Magma V2.20-10    Tue Mar  3 2015 21:01:28 on mathcompprd01 [Seed = 3964572440]
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Loading startup file "/home/eobr007/.magma.startup"

Loading "sign.m"
> 
> n := 6;
> G := PermutationGroup ("3A6", 1);
> p := 5;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G and Degree (x) eq 6];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are  [ 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 4, 4, 2 ]
Composition Factors of G is 
    G
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  7
Order of G is  4320
... #O is now  432
... #O is now  1512
... #O is now  3672
... #O is now  5832
... #O is now  7992
... #O is now  10152
... #O is now  10872
... #O is now  11592
Proved no regular orbit
========================================
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 4, 2 ]
Composition Factors of G is 
    G
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  7
Order of G is  2160
... #O is now  1080
... #O is now  2160
... #O is now  3240
... #O is now  4320
... #O is now  4680
... #O is now  5760
... #O is now  6120
... #O is now  7200
... #O is now  8280
... #O is now  9360
... #O is now  9720
... #O is now  10800
... #O is now  11016
... #O is now  11286
... #O is now  11646
... #O is now  11862
... #O is now  12942
... #O is now  13212
... #O is now  13572
Proved no regular orbit
========================================
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 4 ]
Composition Factors of G is 
    G
    |  Alternating(6)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  6
Order of G is  1080
Found regular orbit
========================================
> 
> n := 7;
> G := PermutationGroup ("3A7", 1);
> p := 5;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G and Degree (x) eq 6];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are  [ 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  6  Defining field size =  5
Order of generators  [ 3, 5, 4, 2 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Vector space too small -- no regular orbit
========================================
Input degree =  6  Defining field size =  5
Order of generators  [ 3, 5, 2 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  8
Order of G is  15120
... #O is now  630
Proved no regular orbit
========================================
Input degree =  6  Defining field size =  5
Order of generators  [ 3, 5 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  7
Order of G is  7560
... #O is now  2520
... #O is now  5040
... #O is now  5670
... #O is now  7182
... #O is now  7812
... #O is now  9324
Proved no regular orbit
========================================
> 
> n := 6;
> G := PermutationGroup ("3S6", 1);
> p := 5;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G and Degree (x) eq 6];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are  [ 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 5, 4, 2 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  7
Order of G is  8640
... #O is now  4320
... #O is now  4752
... #O is now  5292
... #O is now  5832
... #O is now  6264
... #O is now  10584
Proved no regular orbit
========================================
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 5, 2 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  7
Order of G is  4320
... #O is now  1080
... #O is now  3240
... #O is now  5400
... #O is now  5760
... #O is now  6120
... #O is now  8280
... #O is now  9360
... #O is now  9720
... #O is now  11880
Proved no regular orbit
========================================
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 5 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(6)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  7
Order of G is  2160
... #O is now  1080
Found regular orbit
========================================
> 
> n := 7;
> 
> G := PermutationGroup ("3S7", 1);
> p := 5;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G and Degree (x) eq 6];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are  [ 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 6, 4, 2 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Vector space too small -- no regular orbit
========================================
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 6, 2 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Vector space too small -- no regular orbit
========================================
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  8
Order of G is  15120
... #O is now  1512
Proved no regular orbit
========================================
> 
> G := PermutationGroup ("3A7", 1);
> p := 7;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G and Degree (x) eq 6];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are  [ 6, 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  6  Defining field size =  7
Order of generators  [ 3, 5, 2 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  7
Order of G is  15120
... #O is now  7560
... #O is now  15120
... #O is now  18900
... #O is now  22680
... #O is now  24570
... #O is now  27090
... #O is now  34650
... #O is now  42210
... #O is now  49770
... #O is now  52290
... #O is now  54810
... #O is now  62370
... #O is now  69930
... #O is now  71820
... #O is now  79380
... #O is now  80640
... #O is now  88200
... #O is now  91980
... #O is now  94500
... #O is now  98280
... #O is now  100170
... #O is now  103950
Proved no regular orbit
========================================
Input degree =  6  Defining field size =  7
Order of generators  [ 3, 5 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  7
Order of G is  7560
... #O is now  3780
... #O is now  7560
... #O is now  9450
... #O is now  10710
... #O is now  11340
... #O is now  12285
... #O is now  13545
... #O is now  17325
... #O is now  21105
... #O is now  24885
... #O is now  28665
... #O is now  32445
... #O is now  33075
... #O is now  36855
... #O is now  40635
... #O is now  44415
... #O is now  45360
... #O is now  49140
... #O is now  51030
... #O is now  54810
... #O is now  58590
... #O is now  62370
... #O is now  63315
... #O is now  63945
... #O is now  64890
... #O is now  68670
... #O is now  70560
... #O is now  72450
... #O is now  76230
... #O is now  76860
... #O is now  80640
... #O is now  81396
... #O is now  82656
... #O is now  86436
... #O is now  88326
... #O is now  89082
... #O is now  90027
... #O is now  90972
... #O is now  91917
... #O is now  95697
... #O is now  96957
... #O is now  98217
... #O is now  100107
... #O is now  103887
... #O is now  105147
... #O is now  106407
... #O is now  107163
... #O is now  109053
... #O is now  109998
... #O is now  110628
Proved no regular orbit
========================================
Consider the following repn 2
Input degree =  6  Defining field size =  7
Order of generators  [ 3, 5, 2 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  7
Order of G is  15120
... #O is now  7560
... #O is now  15120
... #O is now  17640
... #O is now  25200
... #O is now  28980
... #O is now  32760
... #O is now  34650
... #O is now  42210
... #O is now  49770
... #O is now  57330
... #O is now  64890
... #O is now  68670
... #O is now  70182
... #O is now  73962
... #O is now  75852
... #O is now  83412
... #O is now  85302
... #O is now  86562
... #O is now  88452
... #O is now  92232
... #O is now  94752
... #O is now  97272
... #O is now  97398
... #O is now  98028
... #O is now  105588
Proved no regular orbit
========================================
Input degree =  6  Defining field size =  7
Order of generators  [ 3, 5 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  7
Order of G is  7560
... #O is now  3780
... #O is now  7560
... #O is now  8820
... #O is now  12600
... #O is now  16380
... #O is now  20160
... #O is now  21420
... #O is now  22176
... #O is now  22302
... #O is now  23562
... #O is now  25452
... #O is now  27342
... #O is now  28287
... #O is now  30177
... #O is now  33957
... #O is now  37737
... #O is now  41517
... #O is now  45297
... #O is now  49077
... #O is now  49392
... #O is now  50652
... #O is now  54432
... #O is now  58212
... #O is now  58968
... #O is now  62748
... #O is now  66528
... #O is now  70308
... #O is now  71064
... #O is now  74844
... #O is now  78624
... #O is now  79884
... #O is now  80829
... #O is now  84609
... #O is now  85239
... #O is now  89019
... #O is now  89649
... #O is now  90909
... #O is now  92169
... #O is now  95949
... #O is now  96894
... #O is now  98784
... #O is now  100044
... #O is now  100800
... #O is now  102690
... #O is now  103950
... #O is now  104580
... #O is now  106470
... #O is now  107100
... #O is now  108990
... #O is now  109305
... #O is now  110565
Proved no regular orbit
========================================
> 

Total time: 4.960 seconds, Total memory usage: 32.09MB