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> 
> n := 6;
> G := PermutationGroup ("3A6", 1);
> for p in [2, 3, 5] do 
for> L := IrreducibleModules (G, GF(p));
for> L := [ActionGroup (x): x in L];
for> L := [x : x in L | #x eq #G];
for> "Degrees of faithful repns are ", [Degree (x): x in L];
for> f := ProcessReps (L, n);
for> end for;
Degrees of faithful repns are  [ 6, 6, 18 ]
Consider the following repn 1
Input degree =  6  Defining field size =  2
Order of generators  [ 2, 4 ]
Composition Factors of G is 
    G
    |  Alternating(6)
    *
    |  Cyclic(3)
    1
Vector space too small -- no regular orbit
========================================
Consider the following repn 2
Input degree =  6  Defining field size =  2
Order of generators  [ 2, 4 ]
Composition Factors of G is 
    G
    |  Alternating(6)
    *
    |  Cyclic(3)
    1
Vector space too small -- no regular orbit
========================================
Consider the following repn 3
Input degree =  18  Defining field size =  2
Order of generators  [ 2, 4 ]
Composition Factors of G is 
    G
    |  Alternating(6)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  16
Over refined degree limit -- so G has regular orbit
========================================
Degrees of faithful repns are  []
Degrees of faithful repns are  [ 6, 12, 30 ]
Consider the following repn 1
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 4, 4 ]
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  540
... #O is now  2700
... #O is now  4860
... #O is now  7020
... #O is now  7560
... #O is now  8280
... #O is now  10440
... #O is now  11160
... #O is now  12240
Proved no regular orbit
========================================
Consider the following repn 2
Input degree =  12  Defining field size =  5
Order of generators  [ 2, 4, 4 ]
Composition Factors of G is 
    G
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  11
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 3
Input degree =  30  Defining field size =  5
Order of generators  [ 2, 4, 4 ]
Composition Factors of G is 
    G
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  19
Over refined degree limit -- so G has regular orbit
========================================
> 
> n := 6;
> G := PermutationGroup ("6A6", 1);
> for p in [2, 3, 5] do 
for> L := IrreducibleModules (G, GF(p));
for> L := [ActionGroup (x): x in L];
for> L := [x : x in L | #x eq #G];
for> "Degrees of faithful repns are ", [Degree (x): x in L];
for> f := ProcessReps (L, n);
for> end for;
Degrees of faithful repns are  []
Degrees of faithful repns are  []
Degrees of faithful repns are  [ 12, 12 ]
Consider the following repn 1
Input degree =  12  Defining field size =  5
Order of generators  [ 4, 8, 4 ]
Composition Factors of G is 
    G
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  9
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 2
Input degree =  12  Defining field size =  5
Order of generators  [ 4, 8, 4 ]
Composition Factors of G is 
    G
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  9
Over refined degree limit -- so G has regular orbit
========================================
> 
> n := 7;
> G := PermutationGroup ("3A7", 1);
> for p in [2, 3, 5, 7] do 
for> L := IrreducibleModules (G, GF(p));
for> L := [ActionGroup (x): x in L];
for> L := [x : x in L | #x eq #G];
for> "Degrees of faithful repns are ", [Degree (x): x in L];
for> f := ProcessReps (L, n);
for> end for;
Degrees of faithful repns are  [ 12, 30, 48, 48 ]
Consider the following repn 1
Input degree =  12  Defining field size =  2
Order of generators  [ 3, 5 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Vector space too small -- no regular orbit
========================================
Consider the following repn 2
Input degree =  30  Defining field size =  2
Order of generators  [ 3, 5 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  25
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 3
Input degree =  48  Defining field size =  2
Order of generators  [ 3, 5 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  31
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 4
Input degree =  48  Defining field size =  2
Order of generators  [ 3, 5 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  31
Over refined degree limit -- so G has regular orbit
========================================
Degrees of faithful repns are  []
Degrees of faithful repns are  [ 6, 12, 30, 30, 36, 42 ]
Consider the following repn 1
Input degree =  6  Defining field size =  5
Order of generators  [ 3, 5, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Vector space too small -- no regular orbit
========================================
Consider the following repn 2
Input degree =  12  Defining field size =  5
Order of generators  [ 3, 5, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  11
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 3
Input degree =  30  Defining field size =  5
Order of generators  [ 3, 5, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  21
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 4
Input degree =  30  Defining field size =  5
Order of generators  [ 3, 5, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  19
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 5
Input degree =  36  Defining field size =  5
Order of generators  [ 3, 5, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  23
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 6
Input degree =  42  Defining field size =  5
Order of generators  [ 3, 5, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  25
Over refined degree limit -- so G has regular orbit
========================================
Degrees of faithful repns are  [ 6, 6, 9, 9, 15, 15, 21, 21, 21, 21 ]
Consider the following repn 1
Input degree =  6  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
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  22680
... #O is now  24570
... #O is now  32130
... #O is now  39690
... #O is now  47250
... #O is now  51030
... #O is now  58590
... #O is now  60102
... #O is now  63882
... #O is now  65772
... #O is now  68292
... #O is now  70812
... #O is now  74592
... #O is now  82152
... #O is now  84042
... #O is now  84672
... #O is now  86562
... #O is now  94122
... #O is now  96642
... #O is now  97902
... #O is now  101682
... #O is now  104202
Proved no regular orbit
========================================
Consider the following repn 2
Input degree =  6  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
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  1512
... #O is now  9072
... #O is now  16632
... #O is now  18522
... #O is now  22302
... #O is now  26082
... #O is now  27972
... #O is now  30492
... #O is now  38052
... #O is now  40572
... #O is now  43092
... #O is now  43722
... #O is now  51282
... #O is now  58842
... #O is now  62622
... #O is now  70182
... #O is now  73962
... #O is now  75852
... #O is now  77742
... #O is now  79254
... #O is now  86814
... #O is now  90594
... #O is now  91224
... #O is now  98784
... #O is now  106344
Proved no regular orbit
========================================
Consider the following repn 3
Input degree =  9  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  8
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 4
Input degree =  9  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  8
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 5
Input degree =  15  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  11
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 6
Input degree =  15  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  11
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 7
Input degree =  21  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  15
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 8
Input degree =  21  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  14
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 9
Input degree =  21  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  15
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 10
Input degree =  21  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  14
Over refined degree limit -- so G has regular orbit
========================================
> 
> G := PermutationGroup ("6A7", 1);
> for p in [2, 3] do 
for> L := IrreducibleModules (G, GF(p));
for> L := [ActionGroup (x): x in L];
for> L := [x : x in L | #x eq #G];
for> "Degrees of faithful repns are ", [Degree (x): x in L];
for> f := ProcessReps (L, n);
for> end for;
Degrees of faithful repns are  []
Degrees of faithful repns are  []
> 
> G := MatrixGroup ("6A7", 1);
> p := 5;
> L := IrreducibleModules (G, GF(p));
> L := [ActionGroup (x): x in L];
> L := [x : x in L | #x eq #G];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are  [ 12, 12, 24, 48 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  12  Defining field size =  5
Order of generators  [ 3, 5, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  10
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 2
Input degree =  12  Defining field size =  5
Order of generators  [ 3, 5, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  10
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 3
Input degree =  24  Defining field size =  5
Order of generators  [ 3, 5, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  16
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 4
Input degree =  48  Defining field size =  5
Order of generators  [ 3, 5, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  28
Over refined degree limit -- so G has regular orbit
========================================
> 
> p := 7;
> L := [MatrixGroup ("6A7", i): i in [9..11]];
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are  [ 6, 6, 24 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  6  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  6
Order of G is  15120
Found regular orbit
========================================
Consider the following repn 2
Input degree =  6  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  6
Order of G is  15120
Found regular orbit
========================================
Consider the following repn 3
Input degree =  24  Defining field size =  7
Order of generators  [ 3, 5, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  12
Over refined degree limit -- so G has regular orbit
========================================
> 
> n := 6;
> G := PermutationGroup ("3S6", 1);
> for p in [2, 3, 5] do 
for> L := IrreducibleModules (G, GF(p));
for> L := [ActionGroup (x): x in L];
for> L := [x : x in L | #x eq #G];
for> "Degrees of faithful repns are ", [Degree (x): x in L];
for> f := ProcessReps (L, n);
for> end for;
Degrees of faithful repns are  [ 6, 6, 18 ]
Consider the following repn 1
Input degree =  6  Defining field size =  2
Order of generators  [ 2, 5 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(6)
    *
    |  Cyclic(3)
    1
Vector space too small -- no regular orbit
========================================
Consider the following repn 2
Input degree =  6  Defining field size =  2
Order of generators  [ 2, 5 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(6)
    *
    |  Cyclic(3)
    1
Vector space too small -- no regular orbit
========================================
Consider the following repn 3
Input degree =  18  Defining field size =  2
Order of generators  [ 2, 5 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(6)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  17
Over refined degree limit -- so G has regular orbit
========================================
Degrees of faithful repns are  []
Degrees of faithful repns are  [ 6, 12, 30 ]
Consider the following repn 1
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 5, 4 ]
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  5400
... #O is now  6120
... #O is now  10440
Proved no regular orbit
========================================
Consider the following repn 2
Input degree =  12  Defining field size =  5
Order of generators  [ 2, 5, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  11
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 3
Input degree =  30  Defining field size =  5
Order of generators  [ 2, 5, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  19
Over refined degree limit -- so G has regular orbit
========================================
> 
> n := 6;
> L := eval Read ("6S6-p5");
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are  [ 12, 12 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  12  Defining field size =  5
Order of generators  [ 2, 5, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  10
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 2
Input degree =  12  Defining field size =  5
Order of generators  [ 2, 5, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(6)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  10
Over refined degree limit -- so G has regular orbit
========================================
> 
> n := 7;
> 
> G := PermutationGroup ("3S7", 1);
> for p in [2, 3, 5, 7] do 
for> L := IrreducibleModules (G, GF(p));
for> L := [ActionGroup (x): x in L];
for> L := [x : x in L | #x eq #G];
for> "Degrees of faithful repns are ", [Degree (x): x in L];
for> f := ProcessReps (L, n);
for> end for;
Degrees of faithful repns are  [ 12, 30, 96 ]
Consider the following repn 1
Input degree =  12  Defining field size =  2
Order of generators  [ 2, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Vector space too small -- no regular orbit
========================================
Consider the following repn 2
Input degree =  30  Defining field size =  2
Order of generators  [ 2, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  26
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 3
Input degree =  96  Defining field size =  2
Order of generators  [ 2, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  57
Over refined degree limit -- so G has regular orbit
========================================
Degrees of faithful repns are  []
Degrees of faithful repns are  [ 6, 12, 30, 30, 36, 42 ]
Consider the following repn 1
Input degree =  6  Defining field size =  5
Order of generators  [ 2, 6, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Vector space too small -- no regular orbit
========================================
Consider the following repn 2
Input degree =  12  Defining field size =  5
Order of generators  [ 2, 6, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  12
Order of G is  60480
Found regular orbit
========================================
Consider the following repn 3
Input degree =  30  Defining field size =  5
Order of generators  [ 2, 6, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  20
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 4
Input degree =  30  Defining field size =  5
Order of generators  [ 2, 6, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  21
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 5
Input degree =  36  Defining field size =  5
Order of generators  [ 2, 6, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  24
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 6
Input degree =  42  Defining field size =  5
Order of generators  [ 2, 6, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  26
Over refined degree limit -- so G has regular orbit
========================================
Degrees of faithful repns are  [ 12, 18, 30, 42, 42 ]
Consider the following repn 1
Input degree =  12  Defining field size =  7
Order of generators  [ 2, 6, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  11
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 2
Input degree =  18  Defining field size =  7
Order of generators  [ 2, 6, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  13
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 3
Input degree =  30  Defining field size =  7
Order of generators  [ 2, 6, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  19
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 4
Input degree =  42  Defining field size =  7
Order of generators  [ 2, 6, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  25
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 5
Input degree =  42  Defining field size =  7
Order of generators  [ 2, 6, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  27
Over refined degree limit -- so G has regular orbit
========================================
> 
> n := 7;
> L := eval Read ("6S7-p5");
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are  [ 24, 12, 48, 12 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  24  Defining field size =  5
Order of generators  [ 2, 12, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  17
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 2
Input degree =  12  Defining field size =  5
Order of generators  [ 2, 12, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  11
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 3
Input degree =  48  Defining field size =  5
Order of generators  [ 2, 12, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  29
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 4
Input degree =  12  Defining field size =  5
Order of generators  [ 2, 12, 4 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  11
Over refined degree limit -- so G has regular orbit
========================================
> 
> L := eval Read ("6S7-p7");
> "Degrees of faithful repns are ", [Degree (x): x in L];
Degrees of faithful repns are  [ 48, 12, 12 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  48  Defining field size =  7
Order of generators  [ 2, 12, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  27
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 2
Input degree =  12  Defining field size =  7
Order of generators  [ 2, 12, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  9
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 3
Input degree =  12  Defining field size =  7
Order of generators  [ 2, 12, 6 ]
Composition Factors of G is 
    G
    |  Cyclic(2)
    *
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    *
    |  Cyclic(3)
    1
Refined bound on degree is  9
Over refined degree limit -- so G has regular orbit
========================================

Total time: 52.939 seconds, Total memory usage: 64.12MB