f),
1074[
1075    [8,10,7,0],
1076    [0,3,0,4],
1077    [2,0,3,10],
1078    [0,9,0,8]
1079]*One(f),
1080[
1081    [7,3,10,3],
1082    [10,6,5,6],
1083    [0,1,8,9],
1084    [5,7,2,2]
1085]*One(f)]),
1086  Group([[
1087    [10,0,0,0],
1088    [0,10,0,0],
1089    [0,0,10,0],
1090    [0,0,0,10]
1091]*One(f),
1092[
1093    [4,9,4,0],
1094    [9,7,0,7],
1095    [9,0,7,9],
1096    [0,2,9,4]
1097]*One(f),
1098[
1099    [9,7,7,4],
1100    [6,2,7,0],
1101    [10,1,6,3],
1102    [5,3,4,4]
1103] * One(f)])];
1104
1105  f := GF(13);
1106maximals13 := [
1107  Group([[
1108    [7,0,7,3],
1109    [3,2,3,7],
1110    [2,1,9,0],
1111    [0,2,10,4]
1112]*One(f),
1113[
1114    [12,0,0,0],
1115    [0,12,0,0],
1116    [0,0,12,0],
1117    [0,0,0,12]
1118]*One(f),
1119[
1120    [12,10,6,1],
1121    [9,7,7,6],
1122    [6,1,8,3],
1123    [0,6,4,3]
1124]*One(f),
1125[
1126    [1,1,5,9],
1127    [0,3,10,5],
1128    [0,10,12,12],
1129    [0,0,0,1]
1130]*One(f),
1131[
1132    [4,9,7,8],
1133    [3,1,1,12],
1134    [12,5,4,1],
1135    [6,3,4,2]
1136]*One(f),
1137[
1138    [11,11,0,9],
1139    [7,6,6,8],
1140    [9,11,0,5],
1141    [0,5,12,7]
1142]*One(f),
1143[
1144    [10,10,6,2],
1145    [0,9,11,10],
1146    [9,1,7,11],
1147    [8,7,3,12]
1148]*One(f)]),
1149  Group([[
1150    [3,7,4,3],
1151    [2,3,12,4],
1152    [2,9,9,6],
1153    [10,2,11,9]
1154]*One(f),
1155[
1156    [12,0,0,0],
1157    [0,12,0,0],
1158    [0,0,12,0],
1159    [0,0,0,12]
1160]*One(f),
1161[
1162    [12,10,6,1],
1163    [9,7,7,6],
1164    [6,1,8,3],
1165    [0,6,4,3]
1166]*One(f),
1167[
1168    [1,1,5,9],
1169    [0,3,10,5],
1170    [0,10,12,12],
1171    [0,0,0,1]
1172]*One(f),
1173[
1174    [4,9,7,8],
1175    [3,1,1,12],
1176    [12,5,4,1],
1177    [6,3,4,2]
1178]*One(f),
1179[
1180    [2,10,12,9],
1181    [4,8,3,12],
1182    [1,12,3,3],
1183    [12,1,9,9]
1184]*One(f),
1185[
1186    [11,11,0,9],
1187    [7,6,6,8],
1188    [9,11,0,5],
1189    [0,5,12,7]
1190]*One(f)]),
1191  Group([[
1192    [12,0,0,0],
1193    [0,12,0,0],
1194    [0,0,12,0],
1195    [0,0,0,12]
1196]*One(f),
1197[
1198    [7,11,9,9],
1199    [1,9,9,8],
1200    [12,7,1,8],
1201    [5,0,5,8]
1202]*One(f),
1203[
1204    [10,9,0,9],
1205    [7,9,2,11],
1206    [12,9,0,3],
1207    [12,1,5,9]
1208]*One(f),
1209[
1210    [5,3,0,0],
1211    [5,8,0,0],
1212    [5,0,8,3],
1213    [0,8,5,5]
1214]*One(f)]),
1215  Group([[
1216    [3,7,4,3],
1217    [2,3,12,4],
1218    [2,9,9,6],
1219    [10,2,11,9]
1220]*One(f),
1221[
1222    [12,0,0,0],
1223    [0,12,0,0],
1224    [0,0,12,0],
1225    [0,0,0,12]
1226]*One(f),
1227[
1228    [2,2,10,1],
1229    [6,7,2,10],
1230    [2,11,6,11],
1231    [2,2,7,11]
1232]*One(f),
1233[
1234    [11,11,0,9],
1235    [7,6,6,8],
1236    [9,11,0,5],
1237    [0,5,12,7]
1238]*One(f)]),
1239  Group([[
1240    [3,3,12,8],
1241    [5,11,2,12],
1242    [3,3,10,10],
1243    [10,3,8,5]
1244]*One(f),
1245[
1246    [12,0,0,0],
1247    [0,12,0,0],
1248    [0,0,12,0],
1249    [0,0,0,12]
1250]*One(f),
1251[
1252    [12,6,4,0],
1253    [9,1,0,9],
1254    [6,0,1,6],
1255    [0,7,9,12]
1256]*One(f),
1257[
1258    [12,10,11,7],
1259    [5,8,3,11],
1260    [12,7,6,3],
1261    [7,12,8,2]
1262]*One(f)]),
1263  Group([[
1264    [12,0,0,0],
1265    [0,12,0,0],
1266    [0,0,12,0],
1267    [0,0,0,12]
1268]*One(f),
1269[
1270    [12,7,5,6],
1271    [6,3,12,7],
1272    [4,0,5,11],
1273    [6,11,4,1]
1274]*One(f),
1275[
1276    [0,2,5,5],
1277    [9,6,5,5],
1278    [11,0,8,11],
1279    [6,11,4,1]
1280]*One(f),
1281[
1282    [12,2,7,0],
1283    [6,6,5,7],
1284    [11,6,7,11],
1285    [12,11,7,1]
1286]*One(f)]),
1287  Group([[
1288    [12,7,5,2],
1289    [5,7,7,4],
1290    [3,1,12,8],
1291    [4,8,6,6]
1292]*One(f),
1293[
1294    [11,6,4,4],
1295    [3,1,4,4],
1296    [1,7,12,7],
1297    [3,1,10,2]
1298]*One(f),
1299[
1300    [12,0,0,0],
1301    [0,12,0,0],
1302    [0,0,12,0],
1303    [0,0,0,12]
1304]*One(f),
1305[
1306    [10,8,1,1],
1307    [4,0,9,1],
1308    [10,1,0,5],
1309    [0,10,9,3]
1310]*One(f),
1311[
1312    [4,0,0,0],
1313    [5,1,10,0],
1314    [11,9,0,0],
1315    [8,11,8,10]
1316]*One(f),
1317[
1318    [3,5,12,12],
1319    [10,10,7,12],
1320    [1,12,3,8],
1321    [7,1,3,10]
1322]*One(f),
1323[
1324    [1,0,2,7],
1325    [11,1,5,1],
1326    [7,9,5,2],
1327    [10,12,0,4]
1328]*One(f),
1329[
1330    [7,11,12,0],
1331    [2,6,0,1],
1332    [5,0,6,11],
1333    [0,8,2,7]
1334]*One(f),
1335[
1336    [9,2,10,10],
1337    [7,2,0,10],
1338    [10,1,12,11],
1339    [6,10,6,5]
1340]*One(f)]),
1341  Group([[
1342    [12,0,0,0],
1343    [0,12,0,0],
1344    [0,0,12,0],
1345    [0,0,0,12]
1346]*One(f),
1347[
1348    [2,9,5,0],
1349    [12,12,0,4],
1350    [5,1,3,2],
1351    [6,12,10,5]
1352]*One(f),
1353[
1354    [4,9,10,6],
1355    [1,3,9,5],
1356    [6,10,12,7],
1357    [0,2,4,6]
1358]*One(f)]),
1359  Group([[
1360    [1,9,12,0],
1361    [0,12,0,1],
1362    [0,0,12,9],
1363    [0,0,0,1]
1364]*One(f),
1365[
1366    [12,0,0,0],
1367    [0,12,0,0],
1368    [0,0,12,0],
1369    [0,0,0,12]
1370]*One(f),
1371[
1372    [10,12,4,8],
1373    [2,5,10,2],
1374    [6,5,0,12],
1375    [9,5,7,10]
1376]*One(f)]),
1377  Group([[
1378    [12,0,0,0],
1379    [0,12,0,0],
1380    [0,0,12,0],
1381    [0,0,0,12]
1382]*One(f),
1383[
1384    [11,8,10,0],
1385    [1,2,0,3],
1386    [8,0,2,8],
1387    [0,5,1,11]
1388]*One(f),
1389[
1390    [7,2,11,8],
1391    [10,0,12,8],
1392    [12,1,3,7],
1393    [0,6,7,2]
1394]*One(f)] )];
1395