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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