Magma V2.20-10 Thu Dec 11 2014 23:20:04 on mathcompprd01 [Seed = 4264015508]
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Loading startup file "/home/eobr007/.magma.startup"
Loading "code.m"
Loading "sign.m"
>
> n := 7;
>
> p := 3;
> G := eval Read ("plus-cover-s7-3");
> 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 [ 8, 12, 72 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree = 8 Defining field size = 3
Order of generators [ 2, 2, 2, 2, 2, 2, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
1
Vector space too small -- no regular orbit
========================================
Consider the following repn 2
Input degree = 12 Defining field size = 3
Order of generators [ 2, 2, 2, 2, 2, 2, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| 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 = 72 Defining field size = 3
Order of generators [ 2, 2, 2, 2, 2, 2, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
1
Refined bound on degree is 40
Over refined degree limit -- so G has regular orbit
========================================
>
> p := 5;
> G := eval Read ("plus-cover-s7-5");
> 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 [ 8, 20, 20, 28, 40 ]
>
> // f := ProcessReps (L, n);
> for i in [1..#L] do
for> X := AddScalars (L[i]);
for> regular := ProcessReps ([X[1]], n);
for> if not regular then
for|if> "2Sn with all scalars does not act regularly so now proper
subgroups >= 2Sn";
for|if> M := [X[i]: i in [2..#X]];
for|if> f := ProcessReps (M, n: Scalar := false);
for|if> end if;
for> end for;
Consider the following repn 1
Input degree = 8 Defining field size = 5
Order of generators [ 2, 2, 2, 2, 2, 2, 4, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
*
| Cyclic(2)
1
Refined bound on degree is 9
Order of G is 20160
Found regular orbit
========================================
Consider the following repn 1
Input degree = 20 Defining field size = 5
Order of generators [ 2, 2, 2, 2, 2, 2, 4, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
*
| Cyclic(2)
1
Refined bound on degree is 14
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 1
Input degree = 20 Defining field size = 5
Order of generators [ 2, 2, 2, 2, 2, 2, 4, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
*
| Cyclic(2)
1
Refined bound on degree is 14
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 1
Input degree = 28 Defining field size = 5
Order of generators [ 2, 2, 2, 2, 2, 2, 4, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
*
| Cyclic(2)
1
Refined bound on degree is 18
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 1
Input degree = 40 Defining field size = 5
Order of generators [ 2, 2, 2, 2, 2, 2, 4, 2 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
*
| Cyclic(2)
1
Refined bound on degree is 24
Over refined degree limit -- so G has regular orbit
========================================
>
> p := 7;
> G := eval Read ("plus-cover-s7-7");
> 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 [ 8, 28, 32, 40 ]
>
> for i in [1..#L] do
for> X := AddScalars (L[i]);
for> regular := ProcessReps ([X[1]], n);
for> if not regular then
for|if> "2Sn with all scalars does not act regularly so now proper
subgroups >= 2Sn";
for|if> M := [X[i]: i in [2..#X]];
for|if> f := ProcessReps (M, n: Scalar := false);
for|if> end if;
for> end for;
Consider the following repn 1
Input degree = 8 Defining field size = 7
Order of generators [ 2, 2, 2, 2, 2, 2, 3, 6 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
*
| Cyclic(3)
1
Refined bound on degree is 8
Order of G is 30240
Found regular orbit
========================================
Consider the following repn 1
Input degree = 28 Defining field size = 7
Order of generators [ 2, 2, 2, 2, 2, 2, 3, 6 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
*
| Cyclic(3)
1
Refined bound on degree is 16
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 1
Input degree = 32 Defining field size = 7
Order of generators [ 2, 2, 2, 2, 2, 2, 3, 6 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
*
| Cyclic(3)
1
Refined bound on degree is 18
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 1
Input degree = 40 Defining field size = 7
Order of generators [ 2, 2, 2, 2, 2, 2, 3, 6 ]
Composition Factors of G is
G
| Cyclic(2)
*
| Alternating(7)
*
| Cyclic(2)
*
| Cyclic(3)
1
Refined bound on degree is 22
Over refined degree limit -- so G has regular orbit
========================================
Total time: 19.980 seconds, Total memory usage: 32.09MB