Magma V2.20-10 Thu Dec 18 2014 19:58:54 on mathcompprd01 [Seed = 3305144942]
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Loading startup file "/home/eobr007/.magma.startup"
Loading "code.m"
Loading "sign.m"
>
> n := 5;
>
> p := 3;
> G := eval Read ("plus-cover-s5-3");
> G := DerivedGroup (G);
> 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 [ 4, 6 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree = 4 Defining field size = 3
Order of generators [ 3, 2, 6, 3 ]
Composition Factors of G is
G
| Alternating(5)
*
| Cyclic(2)
1
Vector space too small -- no regular orbit
========================================
Consider the following repn 2
Input degree = 6 Defining field size = 3
Order of generators [ 3, 2, 6, 3 ]
Composition Factors of G is
G
| Alternating(5)
*
| Cyclic(2)
1
Refined bound on degree is 6
Order of G is 120
... #O is now 40
Found regular orbit
========================================
>
> p := 5;
> G := eval Read ("plus-cover-s5-5");
> G := DerivedGroup (G);
> 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 [ 2, 4 ]
>
> // f := ProcessReps (L, n);
> for i in [1..#L] do
for> X := AddScalars (L[i]);
for> regular := ProcessReps ([X[1]], n: Scalar := false);
for> if not regular then
for|if> "2An with all scalars does not act regularly so now proper
subgroups >= 2An";
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 = 2 Defining field size = 5
Order of generators [ 3, 2, 3, 3, 4 ]
Composition Factors of G is
G
| Alternating(5)
*
| Cyclic(2)
*
| Cyclic(2)
1
Vector space too small -- no regular orbit
========================================
2An with all scalars does not act regularly so now proper subgroups >= 2An
Consider the following repn 1
Input degree = 2 Defining field size = 5
Order of generators [ 3, 2, 3, 3 ]
Composition Factors of G is
G
| Alternating(5)
*
| Cyclic(2)
1
Vector space too small -- no regular orbit
========================================
Consider the following repn 1
Input degree = 4 Defining field size = 5
Order of generators [ 3, 2, 3, 3, 4 ]
Composition Factors of G is
G
| Alternating(5)
*
| Cyclic(2)
*
| Cyclic(2)
1
Refined bound on degree is 5
Order of G is 240
... #O is now 120
... #O is now 240
... #O is now 320
... #O is now 440
Proved no regular orbit
========================================
2An with all scalars does not act regularly so now proper subgroups >= 2An
Consider the following repn 1
Input degree = 4 Defining field size = 5
Order of generators [ 3, 2, 3, 3 ]
Composition Factors of G is
G
| Alternating(5)
*
| Cyclic(2)
1
Refined bound on degree is 4
Order of G is 120
Found regular orbit
========================================
>
Total time: 0.520 seconds, Total memory usage: 32.09MB