Magma V2.20-10    Thu Dec 11 2014 23:20:04 on mathcompprd01 [Seed = 4264015508]
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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