Magma V2.20-10    Thu Dec 18 2014 19:59:06 on mathcompprd01 [Seed = 4265214587]
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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");
> 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  [ 8, 12, 36 ]
> f := ProcessReps (L, n);
Consider the following repn 1
Input degree =  8  Defining field size =  3
Order of generators  [ 3, 2, 3, 3, 3, 3, 3 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  10
Order of G is  5040
... #O is now  1680
Proved no regular orbit
========================================
Consider the following repn 2
Input degree =  12  Defining field size =  3
Order of generators  [ 3, 2, 3, 3, 3, 3, 3 ]
Composition Factors of G is 
    G
    |  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 =  36  Defining field size =  3
Order of generators  [ 3, 2, 3, 3, 3, 3, 3 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  18
Over refined degree limit -- so G has regular orbit
========================================
> 
> p := 5; 
> G := eval Read ("plus-cover-s7-5");
> 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  [ 8, 20, 20, 28 ]
> 
> // 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>       "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  [ 3, 2, 3, 3, 3, 3, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  8
Order of G is  10080
Found regular orbit
========================================
Consider the following repn 1
Input degree =  20  Defining field size =  5
Order of generators  [ 3, 2, 3, 3, 3, 3, 4 ]
Composition Factors of G is 
    G
    |  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  [ 3, 2, 3, 3, 3, 3, 4 ]
Composition Factors of G is 
    G
    |  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  [ 3, 2, 3, 3, 3, 3, 4 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  18
Over refined degree limit -- so G has regular orbit
========================================
> 
> p := 7; 
> G := eval Read ("plus-cover-s7-7");
> 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, 14, 14, 16, 20 ]
> 
> 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>       "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 =  4  Defining field size =  7
Order of generators  [ 3, 2, 3, 3, 3, 6, 3 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Vector space too small -- no regular orbit
========================================
2Sn with all scalars does not act regularly so now proper subgroups >= 2Sn
Consider the following repn 1
Input degree =  4  Defining field size =  7
Order of generators  [ 3, 2, 3, 3, 3, 6 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(2)
    1
Vector space too small -- no regular orbit
========================================
Consider the following repn 1
Input degree =  14  Defining field size =  7
Order of generators  [ 3, 2, 3, 3, 3, 6, 3 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  9
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 1
Input degree =  14  Defining field size =  7
Order of generators  [ 3, 2, 3, 3, 3, 6, 3 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  9
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 1
Input degree =  16  Defining field size =  7
Order of generators  [ 3, 2, 3, 3, 3, 6, 3 ]
Composition Factors of G is 
    G
    |  Alternating(7)
    *
    |  Cyclic(3)
    *
    |  Cyclic(2)
    1
Refined bound on degree is  10
Over refined degree limit -- so G has regular orbit
========================================
Consider the following repn 1
Input degree =  20  Defining field size =  7
Order of generators  [ 3, 2, 3, 3, 3, 6, 3 ]
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
========================================

Total time: 4.349 seconds, Total memory usage: 32.09MB